J Guénolé

A Prakash

E Bitzek

Influence of intrinsic strain on irradiation induced damage: the role of threshold displacement and surface binding energies

Keywords: FIB, irradiation damage, atomistic simulation, threshold displacement energy, surface binding energy

Focused ion beam (FIB) machining has become a standard tool for sample preparation and in combination with digital image correlation (DIC) for the evaluation of local intrinsic stresses by measuring strain relaxation. However, FIB milling always leads to irradiation damage of the material. Current models for the formation of irradiation damage and the sputter yield are based on two key parameters, the threshold displacement energy (TDE) and surface binding energy (SBE), which are usually determined from unstrained systems with idealized surfaces. Here we use atomistic simulations to determine the TDE and SBE for strained silicon and aluminum and compare the results to full cascade simulations. A clear, material class dependent influence of the strain state on the TDE is observed, and surface amorphisation is shown to significantly increase the SBE of {0 0 1} surfaces.

Introduction

Over the past few decades, the focused ion beam (FIB) technique has established itself in the material science community as an indespensible tool in the field of micro/nano mechanics [START_REF] Tseng | Recent developments in micromilling using focused ion beam technology[END_REF][START_REF] Volkert | Focused ion beam microscopy and micromachining[END_REF], with typical applications including sample preparation for electron microscopy [START_REF] Kang | Ultra-thin TEM sample preparation with advanced backside FIB milling method[END_REF] or atom probe tomography [START_REF] Larson | Field-ion specimen preparation using focused ion-beam milling[END_REF] as well as the fabrication of micro-or nano-objects for mechanical testing [START_REF] Kiener | A further step towards an understanding of size-dependent crystal plasticity: In situ tension experiments of miniaturized single-crystal copper samples[END_REF][START_REF] Kiener | Micro-compression testing: A critical discussion of experimental constraints[END_REF]. In this context, the damage induced by FIB irradiation has been extensively investigated, both through experiments [START_REF] Kiener | FIB damage of cu and possible consequences for miniaturized mechanical tests[END_REF][START_REF] Lugstein | Method to characterize the three-dimensional distribution of focused ion beam induced damage in silicon after 50 kev ga+ irradiation[END_REF][START_REF] Rubanov | FIB-induced damage in silicon[END_REF][START_REF] Cullen | Assessment of surface damage and sidewall implantation in algan-based high electron mobility transistor devices caused during focused-ion-beam milling[END_REF][START_REF] Wang | Surface damage induced by focused-ion-beam milling in a si/si pn junction crosssectional specimen[END_REF] and simulations [START_REF] Tong | Molecular dynamic simulation of lowenergy FIB irradiation induced damage in diamond[END_REF][START_REF] Pastewka | Surface amorphization, sputter rate, and intrinsic stresses of silicon during low energy ga+ focused-ion beam milling[END_REF][START_REF] Xiao | Annealing recovery of nanoscale silicon surface damage caused by ga focused ion beam[END_REF], as well as in studies combining both these approaches [START_REF] Lane | Validating molecular dynamics with direct imaging of radiation damage debris[END_REF]. Most of these studies focus on the influence of ion beam energy, incidence angle and ion type on the damage produced within a specific target material. The measurement of local intrinsic stresses through FIB milling of specific geometries and subsequent determination of the relaxation strain through digital image correlation (DIC) has recently emerged as an innovative application of the FIB [START_REF] Korsunsky | Focused ion beam ring drilling for residual stress evaluation[END_REF]. The relation between the visible surface strain relaxation and the intrinsic stress which existed in the material before FIB milling is, however, not straightforward. Among various factors which might interfere with a proper evaluation of stresses, the interplay of intrinsic stresses and irradiation induced damage is largely unknown.

Only recently, Pastewka et al. [START_REF] Pastewka | Surface amorphization, sputter rate, and intrinsic stresses of silicon during low energy ga+ focused-ion beam milling[END_REF] investigated the influence of ion irradiation with grazing-angles on strained samples through atomistic simulations. Our own recent work has shown a clear influence of strain on the damage induced by FIB [START_REF] Guénolé | Atomistic simulations of focused ion beam machining of strained silicon[END_REF]. Although relatively large strains of the order of 1 -4% were used in these studies, the results are relevant especially for nanostructured materials, which can easily sustain such large strains. For example, Si layers with more than 12% strain were shown to be present in nanoheterostructures [START_REF] Lu | In situ control of atomic-scale si layer with huge strain in the nanoheterostructure nisi/si/nisi through point contact reaction[END_REF]. Consequently, a comprehensive study of the relation between intrinsic strain/stresses and the formation of irradiation induced damage would be of primary importance for assessing the reliability of any stress measurement technique involving FIB milling.

