Djafar Iabbaden
email: djafar.iabbaden@univ-st-etienne.fr

Jonathan Amodeo

Claudio Fusco

Florence Garrelie

Jean-Philippe Colombier
email: jean.philippe.colombier@univ-st-etienne.fr

Dynamics of Cu-Zr metallic glass devitrification under ultrafast laser excitation revealed by atomistic modeling

The physics of metallic glass local devitrification employing ultrafast laser irradiation is the cradle of complex phenomena that are still not understood despite its applicative potential in material processing for nanotechnology. This paper reports a theoretical simulation combining the two temperature model and classical molecular dynamics simulations to unravel the mechanisms that lead to the localized phase transition in Cu-Zr metallic glass. According to observations, the initial composition of amorphous samples plays an essential role, in addition to nonequilibrium thermodynamic processes caused by the laser energy deposition that alters the atomic environment. We further demonstrate that specific compositions devitrify despite its high glass-forming ability. The thermodynamic conditions fostering the emergence of a stable nanocrystalline phase are clearly established. The compressive pressure wave and the rapid heating process caused by ultrafast laser energy deposition synergistically contribute to disrupt the microstructure of the glass significantly, thereby initiating the devitrification process. Results are discussed using additional classical MD simulations that provide valuable insights for interpreting the distinct contributions of temperature and pressure to the phase transformation. Finally, the impact of the formed nanocrystals on the phononic thermal conductivity of the alloy is presented confirming the potential application of the laser-induced devitrification process for the development of a new generation of nanoarchitectured materials.

I.

INTRODUCTION

Ultrafast laser processes causing structural modification in ordered nanocrystalline alloys or metastable systems such as metallic glasses (MGs) have been extensively investigated in experimental and theoretical studies [START_REF] Li | Theoretical fundamentals of short pulse laser-metal interaction: A review[END_REF]. Several applications were the object of a particular focus because of their attractive properties, including magnetic fabrication [START_REF] Shen | Shear-band affected zone revealed by magnetic domains in a ferromagnetic metallic glass[END_REF], electrocatalysis for energy storage [START_REF] Zhang | Amorphous co-doped mos 2 nanosheet coated metallic cos 2 nanocubes as an excellent electrocatalyst for hydrogen evolution[END_REF], coatings properties [START_REF] Valant | Fully transparent nanocomposite coating with an amorphous alumina matrix and exceptional wear and scratch resistance[END_REF], standing ductility [START_REF] Guo | Tensile ductility and necking of metallic glass[END_REF], catalysis [START_REF] Wang | Low-iridium-content irnita metallic glass films as intrinsically active catalysts for hydrogen evolution reaction[END_REF], and optical applications [START_REF] Schlegel | Optical properties of metallic glasses[END_REF]. The fact remains that all these efforts to design a material with exceptional properties are still far from fulfilling all fabrication challenges. One of the approach is to create nanocomposite alloys combining crystalline and amorphous structures [START_REF] Lester | Review and perspectives: shape memory alloy composite systems[END_REF]. These hybrid materials may inherit properties from either the amorphous or nanocrystalline phases, or even exhibit unexpected outstanding properties due to anisotropic characteristics induced by the presence of nanocrystals within the amorphous material [START_REF] Sahoo | Improved magnetoimpedance and mechanical properties on nanocrystallization of amorphous fe68. 5si18. 5cu1nb3b9 ribbons[END_REF][START_REF] Qiu | Enhanced ductility in a zr65cu15al10ni10 bulk metallic glass by nanocrystallization during compression[END_REF][START_REF] Yoon | Strain-enhanced nanocrystallization of a cunitizr bulk metallic glass coating by a kinetic spraying process[END_REF][START_REF] Fornell | Enhanced mechanical properties and in vitro corrosion behavior of amorphous and devitrified ti40zr10cu38pd12 metallic glass[END_REF][START_REF] Pawlik | Glass formability of fe-co-prdy-zr-b alloys and magnetic properties following devitrification[END_REF]. Conventional annealing method is the most popular technique proposed in the literature to achieve devitrification. This consists in maintaining the amorphous sample long enough in a temperature region below the melting temperature and above its glass transition temperature to crystallize [START_REF] Gao | Crystallization behavior of zralnicu bulk metallic glass with wide supercooled liquid region[END_REF][START_REF] Louzguine-Luzgin | Vitrification and devitrification processes in metallic glasses[END_REF][START_REF] Chen | Quasicrystals in a partially devitrified zr 65 al 7.5 ni 10 cu 12.5 ag 5 bulk metallic glass[END_REF]. The main drawbacks of this approach are the spontaneous aspect and the uncontrolled spatial character of the devitrification in MGs [START_REF] Scott | The crystallization kinetics of fe-ni based metallic glasses[END_REF]. New strategies to control the final crystalline phase, the rate of seeds emergence, their location and size are required. In general, this disorder-order transformation depends on the Glass-Forming Ability (GFA) of the material, which translates to its ability to form an amorphous structure [START_REF] Lu | Glass formation criterion for various glass-forming systems[END_REF]. In this context, the ultrafast laser seems to be one the most appropriate tool to overcome this limitation.

Monoatomic metallic structures are difficult to amorphize and tend to remain crystalline due to their low GFA [START_REF] Bhat | Vitrification of a monatomic metallic liquid[END_REF][START_REF] Goryaeva | Influence of an amorphous surface layer on the mechanical properties of metallic nanoparticles under compression[END_REF]. Experimental and theoretical vitrification processes in liquid metals during rapid quenching confirm this behavior, as demonstrated in Al, Ti, Fe, Ni, and Cu [START_REF] Papanikolaou | Large-scale molecular dynamics simulations of homogeneous nucleation of pure aluminium[END_REF][START_REF] Chu | Thermal expansion and recrystallization of amorphous al and ti: A molecular dynamics study[END_REF][START_REF] Mahata | Understanding homogeneous nucleation in solidification of aluminum by molecular dynamics simulations[END_REF][START_REF] Louzguine-Luzgin | Crystallization of fcc and bcc liquid metals studied by molecular dynamics simulation[END_REF][START_REF] Zhang | Atomistic mechanisms for temperature-induced crystallization of amorphous copper based on molecular dynamics simulation[END_REF][START_REF] Zhang | Molecular dynamics investigation of the local structure in iron melts and its role in crystal nucleation during rapid solidification[END_REF][START_REF] Louzguine-Luzgin | Glass-transition behavior of ni: Calculation, prediction, and experiment[END_REF][START_REF] Manukyan | Exothermic self-sustained waves with amorphous nickel[END_REF]. Nevertheless, a novel experimental method known as ultrafast quenching technique with an ultrahigh cooling rate was developed to achieve the amorphization of pure metallic elements Ta and V [START_REF] Zhong | Formation of monatomic metallic glasses through ultrafast liquid quenching[END_REF]. Furthermore, numerous studies have shown that binary alloys have the potential to undergo amorphous-crystal phase transition over a wide range, such as NiZr [START_REF] Guerdane | Crystal growth and melting in nizr alloy: Linking phase-field modeling to molecular dynamics simulations[END_REF][START_REF] Liu | Tracing intermediate phases during crystallization in a ni-zr metallic glass[END_REF][START_REF] Yang | Crystallization of amorphous ni-zr alloys during heating with molecular dynamics simulations[END_REF][START_REF] Kazanc | Molecular dynamics study of pressure effect on crystallization behaviour of amorphous cuni alloy during isothermal annealing[END_REF], CuTi [START_REF] Rogachev | Explosive crystallization in amorphous cuti thin films: a molecular dynamics study[END_REF][START_REF] Rogachev | Self-propagating waves of crystallization in metallic glasses[END_REF], PdSi [START_REF] Faruq | Moleculardynamics simulations of binary pd-si metal alloys: Glass formation, crystallisation and cluster properties[END_REF], FeNi [START_REF] Nguyen-Trong | Simulation on the factors affecting the crystallization process of feni alloy by molecular dynamics[END_REF][START_REF] Yu | Md simulation on crystallization mechanisms of rapidly supercooled fe-ni alloys[END_REF], SiAl [START_REF] Sun | Investigation of partitionless growth of ε-al60sm11 phase in al-10 at% sm liquid[END_REF][START_REF] Zhao | Nucleation kinetics in al-sm metallic glasses[END_REF], SiAu [START_REF] Starikov | Optimized interatomic potential for study of structure and phase transitions in si-au and si-al systems[END_REF], NiAu [START_REF] Nguyen Trong | The structure and crystallizing process of niau alloy: a molecular dynamics simulation method[END_REF], and NiAl [START_REF] An | Two-step crystal growth mechanism during crystallization of an undercooled ni50al50 alloy[END_REF]. The study on NiNb MG highlights that from a thermodynamics point of view, the maximum devitrification occurs around the glass transition temperature (T g ) [START_REF] Lesz | Study on crystallization phenomenon and thermal stability of binary ni-nb amorphous alloy[END_REF][START_REF] Enayati | Crystallization behavior of ni-nb amorphous alloys[END_REF]. Recent work on ZrCo MG provides another pathway to understand the devitrification mechanism, where atomic species and concentration play an important role (Co concentration in the range of 30-90 %) [START_REF] Celtek | The effect of atomic concentration on the structural evolution of zr100-xcox alloys during rapid solidification process[END_REF]. Devitrification process is even sought for multicomponent MG mixtures. As reported in the literature, it concerns ternary alloys such as CuZrPd [START_REF] Morris | Theoretical and experimental studies of devitrification pathways in the zr2cu1-xpdx metallic glass system[END_REF], AlNiCo [START_REF] Atila | On the presence of nanoscale heterogeneity in al70ni15co15 metallic glass under pressure[END_REF], CuZrAl [START_REF] Ryltsev | Computational crystallization of cu-zr-al glass-forming alloys[END_REF][START_REF] Lan | Structure origin of a transition of classicto-avalanche nucleation in zr-cu-al bulk metallic glasses[END_REF], and AlNiLa [START_REF] Sahoo | Glass transition and crystallization of al-ni-la based metallic glasses studied by temperature modulated dsc[END_REF]. Several studies have achieved devitrification in multicomponent amorphous systems in supercooling condition, namely ZrCoAlFe [START_REF] Tan | Effect of fe on crystallization process of zr-co-al-(fe) bulk metallic glasses[END_REF], LaAlNiCu [START_REF] Yang | Anomalous crystallization as a signature of the fragile-to-strong transition in metallic glass-forming liquids[END_REF], Zr-TiNiCuBe [START_REF] Mechler | Crystallization behavior of low temperature pre-annealed zr46. 8ti8. 2ni10cu7. 5be27. 5-bulk glass[END_REF][START_REF] Wollgarten | Decomposition and crystallization of pd40cu30ni10p20 and zr46. 8ti8. 2cu7. 5ni10be27. 5 metallic glasses[END_REF], and ZrTiCuNiAl [START_REF] Kühn | Limited quasicrystal formation in zr-ti-cu-ni-al bulk metallic glasses[END_REF]. The authors support that the atomic element size and the stoichiometry of mixtures are fundamental ingredients to realize devitrification.