The threshold displacement energy (TDE) and the surface binding energy (SBE) are traditionally used to assess the resistance of a material to irradiation damage. Atomistic simulations are uniquely positioned to determine these properties. Pioneering molecular dynamics calculations of the TDE date back to more than fifty years ago [START_REF] Gibson | Dynamics of radiation damage[END_REF][START_REF] Erginsoy | Dynamics of radiation damage in a body-centered cubic lattice[END_REF]. The lack of computational power and of sophisticated interatomic potentials, however, confined these studies to consider pair interactions only, leading to plausible albeit imprecise values. With the development of the embedded atom method (EAM) in the 1980s [START_REF] Foiles | Embedded-atom-method functions for the fcc metals cu, ag, au, ni, pd, pt, and their alloys[END_REF], the simulation of many-body interactions became accessible which led to more reliable modeling of displacement cascades [START_REF] Bacon | Molecular dynamics computer simulations of displacement cascades in metals[END_REF]. Nowadays, calculations of TDE with even more accurate, DFT-informed interatomic potentials [START_REF] Nordlund | Molecular dynamics simulations of threshold displacement energies in fe[END_REF][START_REF] Gonzalez | Molecular-dynamics simulation of threshold displacement energies in batio3[END_REF] and ab-initio calculations [START_REF] Holmström | Threshold defect production in silicon determined by density functional theory molecular dynamics simulations[END_REF] pursue the comprehensive understanding of the formation of irradiation damage. A similar historical trend is observed for the calculation of the SBE. Early atomistic studies in the 1970s using two-body potentials [START_REF] Jackson | Binding energies in cubic metal surfaces[END_REF][START_REF] Jackson | Surface ejection in single crystal sputtering[END_REF][START_REF] Andersen | The depth resolution of sputter profiling[END_REF] were improved by the consideration of many-body interactions [START_REF] Gades | Pair versus many-body potentials in atomic emission processes from a cu surface[END_REF][START_REF] Gades | Surface binding energies of alloys: a many-body approach[END_REF][START_REF] Yang | Atomic scale calculations of tungsten surface binding energy and beryllium-induced tungsten sputtering[END_REF]. We note here that the calculation of TDE and SBE via atomistic simulations has traditionally been carried out on stress free crystalline structures close to the equilibrium state; the influence of intrinsic strain, to the best of your knowledge,

has not yet been considered.

In this work, we address the influence of strain on irradiation damage with a detailed atomistic study of fundamental material properties characterizing the propensity of ion irradiation to induce damage in a material. We present for the first time the computation of the TDE as function of strain using silicon and aluminum as model materials for semiconductors and metals. Furthermore, we compute the surface binding energy (SBE) as function of strain using a statistical approach for amorphized surfaces. These properties are finally correlated with the results of full collision cascade simulations of strained materials.

Methods

Atomistic simulations

A key aspect of atomistic simulations is the modeling of interatomic interactions. In the current work, we use recent semi-empirical potentials which are fitted to data from density functional theory (DFT) calculations to model the interaction in pure silicon and pure aluminum. The Si-Si interactions are modeled with the three-body potential from Stillinger and Weber [START_REF] Stillinger | Computer simulation of local order in condensed phases of silicon[END_REF] (denoted in the followoing by SW ), which has been further optimized by Pizzagalli et al. [START_REF] Pizzagalli | A new parametrization of the stillinger-weber potential for an improved description of defects and plasticity of silicon[END_REF] to better reproduce the mechanical properties as well as the TDE of silicon. The Al-Al interactions are modeled by the embedded atom method (EAM) potential of Pun and Mishin [START_REF] Pun | Development of an interatomic potential for the ni-al system[END_REF], developed for Ni-Al compounds (denoted Pun in the following). For the Ga-[Si,Al] interaction in ion irradiation, the Ziegler-Biersack-Littmark (ZBL) potential is used [START_REF] Ziegler | The stopping and range of ions in matter[END_REF]. This universal repulsive potential is designed to represent high energy atom collisions, albeit ignoring atomic bonding [START_REF] Pastewka | Surface amorphization, sputter rate, and intrinsic stresses of silicon during low energy ga+ focused-ion beam milling[END_REF][START_REF] Ziegler | The stopping and range of ions in matter[END_REF].

During a collision cascade, some atoms, in particular the primary knock-on atoms (PKA), have a very high energy. To represent such high-energy interactions, the SW and Pun potentials are smoothly merged to the ZBL potential for short inter-atomic distances following the procedure outlined in Ref. [START_REF] Holmström | Atomicscale effects behind structural instabilities in si lamellae during ion beam thinning[END_REF][START_REF] Nordlund | Effect of the interatomic si-sipotential on vacancy production during ion implantation of si[END_REF].

The merging is made for distances between 1.7 -2.0 Å and 1.8 -2.1 Å for Si and Al, respectively. For details of the joining procedure and the influence of the cutoff, see Nordlund et al. [START_REF] Nordlund | Molecular dynamics simulations of threshold displacement energies in fe[END_REF]. These authors acknowledge the subjective approach commonly used in the literature and recommended the use of simulations based on the density functional theory to highlight the choice. Such ab-initio simulations being out of the scope of the present study, the potential used in the current work is merged based on available literature data on Si [START_REF] Holmström | Atomicscale effects behind structural instabilities in si lamellae during ion beam thinning[END_REF][START_REF] Nordlund | Effect of the interatomic si-sipotential on vacancy production during ion implantation of si[END_REF]. Since no previous studies are available for Al, the merging region is defined proportional to the one for Si, based on the nearest neighbor distance in the Al fcc structure.

The present atomistic simulations are performed with the open-source software LAMMPS (version 7 Dec 2015) [START_REF] Plimpton | Fast parallel algorithms for short-range molecular dynamics[END_REF] running on both central processing unit (CPU) and graphics processing unit (GPU) [START_REF] Brown | Implementing molecular dynamics on hybrid high performance computers -short range forces[END_REF][START_REF] Brown | Implementing molecular dynamics on hybrid high performance computersparticle-particle particle-mesh[END_REF][START_REF] Brown | Implementing molecular dynamics on hybrid high performance computers three-body potentials[END_REF]. Samples are cut from bulk materials and statically relaxed using the conjugate gradient algorithm. The molecular dynamics (MD) simulations are performed with a default timestep of 1.0 fs. Strain is introduced by homogeneously rescaling the coordinates of the atoms and the simulation box in the periodic directions. For bi-axial and uni-axial applied strain, the other directions are kept stress free, allowing for the corresponding Poisson contraction. This models typical experimental situations, e.g. in strained semiconductor devices [START_REF] Bedell | Strain scaling for cmos[END_REF]. More details on the specific MD simulations are given below.

Atomistic configurations are post-processed and visualized using Ovito [START_REF] Stukowski | Visualization and analysis of atomistic simulation data with ovitothe open visualization tool[END_REF].

The analysis of irradiation induced damage is performed by using the diamond structure identification method [START_REF] Maras | Global transition path search for dislocation formation in ge on si(001)[END_REF] and the common neighbour analysis (CNA) method [START_REF] Stukowski | Structure identification methods for atomistic simulations of crystalline materials[END_REF] for silicon and aluminum, respectively.

Threshold displacement energy

The TDE is an intrinsic property of bulk materials. It corresponds to the energy required to move an atom from its original stable position to a meta-stable position, creating a point defect. This threshold is, however, highly anisotropic.

In crystals, it depends on the crystallographic direction and on the thermal noise, which can displace the atoms slightly from their ground state positions.

The determination of an averaged TDE can, however, be performed using a statistical approach [START_REF] Holmström | Threshold defect production in silicon determined by density functional theory molecular dynamics simulations[END_REF].

In our work, we compute the TDE by using the following scheme, similar to Nordlund et al. [START_REF] Nordlund | Molecular dynamics simulations of threshold displacement energies in fe[END_REF]. A perfect bulk crystal of 8000 atoms is thermalized at given temperatures (36 K and 300 K) and zero pressure. A velocity v θ,φ corresponding to an energy of 2 eV is attributed to a randomly chosen atom in a random direction characterized in a spherical coordinate system by (θ, φ), and a MD simulation is preformed in the NVE ensemble for 6 ps. v θ,φ is then increased by steps of 2 eV till the detection of a defect, at an energy E TDE (θ, φ).

Note that only the formation of Frenkel pairs (as detected by the Voronoi cell analysis [START_REF] Rycroft | Voro++: A three-dimensional voronoi cell library in c++[END_REF][START_REF] Stukowski | Structure identification methods for atomistic simulations of crystalline materials[END_REF]) is considered here. The averaged TDE value is constructed over N = 1000 randomly chosen directions:

TDE =   2π ψ=0 π φ=0 E TDE (ψ, φ)   × N -1 .

Surface binding energy

The SBE is a property related to the surfaces of materials, which characterizes the binding strength of surface atoms. Commonly likened to the sublimation energy [START_REF] Kudriavtsev | Calculation of the surface binding energy for ion sputtered particles[END_REF], it is possible and more accurate to determine this quantity from atomistic simulations [START_REF] Kelly | The surface binding energy in slow collisional sputtering[END_REF][START_REF] Yang | Atomic scale calculations of tungsten surface binding energy and beryllium-induced tungsten sputtering[END_REF]. In this work, we compute the SBE in a scheme similar to Yang et al. [START_REF] Yang | Atomic scale calculations of tungsten surface binding energy and beryllium-induced tungsten sputtering[END_REF]. Furthermore, we consider a statistical approach to evaluate the SBE from an amorphous surface, as described below.