Due to the high GFA of some alloys, devitrification can be challenging. This was confirmed by comparing the nucleation rates of two amorphous alloys using a crystal/liquid interfacial setup. The work highlights a significantly slower crystal growth rate for CuZr compared to low-GFA NiAl [START_REF] Tang | Anomalously slow crystal growth of the glass-forming alloy cuzr[END_REF]. To reduce the large GFA of CuZr MG, different methods were proposed with the aim of activating devitrification. We can mention the sandwiching method that consists in confining CuZr MG between two pure Zr and Cu layers that allows the emergence of nanocrystals [START_REF] Duan | Crystallization behavior of a confined cuzr metallic liquid film with a sandwich-like structure[END_REF]. The work [START_REF] Hu | Physical origin of glass formation from multicomponent systems[END_REF] relies on a seeding method where a BCC crystalline structure is inserted within the amorphous material to trigger devitrification. Furthermore, the devitrification of CuZr MG using X-ray was confirmed experimentally, but no mechanism was proposed for such a process [START_REF] Cullinan | Kinetics and mechanisms of isothermal devitrification in amorphous cu50zr50[END_REF]. In laser processing, ultrafast laser irradiation can be used to induce the amorphous-crystal transformation [START_REF] Prudent | High-density nanowells formation in ultrafast laser-irradiated thin film metallic glass[END_REF]. However, the mechanism and thermodynamic conditions behind this transformation remain largely unknown [START_REF] Antonowicz | Devitrification of thin film cu-zr metallic glass via ultrashort pulsed laser annealing[END_REF][START_REF] Peng | Experimental and theoretical investigations of laser-induced crystallization and amorphization in phase-change optical recording media[END_REF][START_REF] Cao | Femtosecond laser-induced crystallization in glasses: growth dynamics for orientable nanostructure and nanocrystallization[END_REF][START_REF] Mcanany | Evolution of glass structure during femtosecond laser assisted crystallization of labgeo5 in glass[END_REF][START_REF] He | Size-controlled oriented crystallization in sio 2-based glasses by femtosecond laser irradiation[END_REF][START_REF] Shieh | Near-infrared femtosecond lasercrystallization of amorphous silicon[END_REF][START_REF] Zhang | Femtosecond laser-induced phase transformations in amorphous cu77ni6sn10p7 alloy[END_REF][START_REF] Zhou | Crystallization of amorphous ge2sb2te5 films induced by an ultraviolet laser[END_REF][START_REF] Zhang | Crystallization of amorphous ge2sb2te5 films induced by a single femtosecond laser pulse[END_REF][START_REF] Teng | Space-selective crystallization of glass induced by femtosecond laser irradiation[END_REF]. An attempt was made to study ultrafast laser interactions with amorphous CuZr targets using atomistic computations but no successful transition from amorphous to crystalline structure was reported [START_REF] Marinier | Femtosecond laser ablation of cu x zr 1-x bulk metallic glasses: a molecular dynamics study[END_REF].

In the physical vapor deposition (PVD) process, MG thin films are engineered with specific properties that differ from the substrate that can be designed for specific optical, thermal and mechanical applications. Laser irradiation has the significant advantage of being able to process the film without affecting the substrate [START_REF] Wu | Ablation and patterning of carbon nanotube film by femtosecond laser irradiation[END_REF][START_REF] Krueger | Femtosecond-pulse laser processing of metallic and semiconducting thin films[END_REF]. This versatility enables MG devitrification and thus the creation of a composite at a specific location using a single-step treatment, rather than multiple steps or processes making this experimental method highly adaptable. Ideal laser conditions remain hard to reach while the elementary physical processes responsible for the laser-matter reaction are still ambiguous. Our study relies on a theoretical approach that combines a two temperature model (TTM) and classical molecular dynamics (MD) simulations used to investigate laser conditions and CuZr composition as well as to analyze the devitrification mechanisms at the surface of thick irradiated samples. First, several CuZr compositions are tested to identify stable MG to be subjected to the laser treatment. Then, the impact of the laser on the sample is investigated in terms of pressure waves propagation and temperature as well as local atomic rearrangements with the aim of justifying the occurrence of nanocrystals within the glassy matrix. Results are discussed in the light of additional classical MD simulations following relevant thermomechanical paths. The study concludes with a discussion about thermal conductivity calculations performed on the nanostructured MG.

II. COMPUTATIONAL DETAILS

The laser-material interaction process in amorphous (α) CuZr alloys is modelled using a TTM-MD hybrid method [75-79] as implemented in the LAMMPS software [START_REF] Thompson | Lammps-a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales[END_REF][START_REF] Plimpton | Fast parallel algorithms for short-range molecular dynamics[END_REF] [START_REF] Mendelev | Development of a semi-empirical potential suitable for molecular dynamics simulation of vitrification in cuzr alloys[END_REF]. Each 3D-periodic 8.13 × 8.13 × 8.13 nm 3 simulation cell is filled with 31250 atoms and is subjected to a classical amorphization cycle using MD as described in Ref. [START_REF] Iabbaden | Molecular dynamics simulation of structural evolution in crystalline and amorphous cuzr alloys upon ultrafast laser irradiation[END_REF]. First, the system is heated up to 2000 K in the liquid state at a rate of 10 13 K.s -1 and then it is quenched down to 300 K using a rate of 10 11 K.s -1 where another equilibration run is performed during 100 ps in the NPT ensemble (isothermal-isobaric) using the Nosé-Hoover thermostat and barostat [START_REF] Evans | The nose-hoover thermostat[END_REF]. An MD timestep of δt=1 fs is used for all simulations. Then the obtained amorphous cell is replicated in the three direction of space to extend the sample size, following the classical procedure of Cao et al [START_REF] Cao | Structural processes that initiate shear localization in metallic glass[END_REF]. Finally, the simulation box is extended twice (vacuum region) in the X-direction to create the surface of the material and is further equilibrated for another 100 ps.

The TTM-MD equations are solved on an electronic grid of 702 × 1 × 1 during 30 ps. Ultrafast laser operating conditions of pulse duration τ =100 fs and absorbed fluence F abs =34 mJ/cm 2 are employed to preclude the system from ablation. After the laser pulse, the system is tracked during 16 ns without thermomechanical constrains. To effectively prevent pressure wave reflection at the rear surface of the bulk sample, a damping region known as the Non-Reflecting Boundary Condition (NRBC) is employed, as outlined in Ref [START_REF] Iabbaden | Molecular dynamics simulation of structural evolution in crystalline and amorphous cuzr alloys upon ultrafast laser irradiation[END_REF]. This region is characterized by a damping coefficient γ damp =2.5 10 -3 eV ps Å-2 . The TTM solver incorporates electronic properties, as documented in Ref. [START_REF] Iabbaden | Molecular dynamics simulation of structural evolution in crystalline and amorphous cuzr alloys upon ultrafast laser irradiation[END_REF], which compiles data from multiple sources, including Refs. [START_REF] Marinier | Femtosecond laser ablation of cu x zr 1-x bulk metallic glasses: a molecular dynamics study[END_REF][START_REF] Iabbaden | Molecular dynamics simulation of structural evolution in crystalline and amorphous cuzr alloys upon ultrafast laser irradiation[END_REF][START_REF] Choy | Thermal conductivity of amorphous alloys above room temperature[END_REF][START_REF] Garoche | Comparison between amorphous and crystalline phases of copper-zirconium alloys by specific-heat measurements[END_REF]. It is assumed that these electronic properties exhibit minimal variation with changes in composition within amorphous CuZr alloys. All the structural analysis are performed using the Common Neighbor Analysis (CNA) [START_REF] Stukowski | Structure identification methods for atomistic simulations of crystalline materials[END_REF] and Polyhedral Template Matching (PTM) [START_REF] Larsen | Robust structural identification via polyhedral template matching[END_REF] algorithms as implemented in the OVITO software [START_REF] Stukowski | Visualization and analysis of atomistic simulation data with ovito-the open visualization tool[END_REF] applied here to Cu and Zr sublattices.

Considering the high GFA of CuZr systems in the range 30≤%-Zr≤50 [START_REF] Hao | Microscopic origin of slow dynamics at the good glass forming composition range in zr 1-x cu x metallic liquids[END_REF], the strategy is to build a stable Zr-rich amorphous structure to boost the probability to activate devitrification. For this purpose, six structures with different compositions are tested. The final results are illustrated in Figure 1 where the CNA algorithm is used without chemistry considerations. crystal.

An additional simulation is performed on the α-Cu 21.9 Zr 78.1 sample to verify that the structure is stable and does not undergo spontaneous crystallization. The sample is subjected to an additional equilibration simulation of 100 ns in the NPT ensemble at 300 K and 1 bar using the Nosé-Hoover thermostat and barostat. The results confirm the metastable character of the glass where no crystal is detected (see supplementary materials). In the following, the amorphous α-Cu 21.9 Zr 78.1 is selected as the initial structure to investigate the devitrification process triggered by ultrafast laser irradiation. This amorphous cell is replicated up to 211.31 × 7.61 × 10.50 nm 3 size.

B. Ultrafast laser irradiation of α-Cu21.9Zr78.1

Figure 3 shows a specific region within the α-Cu 21.9 Zr 78.1 at t∼8 ns after the laser energy deposition.

The CNA algorithm recognizes the emergence of BCClike crystalline germs within the amorphous matrix. This structure matches the prediction of the CuZr phase diagram at high-temperature where a solid solution of Cu in the BCC β-Zr phase is expected for this specific composition [START_REF] Zhou | Phase stability for the cu-zr system: first-principles, experiments and solution-based modeling[END_REF]. The characteristic size of the crystalline nanocrystals that nucleate in the subsurface region is lower than 1 nm. The growth of the crystalline phase deeper inside the material is shown in Figure 4.

Figure 4(a) indicates that the first crystal seeds within the Cu 21.9 Zr 78.1 amorphous structure do not form instantly after the laser pulse but at t∼8 ns in a region located at X∼63 nm. As the seeds grow, they coalesce to form a crystallization front at t=9 ns and travel through the devitrified region that reaches a final thickness of ∼30 nm at the end of the process. The freshly nucleated crystal phase is not transient and survives until the end of the simulation at t=16 ns. Furthermore, Figure 4(b) emphasizes the devitrified region at t=16 ns where the PTM analysis clearly shows crystallographic planes. The CuZr nanocrystals have the global Cu (21.9 %) and Zr (78.1 %) concentrations without segregation/crystallization effects. A detailed analysis was performed to identify the number of BCC-like atoms and the propagation velocity of the crystal front. The results are shown in Figure 5.

Figure 5 provides the variation of the crystallization front relative position ∆X=X(t)-X(0) with X(0)=63 nm as function of time. At t=9 ns, the fraction of crystalline phase is originally ∼5 %. Beyond t=9 ns, the crystallization front travels the sample which permits the crystalline phase fraction to increase up to 55 % at t=16 ns. The front propagates toward the melted surface (-X direction) with an average velocity of 2.77 m.s -1 (∼100 times slower than the sound velocity in air). This means that the crystallization is partial, localized (∼0-30 nm) and relatively slow as compared e.g., to the devitrification of CuTi amorphous alloys that occurs only under supercooling condition with a crystallization front velocity of ∼40 m.s -1 [START_REF] Rogachev | Self-propagating waves of crystallization in metallic glasses[END_REF].

To track the emergence of crystalline solid solution during devitrification, a complementary analysis involving RDFs at several key times is computed in the devitrified region (35≤X≤63 nm), see Figure 6. At t=0 ns, we observe that the structure is amorphous, characterized by the presence of the second peak double splitting. At t=5 ns, the decrease of the first peak intensity together with the disappearance of the double splitting and the appearance of a broader second peak indicate that the system liquefies in this region. Beyond t=5 ns, the intensity of the first peak starts to increase and the shape of RDFs becomes sharper confirming a local ordered atomic rearrangements. The first and second peaks reach their maximum at t=16 ns where no double peak is observed. Instead, a single narrowed peak that indicates the growth of a crystalline structure within the amorphous material is detected.

C. Origins of the devitrification process

When the laser energy is delivered, the system is driven to a nonequilibrium state where electrons are hot and the lattice is still relatively cold. Therefore, a process of electron-phonon relaxation takes place to balance the energy. The two temperature dynamics defines an ionic temperature gradient inducing stress accumulation that manifests in the form of a compression pressure wave followed by a rarefaction pressure wave due to relaxation of the system. Pressure waves operate at times between t=0-200 ps. The computed spatial evolution of pressure is shown in Figure 7.

At t=5 ps, the pressure reaches its maximum value of ∼4 GPa and gradually dwindles to ∼3.1, 2.2, 1.7, 0.2 GPa associated to t=15, 20, 30, and 200 ps respectively. Moreover, a negative pressure of ∼-1 GPa corresponding to the rarefaction pressure wave propagation is detected at t=80-100 ps. As mentioned previously, the amorphous-crystal transformation starts at t∼8 ns, much later after the complete absorbance of the pressure waves.

To interpret the devitrification phenomenon, in the following we further investigate the local atomic rearrangements evolution of the sample during the process. All MG exhibit a unique fraction of polyhedra atomic configurations, which is considered as the footprint of the amorphous structure. In this context, it is generally argued that the formation/breakage of the polyhedra network has a major impact on the glass phase stability [START_REF] Leocmach | Roles of icosahedral and crystal-like order in the hard spheres glass transition[END_REF]. Here, we track the proportions of the two most prevalent polyhedra, namely <0, 1, 10, 4> (Z15 I1 ) and <0, 2, 8, 5> (Z15 I2 ), in the devitrified region as well as in a nondevitrified domain. The polyhedra fraction evolution is shown in Figure 8.