Considering the free surface of a perfect crystal at 0 K, a velocity normal to this surface is prescribed to an atom, and MD simulation is performed in the NVE ensemble for 2 ps. Being initially large enough to tear off the atom from the surface, this velocity is decreased step-wise until the atom remains attached to the surface. The energy corresponding to the step right before this last stage is then defined as the SBE. Note that the system being at 0 K without any thermal noise, all the atoms belonging to as-cut {0 0 1} surfaces in FCC and diamond structures are equiva-lent. Therefore, no statistical approach is required in this case. Due to covalent bonding, silicon surfaces undergo local reconstruction, as described in the Results section. This reconstruction is obtained by relaxing a pre-disturbed (0 0 1) silicon surface.

We extend this approach by using an amorphous surface instead of a perfectly crystalline one to better model the situation during FIB milling. The amorphous structure is obtained by the "random method" described elsewhere [START_REF] Guénolé | Plasticity in crystalline-amorphous coreshell si nanowires controlled by native interface defects[END_REF].

In short, the method consists of filling up a given volume with randomly distributed atoms, by following the density of the amorphous phase. The system is then statically relaxed, annealed at high temperature and statically relaxed again. The resulting silicon amorphous structure has been shown to be in good agreement with the one obtained by the means of other methods [START_REF] Guénolé | Plasticity in crystalline-amorphous coreshell si nanowires controlled by native interface defects[END_REF]. In this case, the atoms belonging to the surface are, however, not well defined. We separate surface atoms from bulk atoms by computing the Voronoi volume of each atoms in the system, and define surface atoms as those atoms with a volume above a specific threshold. A good threshold volume was found to be 30 Å3 . The SBE for each of these surface atoms is then calculated as described above. The SBE for such an amorphous surface is then obtained by averaging the SBE of individual atoms constituting the surface.

Collision cascades

The irradiation of strained materials is studied by atomistic simulations of full collision cascades. Samples are cut from the bulk and homogeneously scaled to fit the lattice parameter at 300 K and thermalized at 300 K by using successively the NVE and NVT ensembles for a total time of 20 ps. Samples are then uniaxially strained and successive cascade simulations are finally run using this initial structure.

During a collision cascade, the heat spike regime requires sufficiently strong energy dissipation while not perturbing the dynamics of the high velocity particles. The kinetic energy provided by the fired ions is therefore dissipated by using a thermostatted region of 2 nm thickness, parallel to the ion beam and as far as possible from the initial position of the fired ion. Consequently, the position of the thermostatted layer must be adapted for each collision cascade.

In this layer, the temperature is controlled by a Berendsen thermostat [START_REF] Berendsen | Molecular dynamics with coupling to an external bath[END_REF].

The thermostatted region acts as an barrier for ion propagation [START_REF] Holmström | Atomicscale effects behind structural instabilities in si lamellae during ion beam thinning[END_REF], but the influence on the damage formation is negligible and a similar scheme has been previously used successfully [START_REF] Holmström | Atomicscale effects behind structural instabilities in si lamellae during ion beam thinning[END_REF][START_REF] Guénolé | Atomistic simulations of focused ion beam machining of strained silicon[END_REF].

The positions of the Ga + ion are randomly chosen at a distance of 2 nm from the (0 0 1) surface by following a normal distribution with a standard deviation of 2 nm typical for atomistic simulations [START_REF] Russo | Trench formation and lateral damage induced by gallium milling of silicon[END_REF][START_REF] Holmström | Atomicscale effects behind structural instabilities in si lamellae during ion beam thinning[END_REF][START_REF] Das | Mechanisms of material removal and mass transport in focused ion beam nanopore formation[END_REF]. The velocity corresponding to a kinetic energy of 5 keV and in the direction of the beam is attributed to the ion. A MD simulation of the collision cascade is then performed for a maximum time of 15 ps with a variable timestep to ensure that no atoms would be displaced by a distance larger than 0.01 nm during one MD step. Because of the high energy involved, sputtering can occur. An atom is considered as sputtered and then removed from the simulation if it leaves the simulation box, i.e. the distance between the atom and the closest surface is larger than two times the cutoff of the potential. For all ions, the collision cascade is finished by the end of these 15 ps, with a final global temperature below 400 K. A final MD simulation is performed for 15 ps to slowly cool down the system from the current temperature to 300 K, so as to get the structure ready for the next collision cascade.