At t=0 ns, Figure 8 shows a significant fraction of polyhedra in the initial structure c.a., 2.4 and 4.2 % in both regions for Z15 I1 and Z15 I2 , respectively. However, these fractions quickly drop down to 1.1, and 2.1 % at t=0.05 ns in the region that will devitrify. No significant variation of the polyhedra fraction was noticed in the non-devitrified region. The insets in both Figure primarily within t=0-0.05 ns. This time interval aligns with the period during which both the compression wave and the temperature peak progress, as depicted in Figures 7 and9, respectively. On contrary, the rarefaction wave has the same maximum amplitude of ∼-1 GPa within both the devitrified and non-devitrified investigated regions. Furthermore, it is worthy to notice that while the pressure quickly vanishes after t=0.2 ns, the polyhedra breaking process stops and a steady-state regime sets in with a proportion of 0.9 % Z15 I1 and 1.9 % of Z15 I2 until ∼5 ns in the devitrified region. An intermediate regime, associated with the frustration and recombination of polyhedra is recorded within the devitrified region at t∼5-8 ns time range whereas the non-devitrified region is found to have a constant proportion of Z15 I1 and Z15 I2 polyhedra equivalent to those observed before the laser energy deposition. When the system devitrifies at t>8 ns, the fraction of both Z15 I1 and Z15 I2 decreases to 0.3 and 0.7 % in the devitrified region, respectively.

Investigating more carefully the time-evolution of the temperature profile (Figure 9), we notice at t=5 ps the amorphous-liquid transition in the X<40 nm region with a maximum temperature T ∼3000 K (T m ≈1440 K). Moreover, the temperature drops from ∼1800 to 1250 K in the devitrified region for 1≤t≤8 ns marking a thermal relaxation of the amorphous sample. At t=8 ns, T ∼0.87 T m and this corresponds to the time where the first crystal seed is formed as shown in Figure 3. The temperature gradually decreases to T ∼780 K slightly below the theoretical temperature T g ∼830 K. At t=16 ns, the amount of crystalline structure becomes relatively stable, and the crystallization wave ceases to propagate. As a consequence, we conclude that the fast cooling stage from T m to T g is a determinant mechanism to promote the devitrification process in a region where the local atomic skeleton made of the Z15 I1 and Z15 I2 polyhedra has already undergone significant disorganization. In addition, it is noteworthy that the temperature in the non-devitrified zone is below T g . This confirms that the optimal temperature range to favor crystal nucleation is in the vicinity of T g . This thermodynamics kinetic tendency is fostered by the sharp increase of the viscosity below T g that prevents any substantial atoms reorganization.

In the following, a computation is performed to determine the critical temperature T c below which the crystals are formed and compare it to the previous temperature determined at 8 ns (∼0.87 T m ). An additional brick of comprehension is brought by invoking classical nucle- ation models [START_REF] Fanfoni | The johnson-mehlavrami-kohnogorov model: a brief review[END_REF][START_REF] Fokin | Homogeneous crystal nucleation in silicate glasses: A 40 years perspective[END_REF]. The standard Classical Nucleation Theory (CNT) assumes that devitrification occurs in two correlated distinct stages namely nucleation and growth. The devitrification that intervenes in α-Zr 78.1 Cu 21.9 is homogeneous, in contrast to the heterogeneous process that may intervene due to impurities or crystalline seeds already present in the amorphous structure.

As shown in Figure 3, the nucleation starts with the emergence of a nucleus with a minimal critical size (∼2-5 Å ) that settles within the amorphous matrix [START_REF] Cormier | Nucleation in glasses-new experimental findings and recent theories[END_REF]. Assuming that the formed nucleus has a spherical shape, the change of Gibbs free energy in an undercooled liquid is defined by Equation 1 as:

∆G crystal (T ) = - 4πr 3 3 ∆G V (T ) + 4πr 2 σ C-G (1)
where ∆G V represents the free energy difference per volume between the glassy and the crystalline states, σ C-G is the crystal-glass interfacial free energy, and r is the radius of the crystal nucleus.

During the devitrification ∆G

V (T )≈∆H m 1 -T Tm
where ∆H m is the melting enthalpy. The critical temperature Tc below which the nucleus survives within the liquid environment during the devitrification is provided by:

T c = T m 1 - 2σ C-G ∆H m r (2)
σ C-G =0.11 J/m 2 is a reasonable approximation in the composition range of ∼40-78.1 %, σ C-G is assumed to not vary substantially [START_REF] Kang | Interfacial free energy controlling glass-forming ability of cu-zr alloys[END_REF]. ∆H m =8.20×10 9 J/m 3 [START_REF] Yamaguchi | Thermodynamic investigation of the cu-zr system[END_REF], and r≈5 Å. We end up with a final value of T c ≈0.94 T m , whereas at t=8 ns when the devitrification starts T ≈0.87 T m which is below the predicted T c . Therefore, we can conclude that the CNT is able to successfully predict a temperature range for CuZr MG devitrification confirmed by MD simulation. However, at this stage, there is no clear evidence indicating the exclusive influence of either temperature or compressive pressure effects on the observed devitrification process under the modeled ultrafast laser operating conditions.

D. Thermal vs. compressive effects

Additional classical MD simulations (i.e., without relying on the TTM model) aiming at decorrelating the influence of the temperature and compressive wave on the devitrification process are presented in the following. The two additional simulations use as an input a subset of the original virtual sample described in Figure 4 with dimensions 8.13×8.13×8.13 nm 3 , at t=0. The corresponding subsystem is subjected to stress (P xx ) and temperature cycles as close as those induced by the laser in the region where the transformation begins. While classical MD simulations do not reproduce the same exact dynamics as the TTM-MD approach, they may still offer valuable insights to help interpreting the phase transformation.

Two simulations are carried out without constraints on the sample volume and total energy. Firstly, the sample is heated from 300 K to 1000 K for 15 ps and then annealed at constant temperature for additional 85 ps before cooling down to 300 K over a period of 20 ns. This cycle exactly replicates the thermal conditions imposed by the laser in the region X∼60 nm of the original sample (see Figure 4). Meanwhile, each component of the stress tensor is maintained at 0 GPa during the whole simulation process. In the second simulation, the same thermal cycle is followed, but P xx is increased from 0 to 3 GPa during the first 15 ps, i.e., during the heating process from 300 to 1000 K, before it is gradually reduced down to 0 GPa during the following next 85 ps. As in the other simulation, the sample is cooled down to 300 K between times t=100 ps and 20 ns. For further analysis, the local crystallography and Polyhedra evolution are monitored in the transformed zone along the entire process for both simulations. Results are depicted in Figure 10.

The left panel of Figure 10 illustrates the time evolution of <0,2,5,8> Polyhedra in the transformed zone of the sample subset for the two model simulations. The results demonstrate that the number of polyhedra broken during the initial stages of both simulations i.e., with or without the P xx cycle, is of a similar magnitude. This finding further confirms the predominant role of temperature in driving this process. However, only the simulation with the P xx cycle exhibits a phase transformation initiation similar to the one observed in the ultrafast laser simulation (Figure 10, right panel). Investigating more carefully the evolution of the polyhedra during the first 50 ps, one can see that the number of polyhedra decreases slightly more when the sample is subjected to a stress pulse concomitant to the heating process. Thus, the P xx cycle acts as a hint upon the glass microstructure stability that helps the temperature at devitrifying the glass, in the operating conditions of the ultrafast laser simulated in the previous section. We believe that a similar process takes place in the laser simulation described in the previous section. Additional Gibbs-free energy calculations using the PM7 semi-empirical method that aim at characterizing the time-evolution of the transformation are presented in the Supplementary Information.

IV. APPLICATION TO PHONONIC THERMAL CONDUCTIVITY

In this last section, MD is employed to compute the phononic thermal conductivity (κ a ) in the partially devitrified glass. It has been demonstrated in recent studies that there is a possibility to improve κ a of materials by using a femtosecond laser treatment on nanoparticles. This was mainly achieved in alumina and titanium dioxide as reported in the works of Ha et al [START_REF] Ha | Enhanced thermal conductivity of alumina nanoparticle suspensions by femtosecond laser irradiation[END_REF][START_REF] Ha | Enhancement of thermal conductivity of titanium dioxide nanoparticle suspensions by femtosecond laser irradiation[END_REF]. However, to our knowledge, no literature discussed the improvement of κ a in amorphous compounds post-treated with an ultrafast laser.

Furthermore, since amorphous CuZr alloys exhibit low κ a values, the objective here is to examine the possible influence of crystal growth on κ a .