Results

Threshold displacement energy

The TDE is calculated at a given uniaxial applied strain in the [010] direction for 1000 randomly chosen spatial directions. The average and the standard deviation of this average, i.e. standard error, are calculated over the entire population, leading to one data point per strain value. Fig. 1 shows the TDE at 36 K and 300 K. Temperatures of 36 K and lower are commonly used in atomistic simulations [START_REF] Nordlund | Molecular dynamics simulations of threshold displacement energies in fe[END_REF][START_REF] Holmström | Threshold defect production in silicon determined by density functional theory molecular dynamics simulations[END_REF] and therefore included in the present work. Fig. 1 shows a global increase of the TDE from 36 K to simulations at 300 K, however, the trends with respect to strain remain unchanged.

The TDE is usually determined using unmodified potentials [START_REF] Nordlund | Molecular dynamics simulations of threshold displacement energies in fe[END_REF][START_REF] Gonzalez | Molecular-dynamics simulation of threshold displacement energies in batio3[END_REF]. For the simulations of collision cascades, however, modified potentials are used in which the the ZBL potential is merged to the material specific potential for short interaction distances to improve the description of high energy collisions [START_REF] Nordlund | Molecular dynamics simulation of ion ranges in the 1100 kev energy range[END_REF][START_REF] Nordlund | Defect production in collision cascades in elemental semiconductors and fcc metals[END_REF]. It is therefore important to determine the TDE also for the modified potential. Fig. 2 shows the TDE at 36 K as a function of uniaxial applied strain along the [010] direction for the original potentials (red) and the potentials modified by merging the ZBL potential (green). We note that the data corresponding to the material specific multi-body potentials is identical to that presented in Fig. 1 at 36 K. Further details on the distribution of TDE values used for averaging are presented as box-and-whisker plots in Fig. 2a,b. Such box-and-whisker plots represent the two central quartiles in a box, the central line being the median.

The highest and lowest quartiles are represented by the whiskers.

To emphasize the influence of the merging of the ZBL to the material specific potentials, the cohesive energies of perfect Si (Fig. 2c) and Al (Fig. 2d) crystals are calculated as a function of hydrostatic strain, which is applied by homogeneously scaling the coordinates of the fully periodic atomistic structure.

Here, the strain is represented as nn/nn 0 with nn being the nearest neighbor distance and nn 0 being the nearest neighbor distance of the crystalline ground state.

The TDE as function of applied strain for certain specific directions is shown Samples are globally stress-free and undergo Poisson contraction. The strain state of directions normal to the tensile (compressive) applied strain are under compression (tension). Note that not only the exact direction normal or parallel to the imposed strain, but all the directions included in a solid angle of 60 • are considered for this purpose. In these cases, the TDE was averaged over 200-300 values, less than the 1000 values used for the all directions averaged TDE. Hence, the standard error is slightly increased, emphasizing the weaker statistics. Fig. 4 shows the TDE at 36 K as function of applied strain for different applied strain modes: uniaxial (red), equibiaxial (blue) and hydrostatic (green).

As before, the directions not strained are stress-free. The resulting strain states of the system are thus more complex; samples with compressive (tensile) uniaxial/biaxial applied strain exhibit tensile (compressive) strain in the perpendicular directions.

Surface binding energy

Fig. 5 shows the SBE as function of uniaxial applied strain calculated for different situations. As a reference, the experimental values of sublimation energy are also provided [START_REF] Chase | NIST-JANAF Thermochemical Tables Set[END_REF], see also the Supplementary Materials [START_REF][END_REF]. Direct computations or measurements of the SBE are rarely found in the literature.

In our work, the SBE is calculated from MD simulations for {0 0 1} Si and Al surfaces (Fig. 5). Unlike metals, covalent materials like silicon undergo short range surface reconstruction. For the 0 0 1 surfaces considered here, the reconstruction follows the π-bonded chain model of Pandey [START_REF] Pandey | New π-bonded chain model for si(111)-(2 × 1) surface[END_REF], named p (2 × 1) for symmetry reasons, and characterized by the formation of bonds between surface atoms in the 0 1 1 directions. Instead of being two times coordinated, the reconstructed surface atoms are three times coordinated and thus more difficult to sputter. The SBE for as-cut and reconstructed Si surfaces are consequently different as can be seen in Fig. 5a.

As described in the methods section, we also calculate an average SBE for an amorphous surface. The data points shown with black triangles in Fig. 5 along with the standard deviation, show a clear increase of the energy required to sputter an atom from an amorphous Si surface, in comparison to as-cut surfaces. The SBE of an amorphous Al surface appears also slightly larger than for an as-cut surface. As indicated by the standard deviation, however, significant data spread is observed.

A table summarizing SBE data is provided in the Supplementary Materials [START_REF][END_REF].