Practically, κ a is calculated in both the amorphous and composite structures employing the Green-Kubo method as implemented in LAMMPS [START_REF] Surblys | Application of atomic stress to compute heat flux via molecular dynamics for systems with many-body inter-actions[END_REF][START_REF] Boone | Heat flux for many-body interactions: corrections to lammps[END_REF][START_REF] Surblys | Methodology and meaning of computing heat flux via atomic stress in systems with constraint dynamics[END_REF]. The phonon thermal conductivity is given by the following equation:

κ a = V 3k B T 2 ∞ 0 ⟨J(0)J(t)⟩dt (3)
where V , k B , T , J, and t describe volume, Boltzmann constant, temperature, instantaneous heat flux (with contributions from all components J x , J y , and J z ), and time respectively. We use the initial (amorphous) and final (composite) configurations obtained from the laser-matter interaction simulation and probe the temperature sensitivity of the thermal conductivity. The thermal conductivity is computed in the 300-900 K temperature range. For this purpose, we first distribute the atom velocities and then equilibrate the system during 20 ps within the NVE ensemble using a MD timestep of 1 fs. Then, we used a statistical method to compute the averaged value of the spontaneous heat autocorrelation flux < J(0)J(t) > during 400 ps in the NVE ensemble. The result is illustrated in Figure 11. κ a of both the nanocomposite and amorphous structures decreases when the temperature increases due to the rise of the phonon-phonon scattering rate [START_REF] Ziman | Electrons and phonons: the theory of transport phenom[END_REF]. κ a of the amorphous structure also decreases significantly by 72 % (1.30 W m -1 K -1 at 300 K to 0.36 W m -1 K -1 at 900 K), whereas the composites one decreases by 92 % (47.33 W m -1 K -1 at 300 K to 3.74 W m -1 K -1 at 900 K). These results show that κ a of the nanocomposite is ∼36 and ∼9 times larger than the one of the amorphous phase at T =300, 900 K, respectively. Therefore, the presence of nanocrystals within the amorphous α-Zr 78.1 Cu 21.9 structure leads to the sharp increase of κ a confirming that the local devitrification of amorphous structures is a promising approach for the creation of high-performance materials with exceptional properties at room temperature.

V. SUMMARY

In this study, the TTM-MD method is used to investigate the devitrification process induced by an ultrafast laser irradiating an α-Cu 21.9 Zr 78.1 glass. Our results show that the ultrafast laser can be used to devitrify α-Cu 21.9 Zr 78.1 leading to nucleation of BCC (solid solution) nanoprecicipitates localized at a few tens of nanometers below the sample surface. At the investigated fluency and pulse duration laser conditions, the main mechanism behind this phase transition is found to be the local atomic rearrangements (breaking of polyhedra) mostly induced by the heating and thermal relaxation cycles, assisted by the compressive wave generated by the laser. The temperature plays here a major role where the highest crystallization occurs at temperatures over T g . Importantly, we observed that the crystalline nanoprecipitates are not transient but rather stable over time within the amorphous matrix. These results show that the ultrafast laser pulse technique can be used to generate very localized devitrification that promotes glass architecturation i.e., from the laser focalisation at the sample surface to the in-depth controlled precipitation, suggesting that this method could be further employed in materials processing to create new nanoarchitectured systems, with enhanced material properties and efficiency, for modern industrial technologies.

DECLARATION OF COMPETING INTEREST

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

Figure 1 .

 1 Figure 1. Cu1-xZrx MG samples produced after the amorphization cycle. The compositions are: a) Cu19.4Zr80.6, b) Cu19.9Zr80.1, c) Cu21.9Zr78.1, d) Cu23.5Zr76.5, e) Cu24.9Zr75.1, and f) Cu26Zr74. The local atomic structure is characterized using CNA (blue=BCC-like configurations, grey=amorphous).

Figure 1

 1 Figure 1 presents the local structures analysis obtained for the various stochiometries after the amorphization process. The different compositions exhibit a competition between the amorphous and crystalline phases. Three contrasted behaviors are observed. Firstly, in Figure 1 a), the α-Cu 19.4 Zr 80.6 partially crystallizes during the process with ∼40 % of the atoms characterized by a BCC-like structure. Secondly, in Figure 1 b), the α-Cu 19.9 Zr 80.1 is also partially crystallized with BCClike clusters corresponding to 4 % of the total amount of atoms. Finally, the last samples are completely stabilized MGs as illustrated in Figure 1 c), d), e) and f) corresponding to α-Cu 21.9 Zr 78.1 , α-Cu 23.5 Zr 76.5 , α-Cu 24.9 Zr 75.1 and α-Cu 26 Zr 74 , respectively. A complementary analysis based on Radial Distribution Function (RDFs) is shown in Figure 2. The results reveal that for the completely vitrified amorphous structures α-Cu 26 Zr 74 , α-Cu 24.9 Zr 75.1 , α-Cu 23.5 Zr 76.5 and α-Cu 21.9 Zr 78.1 a double splitting of the RDFs second peak typical of amorphization is noticed whatever the stoichiometry. On the contrary, a single pronounced peak is observed for the α-Cu 19.4 Zr 80.6 structure which is the footprint of an already existing

Figure 2 .

 2 Figure 2. RDFs of the various CuZr MGs after the amorphization process. The complete amorphization of the sample is characterized by the double splitting of the second peak.

Figure 3 .

 3 Figure 3. Nucleation of BCC-like nuclei (∼15 atomic plans) within the amorphous α-Cu21.9Zr78.1 at t∼8 ns after the laserenergy deposition.

Figure 4 .

 4 Figure 4. α-Cu21.9Zr78.1 atomic configurations after ultrafast laser irradiation as a function of time. Emphasize of the devitrified region: a) global view of the devitrified region located at 35≤X≤63 nm, b) magnification of a devitrified subdomain at t=16 ns. The atoms are colored according to their local atomic structure computed using the PTM algorithm. Atoms colored in grey rely to hidden amorphous and liquid domains.

Figure 5 .

 5 Figure 5. Mean position of the crystallization front's propagation toward the surface versus time at t=8-16 ns during the devitrification process in the α-Cu21.9Zr78.1 MG sample. In blue, we can notice the formed crystalline BCC-like atoms at t=9, 11, 13 and 16 ns.

Figure 6 .

 6 Figure 6. RDFs evolution in the α-Cu21.9Zr78.1 sample at different times during the devitrification process. The double splitting of the secondary peak typical of the amorphous state disappears proving the emergence of a crystalline structure.

  8(a) and (b) show that a significant reduction in the fraction of polyhedra within the devitrified region occurs

Figure 7 .

 7 Figure 7. Spatial evolution of the local pressure profile in α-Cu21.9Zr78.1 at t=0-200 ps. The laser processing conditions are τ =100 fs, F abs =34 mJ/cm 2 for the pulse duration and absorbed fluence respectively. A devitrified zone (in salmon), a non-devitrified zone (in aqua) are chosen to compare the impact of pressure on polyhedra, and NRBC region (in gray).

Figure 8 .

 8 Figure 8. Time evolution of the polyhedra at t=0-16 ns within the α-Cu21.9Zr78.1 MG in the devitrified region located at 35≤X≤63 nm and in a non-devitrified domain located at 65≤X≤93 nm, a) <0, 1, 10, 4>, b) <0, 2, 8, 5>. A zoom in the time range of 0-0.2 ns is provided.

Figure 9 .

 9 Figure 9. Spatial evolution profile of the local lattice temperature in α-Cu21.9Zr78.1 at several key times 0.005, 0.5, 1, 5, 8, 10, 14, and 16 ns of the devitrification process. A devitrified zone (in salmon) and a non-devitrified zone (in aqua) are chosen to investigate the impact of temperature on the devitrification process.

Figure 10 .

 10 Figure 10. Polyhedra evolution and devitrification in the model classical MD simulations. Left panel: evolution of the fraction of <0,2,5,8> Polyhedra in the simulation (i) without stress (blue curve) and (ii) with a preliminary Pxx=0↗ 3 ↘0 GPa cycle, as computed in the transformed zone emphasized in the right panel (black-dashed lines). The red domain highlights a high-PT condition period during which the <0,2,5,8> fraction decreases in the simulation with stress cycle. Right panel: final atomic configurations for simulations with and without stress. In blue, we notice the formed crystalline BCC-like atoms (solid solution).

Figure 11 .

 11 Figure 11. Phononic thermal conductivity of α-Zr78.1Cu21.9 in the amorphous phase and in the nanocomposite at various temperatures. Note the factor 36 between the two phases at T =300 K.

  . Several initial random solid solutions with BCC-like crystalline structure and various stoichiometry including Cu 19.4 Zr 80.6 , Cu 19.9 Zr 80.1 , Cu 21.9 Zr 78.1 , Cu 23.5 Zr 76.5 , Cu 24.9 Zr 75.1 , and Cu 26 Zr 74 were first modeled using the embedded atom model parameterization of Mendelev et al

ACKNOWLEDGMENTS

We gratefully acknowledge the ANR project ME-GALIT (ANR-18-CE08) and the project FORMEL of the Pack Ambition Research program of the Auvergne Rhône-Alpes Region for supporting this work. Numerical computations were performed on the HPC resources from GENCI-TGCC and CINES, project gen7041.

SUPPLEMENTARY MATERIAL

Supplementary material associated with this article can be found, in the online version.


Belkacem Tarek Benkhaled

Kedafi Belkhir

Thomas Brossier

Camille Chatard

Alain Graillot

Barbara Lonetti

Anne-Françoise Mingotaud

Sylvain Catrouillet

Sébastien Blanquer

Vincent Lapinte

3D fabrication of Shape-Memory polymer networks based on coumarin Photo-Dimerization

come   L'archive ouverte pluridisciplinaire

Introduction

Shape-memory polymers (SMP)s (e.g. shape-memory thermal transition) are a class of materials capable to return to their original (permanent) shape from a deformed (temporary) one, in response to an external stimulus. For example, thermal transition shape-memory polymers maintain their temporary shape below a transition temperature (Tg or Tm) and recover their permanent shape by heating. To satisfy such typical behavior, the SMP must provide a combination of: i/ irreversible network, to fix the system and guarantee the permanent shape, with ii/ a reversible network which can be obtained by the weak interactions between the polymer chains and will insure the temporary state. The shape recovery is due to the entropy elasticity induced by the permanent network. The reversible deformation including contraction, elongation and bending can be used to remotely animate objects as robots, artificial muscles and actuators but well-defined objects are required. Recently, the development of additive manufacturing such as stereolithography (SLA) revolutionized this approach and allows the fabrication of sophisticated objects with high porosity or complex geometry. [START_REF] Blanquer | Surface curvature in triply-periodic minimal surface architectures as a distinct design parameter in preparing advanced tissue engineering scaffolds[END_REF][START_REF] Guo | Recent advances in ink-based additive manufacturing for porous structures Additive Manufacturing Part[END_REF] This SLA consists in the photo-crosslinking of a polymer resin bearing photoactive units like methacrylate or epoxy. However, the family of photo-dimerizable units like anthracene, stilbene, cinnamoyl and coumarin [START_REF] Sims | Nondestructive Photo-Cross-Linking of Microphase-Separated Diblock Polymers through Coumarin Dimerization[END_REF] is increasingly investigated in the field of photo-curing polymer. Indeed, they present the considerable advantage to reversibly dimerize without any photo-initiator to activate the crosslinking is a considerable advantage. [START_REF] Jagtap | A review on self-initiated and photoinitiator-free system for photopolymerization[END_REF] Other photoinitiator-free initiator systems like electron-donor-acceptor tandem by using bismaleimides (BMI) as electron acceptors [START_REF] Wagner | Photoinitiator-free photopolymerization of acrylate-bismaleimide mixtures and their application for inkjet printing[END_REF] , thiol-ene photoclick reaction 6 have also been employed for the crosslinking of polymeric materials. We selected photochromic coumarins due to their easy functionalization, simple reversible dimerization and easy accessibility on the chemical marketed. [START_REF] Korchia | Light-switchable nanoparticles based on amphiphilic diblock, triblock and heterograft polyoxazoline[END_REF][START_REF] Korchia | Photodimerization as an alternative to photocrosslinking of nanoparticles: proof of concept with amphiphilic linear polyoxazoline bearing coumarin unit[END_REF] SMPs based on coumarin chemistry were already reported with poly(caprolactone) [START_REF] Defize | Shape Memory Behavior of Emulsion-Templated Poly(ε-Caprolactone) Synthesized by Organocatalyzed Ring-Opening Polymerization[END_REF]10,[START_REF] Wu | The design of triple shape memory polymers with stable yet tunable temporary shapes by introducing photo-responsive units into a crystalline domain[END_REF] , polyimide [START_REF] Li | Dual-method molding of 4D shape memory polyimide ink[END_REF] , poly(vinyl alcohol) [START_REF] Zhao | Photoinduced shape fixity and thermal-induced shape recovery properties based on polyvinyl alcohol bearing coumarin[END_REF] or polyurethane [START_REF] Wu | Synthesis of triple shape memory polyurethanes by introducing photo-responsive coumarin units into the crystalline soft segment Materials Today[END_REF][START_REF] Salgado | Functional properties of photo-crosslinkable biodegradabe polyurethane nanocomposites Polymer Degradation and Stability[END_REF] , however none of them have been used in 3D printing with SLA. Our system is based on coumarin functionalized by methacrylate moiety. This monomer is copolymerized with a 2-ethylhexyl methacrylate (EHMA) to obtain a polymethacrylate backbone P(EHMA-co-CoumMA). EHMA acts as internal plasticizer allowing material deformations essential to recover the initial shape after heating above glass temperature (Figure 1). The homologous acrylate copolymers in acrylate series were already described by Lon et al. [START_REF] Trenor | evelopment of a light-deactivatable PSA via photodimerization The[END_REF] for photoreactive pressure-sensitive adhesives (PSA) application. However, they employed another synthetic route. First, they copolymerized 2-ethylhexyl acrylate and 2-hydroxyethyl acrylate before modifying a part of alcohol groups with 7-chlorocarbonylmethoxycoumarin. In addition, P(EHMA-co-CoumMA) has already been reported by Demirelli et al. [START_REF] Ayaz | Polymers Based on Methacrylate Bearing Coumarin Side Group: Synthesis via Free Radical Polymerization, Monomer Reactivity Ratios, Dielectric Behavior, and Thermal Stabilities International Scholarly Research Network[END_REF] without any description of the resulting materials even if they demonstrated through a kinetic study on the copolymerization the ideal character of P(EHMA-co-CoumMA) with a r=0.45 for coumarin monomer. The use of polymers bearing photoactive coumarin units in SLA was only reported by Matsuda et al. [START_REF] Matsuda | Molecular design of photocurable liquid biodegradable copolymers. 1[END_REF] and never used to fabricate SMP materials. Consequently, we investigated in this study the SMP properties of P(EHMA-co-CoumMA) synthesized with various ratios of CoumMA and the casted on largescale photo-crosslinked films. We further used P(EHMA-co-CoumMA) in SLA. A butterfly design presenting SMP properties was built as a proof of concept by SLA. Characterization 1 H and [START_REF] Zhao | Photoinduced shape fixity and thermal-induced shape recovery properties based on polyvinyl alcohol bearing coumarin[END_REF] C spectra were recorded in CDCl3 using a Bruker Advance DRX 400 (400 MHz). For 1 H NMR, chemical shifts were referenced to the peak of residual non-deuterated solvent at 7.26 ppm for CDCl3. Molar masses and dispersity of polymers were determined by size exclusion chromatography (SEC) using a PL-GPC50 Plus equipped with a RI refractive index detector.

Polar Gel M column was used at 50 °C with dimethylacetamide (DMAc) (+0.1% LiCl weight) flow rate of 0.8 mL.min -1 , calibrated with PMMA standards. UV-dimerization of the coumarinated films was performed in a cylindrical photochemical reactor ''Rayonnet RPR-200'' equipped with 16 symmetrically placed lamps with emission maximum at 350 nm (UV-B). UV-visible analyses were conducted using a Perkin Elmer lambda 35 UV-visible spectrometer equipped with a PTP-1 + 1 Peltier system in quartz vial (length = 1 cm). A small lamellar film was introduced in quart z cell to follow the kinetic of crosslinking (dimerization of coumarin moieties). DSC analyses were carried out using a Mettler Toledo (Mettler Toledo, France) DSC1 calorimeter. Nitrogen was used as the purge gas. Thermal properties were recorded between 0 and 60 °C at a heating rate of 5 °C.min -1 . The stress-strain measurements on films were performed using an Instron 5533 tensile tester equipped with a 10 KN static load cell and specimen gripe. The results were interpreted on a Bleuhill3 software. The tensile measurements were performed zed on the lamellar shape films (1.5x15 cm) according to the ISO's norms (ISO 527-3). The traction rate of samples was 1 mm/s for all the runs, with 0.1N preload. Three samples were used to obtain the average data. The tensile modulus (Young's modulus) was calculated as the slope in the linear region of the stress-strain curve corresponding to 5-10% strain (following the ISO's norm ISO-844 2014) using the equation 1:

E= (1)
with E the Young's modulus (Pa), δ the stress (Pa) calculated from the equation σ = F/S, where F is the force (newton) and S the nominal cross-section (or surface) of the sample (m 2 ).