Irradiation cascades

In order to study the effect of the aforementioned influence of strain on TDE and SBE on irradiation damage, atomistic simulations of ion irradiation were performed on strained silicon samples. The evolution of irradiation induced damage throughout the sample is shown in Fig 6. Only stable damage configurations are considered here. During a typical collision cascade, the area where the collisions occur is in the so-called heat spike regime. The very high temperature reached at the atomic scale melts the sample locally resulting in significant amount of damage. However, with almost all excess thermal energy being dissipated before the occurrence of the next collision cascade, the melted region undergoes a dramatic recrystallization.

The remaining damage is then extremely stable at the temperature considered in this study.

The amount of damage can be obtained by evaluating the structural environment of each atom. The atoms are classified as perfectly crystalline (diamond cubic or fcc), or as defect atoms. Note that this essentially results in surface atoms being classified as defect atoms, as seen in Fig. 6(c). For irradiation up to some tens of ions, damage is primarily localized in the region around the path of the ion. With 50 ions, the damaged area is significantly larger and a clear amorphous zone can be observed. Further increase in ion dosage increases the damaged zone dramatically. A large fully amorphous region is formed, surrounded by smaller disordered regions.

Counting atoms in a perfect crystallographic environment and those classified as defect allows the quantification of the damage induced by the irradiation.

Tab. 1 presents the amount of atoms classified as perfect and defect, along the sputtered atoms. The ratio over the entire sample of atoms classified as defect because of ion irradiation is presented in the last row. Before irradiation, atoms belonging to the free surface are also classified as defects; the number of defect atoms due to irradiation is zero. Without applied strain, the irradiated sample exhibits a fraction of 11.2% of defects due to irradiation. A similar fraction is also observed for samples irradiated under compressive applied strains. By contrast, the fraction of defect atoms due to irradiation shows a significant increase for tensile applied strains. Quantifying sputtered atoms reveals slight variations with strain. With both compressive and tensile applied strain, the sputter yield is increased by approximately 1%. For a compressive applied strain of -4%, Atoms not in perfect cubic diamond structure environment are counted as Defect atoms.

Note that the sample before irradiation (first column) shows Defect atoms because of the free surface. The ratio of atoms corresponding to irradiation induced damage, named Irradiation defect atoms, is the ratio over the entire sample of the sum of Defect atoms and Sputtered atoms, reduced by removing surface atoms (e.g. Defect atoms before irradiation).

the sample undergoes local surface boiling, which leads to brutal sputtering for some incident ions only. The final amount of sputtered atoms is thus larger than for the other simulations. Such stochastic effects are hard to prevent in such short time-scale simulations, but don't contradict the other results.

Discussion

Our results show a clear influence of the strain state on the TDE. The various aspects which could contribute to this influence are discussed in the following.

Influence of interatomic potential

While performing atomistic simulations of ion irradiation, it is commonly accepted practice to add a strong repulsive part to the interatomic potential describing the target material, see sec. 2.1. The details of the merging of these two potentials -SW/ZBL and Pun/ZBL for Si and Al, respectively-are known to be subjective rather than based on physical principles [START_REF] Nordlund | Molecular dynamics simulations of threshold displacement energies in fe[END_REF] and to strongly influence the resulting interatomic interactions. According to our results, joining

the ZBL to the SW potential doesn't change the strain dependency but lowers the TDE (Fig. 2a). This decrease of the TDE in Si is, however, negligible and is smaller than the decrease of the TDE due to temperature variation (Fig. 1a).

Surprisingly, our results show a completely different effect for Al (Fig. 2b The difference can be explained by the fact that the description of the covalent bonding in the SW potential does not take into account the environment of the bonds, whereas the EAM potential is environment-dependent. Consequently, any modification of the EAM potential should in principle not only involve the pair-part of the potential, but also the environment-dependent terms. However, this is not usually considered [START_REF] Nordlund | Molecular dynamics simulations of threshold displacement energies in fe[END_REF].

The present results suggest that realistically modeling the formation of ion irradiation damage and sputtering in metals requires a more sophisticated treatment of the short-range interactions, and highlight the importance of using identical potentials when interpreting collision cascades in terms of the TDE.