Synthesis of 7-(11-acryloyloxyundecyloxy)-4-methyl coumarin (CoumMA)

Step 1. Synthesis of 7-(11-hydroxyundecyloxy)-4-methyl coumarin (CoumOH)

In a single-neck round-bottom flask, 7-hydroxy-4-methylcoumarin (39.0 g, 0.22 mol) was dissolved in 675 mL of ethanol. Potassium carbonate (33.0 g, 0.24 mol, 1.1 eq) and 11-bromo-1-undecanol (50.0 g, 0.20 mol, 0.9 eq) were then successively added. The mixture was stirred at 85 °C for 72 hours. The mixture was filtered to remove insoluble salts. The filtrate was then concentrated under vacuum, and the yellow solid was dissolved in 900 mL of dichloromethane.

The solution was washed with 3x150 mL of NaOH 1M, 1x150 mL of HCl 0.5M and 1x150 mL of deionized water. The organic phase was dried over anhydrous sodium sulfate, then concentrated under vacuum until no solvent remained. The beige solid was triturated in 1L of diethyl ether, then filtrated and dryed under vacuum at room temperature, CoumOH was obtained as a white powder in 82% yield (56.7 g). Step

Methacrylation of 7-(11-hydroxyundecyloxy)-4-methylcoumarin (CoumMA)

In a two-neck round-bottom flask, CoumOH (56.7 g, 0.164 mol) was dissolved in 300 mL of dichloromethane. Triethylamine (19.9 g, 0.196 mol, 1.2 eq) was then added. The mixture was cooled down to 0 °C with an ice bath, and methacryloyl chloride (18.8 g, 0.180 mol, 1.1 eq) was added dropwise under argon. When the addition was complete, the ice bath was removed and the mixture was stirred at room temperature for 1 h. The mixture was diluted in 900 mL of dichloromethane, and the solution was successively washed with 2x150 mL of HCl 0.5M, 2x150 mL of NaOH 1M and 1x150 mL of deionized water. The organic phase was dried over anhydrous sodium sulfate, then concentrated under vacuum. CoumMA was obtained as a white powder in 89% yield (60.6 g). Typical procedure for the synthesis of P(EHMA-co-CoumMA) copolymers

Three amorphous statistical copolymers with different composition P(EHMA80-co-CoumMA20), P(EHMA50-co-CoumMA50) and P(EHMA80-co-CoumMA20)) were successfully synthetized. The protocol is illustrated with P(EHMA80-co-CoumMA20) synthesis.

In a two-neck round-bottom flask, CoumMA (11.0 g, 26.

Typical procedure of film process

An amount of P(HEMA-co-CoumMA) (100 g) was dissolved in 100 mL of DCM. 4 hours of stirring were required to obtain the complete dissolution of the polymer. The solution was poured in a Pyrex flat inner (15×11 cm). The solvent was evaporated first under fume hood during 12 hours, then the film was subsequently put in an oven at 60 °C for 3 hours, and finally dried in a vacuum oven at 30 °C during 1 hour. The resulting film was cross-linked under UV irradiation at 365 nm, during 3 hours.

3D printing

The resin formulation was prepared to SLA process by mixing P(EHMA-co-CoumMA) with a non-reactive solvent (DMAc) at 75 wt%. The solution was stirred overnight at 25 °C and yielded a homogeneous reactive solution providing an optimal pattern resolution.

3D butterfly was designed from Rhinoceros 3D using the STL format. The 3D structure was built by SLA from the resin mentioned above by using a 385 nm digital light processing (DLP) apparatus (Asiga Max X43, Australia). The 3D objects were constructed layer-by-layer by photo-crosslinking with a thickness of 200 μm. Each layer was illuminated over an intensity of 40 mW/cm² for a specific duration of 600 s. After building, the object was washed with DCM and dried at room temperature.

Shape memory folding deployment test

Rectangular samples (1.5×15 mm) were used to test the shape memory performance of the films. The test was performed using the following steps: (i) heating the samples to a target temperature > Tg in the oven and holding them for 10 min; (ii) bending the samples into "U" shape. The "U" shaped samples were then quickly removed from the oven and frozen in an intermediary shape at room temperature with a constant external force. Later, the specimens were reheated above the thermal deformation temperature to measure the bending angle θi every ten seconds. The final bending angle was noted θmax and defined by equations 2 and 3:

Shape recovery ratio:

= × 100 (2)
Shape recovery rate:

= × (3)

Results and discussion

A series of photoactive copolymers P(EHMA-co-CoumMA) was synthesized using AIBN and starting from ethylhexyl methacrylate (EHMA) and a methacrylate comonomer bearing coumarin unit in pendent position (CoumMA) (Figure 1). CoumMA was produced via a twostep route from umbelliferon as previously reported by our group. [START_REF] Oudin | Amphiphilic polymers based on polyoxazoline as relevant nanovectors for photodynamic therapy[END_REF] First, a C11 spacer chain was grafted on umbeliferone before methacrylating the terminal alcohol group. The CoumMA monomer was produced in 100 grams range in 73% global yield. %CoumMA in P(EHMA-co-CoumMA) ranged from 20 to 80% with similar molecular weight (Mn, sec around 45,000 g/mol)

(Table S1) corresponding to 22.5, 53.75 and 86.0 coumarin units per chain. The respective EHMA and CoumMA ratios were estimated by 1 H NMR spectroscopy using -CH2-C-CH3-(from polymer backbone) signal at 1.9-0.6 ppm related to coum-CH3 (from coumarin moiety) signal at 2.3 ppm.

Large size films (20 x 30 cm) were molded by casting of DCM solution of each copolymer P(EHMA-co-CoumMA). Homogeneous films with smooth surface without any trapped air bubbles in the materials were obtained. The transparency of the films is clear on the pictures of Figure 2. No color of P(EHMA80-co-CoumMA20) film was observed while a yellowing appeared progressively in the case of the P(EHMA50-co-CoumMA50) and P(EHMA20-co-CoumMA80) films, as illustrated in the transmittance spectra obtained using UV spectroscopy. [START_REF] Lin | Transparent semi-crystalline polymeric materials and their nanocomposites: a review[END_REF] The color of materials is linked to the number of coumarin rings. Higher ratio of coumarins per chain lead to more colored films while preserving transparency. P(EHMA-co-CoumMA) films were characterized by DSC monitoring the glass transition temperature as shown in Figure 3B.

The Tg values ranged from 1 to 17 °C for 20, 50 and 80% of coumarin units (Figure 3C) in accordance with a linear relationship with the increasing coumarin amount. The low Tg values correspond to flexible films observed at room temperature. The photo-crosslinking of P(EHMA-co-CoumMA) films was undertaken under UV irradiation at 365 nm allowing the dimerization of the photoactive coumarin units according to [2+2] photo-cyclization. No warping of the films was observed during the building of the network in contrast with the material's contraction which sometimes happens during crosslinking as previously reported by Zhao et al. [START_REF] He | Photoinduced bending of a coumarin-containing supramolecular polymer[END_REF] The kinetic of the photoreaction was monitored by UVspectroscopy as illustrated in Figure 3A with the progressive disappearance of the large band centered at 320 nm and attributed to the unsaturation of coumarin. The optimal conversion of the coumarin units into cyclobutene adducts is around 90% after 90 min of illumination instead of 60% as already reported by Long et al. [START_REF] Trenor | evelopment of a light-deactivatable PSA via photodimerization The[END_REF] As expected, the photo-crosslinking induced an increase of the Tg values and consequently the stiffness as represented in Figure 3B and3C. Furthermore, the crosslinking of the P(EHMA-co-CoumMA) chains induced a quasi-linear increase of the Tg value especially high when the coumarin rate increases (Figure 3 b). A ∆Tg of 21 °C for P(EHMA80-co-CoumMA20) compared to a ∆Tg of 39 °C for P(EHMA20-co-CoumMA80) (Figure 3 c).

In all the cases, the Tg before crosslinking remained below room temperature which then could be a positive factor to facilitate the curing of the polymer chains under UV irradiation. [START_REF] Huyck | Photoinduced bending of a coumarincontaining supramolecular polymer[END_REF] The success of the photo-crosslinking paved the way for additive manufacturing by vat photopolymerization such as the stereolithography (SLA). Using a coumarin-based resin with intermediary content of coumarin P(EHMA20-co-CoumMA80), fabrication by SLA using a DLP process was investigated. A proof of concept was chosen representing a butterfly design (37 x 25 x 3.5 mm Figure 4B clearly shows the precise reproduction of the butterfly from the STL format (Figure 4A) with all the details especially regarding the rib's design on each wing. In addition, except a slight contraction of the structure which is due to the solvent extraction, the butterfly design was preserved upon drying step (Figure 4C).

To the best of our knowledge, such performance of processing is reached for the first time by stereolithography using a coumarin-based resin. Photo-crosslinking by coumarin dimerization without using any radical initiators or small molecules is a remarkable opportunity for specific applications where the use of photo-initiator represents a serious limitation such as in biomedical applications. [START_REF] You | Biofabrication and 3D Tissue Modeling[END_REF][START_REF] Mondschein | Polymer structure-property requirements for stereolithographic 3D printing of soft tissue engineering scaffolds[END_REF] Axial tensile tests were conducted to investigate the influence of the crosslinking rate on the mechanical properties of P(EHMA-co-CoumMA) films (Figure 5). The Young's modulus (E) of the films was deduced from the linear elastic region at low strains while the tensile strength (max) and the fracture strain (max) were measured at the break of the samples in the strain experiments. The films became stiffer with increasing coumarin composition as shown by the decrease of elongation at break (from 47.5 to 3.5%) as well as the increase of stress at break (from 2 to 36 MPa) and the elastic modulus ranging from 6.6 to 15.9 MPa. We noted the contrast between the mechanical behavior of P(EHMA80-co-CoumMA20), soft and elastic material and the other materials characterized by stiff and fragile break. SMPs are class of smart and programmable materials which have the capacity to be temporary deformed and then quickly return to their original shape upon triggered thermal stimulation at a specific transition temperature. In our case, P(EHMA-co-CoumMA) is amorphous, therefore the shape-morphing behavior is expected by programming around the glass transition temperature.

The resulting cross-linked materials of a crosslinking present a glass transition temperature higher than the room temperature. Hence a double network is present with a permanent covalent network due to the crosslinked nature of the material and a second network due to the weak interactions responsible for the Tg, which are reversible with temperature. Such a material can present shape memory properties. [START_REF] Behl | A Shape memory polymers[END_REF] Polymers with shape memory properties feature the ability to return from a deformed state (temporary shape) to their original (permanent) shape through an external stimulation. [START_REF] Lendlein | Facile tailoring of thermal transition temperatures of epoxy shape memory polymers[END_REF] Two experiments were conducted to evidence these properties. After crosslinking, a permanent shape of flat films was obtained. The first experiment consisted in twisting the films at 80 °C, and freeze them in a temporary shape at room temperature. The experiment is illustrated with P(EHMA50-co-CoumMA50) in Figure 6A but the same behavior was observed for P(EHMA80-co-CoumMA20)) (Figure S6) and P(EHMA20-co-CoumMA80)

(Figure S7). The twisted films were then heated at 80 °C and recovered their initial shape in a few seconds. To compare the speed of recovery a second experiment was conducted. The films were bent in a unidirectional deformation (Figure 6B). The deformation angles were measured at various times to determine the shape recovery ratio and shape recovery rate according to Equations 2 and 3. The experiment ended when the films recovered their initial shape. The experiments were run for the different compositions at 70, 80 and 100 °C (Figure 6C). As expected, the higher the temperature the faster the recovery was. It is clear that the composition of the polymer also has an influence on the rate of recovery. An increase in the amount of coumarin in the polymer composition led to a decrease of the rate of recovery. This result might seem counterintuitive because a higher crosslinking density would lead to a more rigid material that would recover its shape faster. However, in this case the ratio of coumarin in the polymer also affects the glass transition temperature. Thus, a lower Tg lead to a faster recovery rate probably due to easier movements of the chains to recover. A comparable behavior was already observed on epoxy polymers. 27 As presented earlier, the polymer was successfully crosslinked using stereolithography as a proof of concept of the use of coumarin moieties for 3D printing (Figure 4). Such process opens vast applications for these polymers. But one of the issues of this process relies in the layer printing which might compromise the shape memory properties of the material and the possible low crosslinking ratio. However, the printed butterfly kept the shape memory properties as proved by the movement of the butterfly wings in Figure 7. The initial butterfly shape was fabricated with open wings, and a temporary shape obtained by stressing the butterfly with closed wings and fixed with the temperature below the Tg, 22 °C. By applying a temperature above the Tg with an external heating we assisted to a progressive opening of the wings by simple thermal stimulation. The shape memory effect on the printed butterfly structure allows to open the perspective for such resin to be used in 4D printing.

Conclusion

Photo-crosslinkable polymers based on coumarin chromophore were successfully synthesized and transparent resulting films were prepared in large scale. As expected, the coumarin ratio increased the glass transition temperature of P(EHMA-co-CoumMA) film and its rigidity with high Young modulus and tensile strain. These thermal and mechanical properties were also amplified by photo-crosslinking. All the films exhibit thermal-induced shape memory properties as shown in unfolding and twisting deformations. Decreasing the coumarin ratio results in quicker shape memory effects. Otherwise, the study of the photodimerization of coumarins in P(EHMA-co-CoumMA) allows the use of these polymers as photoprintable resins in stereolithography. They demonstrate the interest of coumarin chemistry in 4D printing resulting from additive fabrication of shape memory materials as illustrated with the movement of butterfly wings during heating.

Aknowledgements

This study was achieved in the framework of the Pheophotodyn project, funded by FEDER n°LR0021768 Occitanie Region. The authors are grateful to the LMP platform of the University of Montpellier for its technical support, and thank Maxime Camas for his help.

Figure 1 .

 1 Figure 1. Synthesis of P(EHMA-co-CoumMA) by radical polymerization followed by its

Figure 2 .

 2 Figure 2. Images (bar: 5 cm) and transmittance spectra of the films before UV-irradiation

Figure 3 .

 3 Figure 3. (a) Kinetic study of a coumarin dimerization under UV exposure at =365 nm

Figure 4 .

 4 Figure 4. (a) 3D printing by stereolithography of a butterfly based on coumarin resin (e.g.

Figure 5 .

 5 Figure 5. Tensile curves and images of the cross-linked films P(EHMA80-co-CoumMA20) in

Figure 6 .

 6 Figure 6. (a) twist of the film (e.g. P(EHMA50-co-CoumMA50)) at 80 °C, (b) Pictures of the

Figure 7 .

 7 Figure 7. Movement of butterfly wings in heating (e.g. P(EHMA20-co-CoumMA80)).

FigureFigure S3 .Figure S7 .

 S3S7 Figure S2. a) 1 H and b) 13 C NMR spectra of CoumMA in CDCl 3 .

  97%), the mixture was cooled down to room temperate. Then, the polymer was precipitated in 1.3 L of a mixture EtOH/Et2O 95/5 v/v, and let to settle before removing the supernatant solvent. Next, the product was dissolved in dichloromethane and concentrated under vacuum. PEHMA-co-CoumMA was obtained as a white powder in 79% yield(25.2 g).  (ppm): 177.91, 177.53, 176.78, 162.24, 161.30, 155.31, 152.53, 125.44, 113.38, 112.64, 111.79, 101.32, 68.60, 67.07, 64.98, 45.16, 44.78, 38.46, 30.46, 29.62-29.33, 29.04, 28.94, 28.15, 26.01, 23.86, 22.95, 22.88, 18.63, 14.11, 10.96. (Figure S3, S4 and S5 (b))

	1 H NMR (CDCl3),  (ppm): 7.41 (d, 1H, HCoumMA), 6.82 -6.63 (m, 2H, HCoumMA), 6.05 (s, 1H,
	HCoumMA), 4.19 -3.36 (br, 6H, 2HEHMA + 4HCoumMA), 2.32 (s, 3H, HCoumMA), 2.07 -0.49 (br, -
	CH2 and -CH3 aliphatic). (Figure S3, S4 and S5 (a))
	13 C NMR (CDCl3),
	5 mmol) was dissolved in 60 mL of
	butanone. 2-Ethylhexyl methacrylate (21.1 g, 0.106 mol) and AIBN (0.22 g, 1.3 mmol) were

added. The mixture was deoxygenated by argon flow for 10 min at room temperature, then heated at 70 °C overnight to perform the polymerization. When the maximal conversion rate was reached (