Influence of strain state

Although merging the potentials with the ZBL potential does influence the magnitude of the TDE, it does not affect its behavior with respect to uniaxial applied strain. The cohesively bonded semiconductor (Si) shows a clear decrease of the TDE with uniaxial tensile applied strain, whereas for the metallic bonded aluminum an opposite trend can be deduced, see Fig. 1. In general, the situation is, however, more complex, as highlighted in Fig. 3 and4: the influence of applied strain on the TDE depends on the spatial direction for which the TDE is determined and the applied strain mode. By looking at hydrostatically strained samples, it is clear that tensile strains decrease the TDE, whereas compressive strains increase the TDE, in both Al and Si, see Fig. 4. This observation is a direct consequence of the anharmonicity of the cohesive energy: the cohesive energy shows a strong increase in hydrostatic compression and a smaller increase in tension [START_REF] Pettifor | Bonding and structure of molecules and solids[END_REF]. The process of creating a Frenkel-pair should thus be influenced to a different degree in tension than in compression. For more complex strain states, which involve both, shortened and elongated bonds and subsequently changed bond angles, like in the case of uni-and biaxial applied strains, the situation is less clear. In these cases, Si and Al show contradictory trends, which could be attributed to the stronger angular dependency of the bonding in Si compared to Al.

Influence of surface morphology

The SBEs calculated in this study are significantly higher than the usually considered values, e.g. the sublimation energy [START_REF] Chase | NIST-JANAF Thermochemical Tables Set[END_REF] or the ones calculated by analytical models [START_REF] Kudriavtsev | Calculation of the surface binding energy for ion sputtered particles[END_REF]. Values for the SBE that are 10-35% larger than the sublimation energy have already been put forward in the pioneering work of Jackson [START_REF] Jackson | Binding energies in cubic metal surfaces[END_REF], who also included the effect of surface relaxation. Similary SBE values were also reported in later studies, highlighting effects of slow collisions processes [START_REF] Kelly | The surface binding energy in slow collisional sputtering[END_REF] or many-body interactions [START_REF] Gades | Pair versus many-body potentials in atomic emission processes from a cu surface[END_REF]. Atomistic simulations take into account the local atomic relaxation around the vacancy left behind by the sputtered atom, and in doing so provide accurate values for the SBE [START_REF] Yang | Atomic scale calculations of tungsten surface binding energy and beryllium-induced tungsten sputtering[END_REF][START_REF] Behrisch | Sputtering by Particle Bombardment: Experiments and Computer Calculations from Threshold to MeV Energies[END_REF]. For MD simulations, the SBE is expected to be up to 40% larger than the sublimation energy [START_REF] Behrisch | Sputtering by Particle Bombardment: Experiments and Computer Calculations from Threshold to MeV Energies[END_REF], see also the recent results on MD simulations on tungsten [START_REF] Yang | Atomic scale calculations of tungsten surface binding energy and beryllium-induced tungsten sputtering[END_REF].

These observations are confirmed by our calculations on aluminium. The SBE for the as-cut Al surface is approximately 30% larger than the sublimation energy.

For covalent materials with directional bonding, the effect of local atomic relaxation can be much stronger than for metals [START_REF] Behrisch | Sputtering by Particle Bombardment: Experiments and Computer Calculations from Threshold to MeV Energies[END_REF], as observed with the sputtering from silicon surfaces [START_REF] Feil | Random and ordered defects on ion-bombarded si(100)-(2x1) surfaces[END_REF][START_REF] Zinovyev | Papers presented at the european materials research society 1993 spring conference, symposium c: Ion beam, plasma, laser and thermally-stimulated deposition processes, strasbourg, france, may 47, 1993 modelling of layerby-layer sputtering of si(111) surfaces under irradiation with low-energy ions[END_REF]. Our calculations on silicon exhibit a similar trend. The SBE for the as-cut {0 0 1} Si surface is approximately 50% larger than the sublimation energy. For the reconstructed {0 0 1} Si surface, the difference is even more pronounced, with a SBE 130% larger than the sublimation energy. A detailed analysis of the atomic mechanisms which take place in the simulations to determine the SBE, reveal crucial aspects which explain the dramatic increase of the values from a as-cut to a reconstructed surface: as an atom is torn off from the surface, its direct neighbors undergo reorganization to lower their energies. The reorganization is more pronounced for the reconstructed surface than for the as-cut surface; in the p(2 × 1) surface, atoms are 3-fold coordinated, compared to the 2-fold coordinated atoms of the the as-cut {0 0 1} Si surface.

It is known from literature that sputtering an atom from a surface is a highly anisotropic process, depending on the angle of ejection [START_REF] Jackson | Surface ejection in single crystal sputtering[END_REF] with respect to the surface. In addition, an anisotropy due to the direction of the sputtered atom with respect to the local crystallography of the surface could be expected for crystalline surfaces. For amorphous surfaces, no anisotropy with respect to local crystallography exists. However, the amorphous surfaces show a certain roughness. The SBE therefore will have different values depending on the local angle of ejection. The averaged SBE is, nevertheless, of the order of the SBE determined for the as-cut and reconstructed surfaces for Al and Si, respectively, see Fig. 5. This relation between the SBE of undamaged and amorphous silicon surfaces is directly related to the coordination number of surface atoms, as mentioned by Gades et al. [START_REF] Gades | Surface binding energies of alloys: a many-body approach[END_REF]; atoms of an as-cut Si surface are 2 times coordinated, whereas atoms belonging to the reconstructed and amorphous Si surfaces in our simulations are 3 times coordinated. As pointed out in the methods section, the surface roughness of amorphous surfaces requires a statistical approach. As a result, the average SBE value shows a large standard deviation, see Fig. 5. Interestingly, the scatter of 2 eV is similar for both model materials used in the current work, emphasizing its dependence on roughness rather than on the material.

The significant increase of the SBE observed for Si has important consequences for the modeling of ion milling processes, as the ions will mostly impinge on an already amorphized surface, for which the widely used estimates of the SBE derived from perfect surfaces or from sublimation energies are inadequate.

Collision cascades and TDE

The atomistic simulations of ion irradiation using strained silicon corroborate the observed trends in the strain dependence of the TDE. The uniaxially strained samples clearly show increased damage formation for tensile strains, see Tab. 1

as predicted by the strain-dependent TDE. This highlights the importance of taking into account the strain state of the milled material for more accurate modeling of FIB milling. In this context, the strain-dependent TDE becomes a material parameter of fundamental importance.

Conclusions

Atomistic simulations have been performed on silicon and aluminum to compute the averaged threshold displacement energy (TDE) and surface binding energy (SBE) of {1 0 0} surfaces for different strain states. In addition, full collision cascades have been simulated for uniaxially strained silicon. Our results suggest that realistically modeling ion irradiation damage in metals requires a more sophisticated treatment of the short-range interactions compared to covalently bonded semiconductors. For both, Si and Al, hydrostatic tensile strains decrease the TDE whereas compressive strains increase the TDE, which is expected from the anharmonic nature of the cohesive energy. For more complex strain states, like in the case of uni-and biaxial applied strains, which involve both, shortened and elongated bonds, the different dependence of the bonding energy on bond angles in metals and semiconductors leads to qualitative differences in the strain dependence of the TDE. Cascade simulations on uniaxially strained silicon confirm this observation and underline the importance of the strain-dependent TDE as a fundamental material parameter. The SBE for realistic (reconstructed or amorphized) surfaces is shown to be significantly larger than the sublimation energy, which is often used as approximation of the SBE. Consequently, models of FIB-milling could be improved by taking into account the strain dependence of the TDE, and SBEs derived from more realistic surfaces.

Figure 1 :

 1 Figure 1: Average threshold displacement energy as function of uniaxial applied strain along the [010] direction at 36 K and 300 K, for (a) Si and (b) Al. Tensile applied strains are taken as positive, compressive applied strains as negative. Error bars correspond to the standard error of the data set (1000 independent values each). Solid lines serve as guides to the eye.

Figure 2 :

 2 Figure 2: Influence of modifying the potential by merging it with the ZBL potential on the threshold displacement energy (TDE) as function of applied strain in [010] direction for (a) Si and (b) Al. The upper plots show the averaged TDE and the corresponding standard error of the data set (1000 independent values each). Solid lines are guides to the eye. The box-andwhisker plots show the distribution of these 1000 TDE values, the inner box line representing the median of each data set. (c) and (d) show the cohesive energies of perfectly crystalline Si and Al, respectively, as a function of hydrostatic strain.

Figure 3 :

 3 Figure 3: Average threshold displacement energy as function of the spatial directions considered, for (a) Si and (b) Al. All directions are considered for the red points. Only the directions in a solid angle of 60 • normal (parallel) to the applied strain direction [0 1 0] are considered for the orange (brown) points. Error bars correspond to the standard error of the data set. Solid lines serve as guides to the eye.

Figure 4 :

 4 Figure 4: Average threshold displacement energy as function of applied strain mode, for (a) Si and (b) Al. Applied strain modes considered are uniaxial ([0 1 0], red), equibiaxial (along [0 1 0] and [1 0 0] blue) and hydrostatic (green). Error bars correspond to the standard error of the data set (1000 independent values each). Solid lines are guides to the eye.

Fig. 6 (

 6 a) shows perspective views of the entire sample after a certain number of fired ions (corresponding to the number of simulated collision cascades). Fig. 6(b) shows projected views of a 4 nm thick slice, extracted from the region with the highest incoming ion density. Fig. 6(c) shows perspective views similar to the first row, excluding the atoms in perfect crystalline environment, and thus providing a better overview of the stable damage produced by the ion irradiation.

Figure 5 :

 5 Figure 5: Surface binding energy for (a) a (0 0 1) silicon surface and (b) a (0 0 1) aluminum surface calculated at different uniaxial tensile applied strains. Empty black circles represent the experimentally determined sublimations energies [55]. Full blue circles: surface binding energy for as-cut surface; full green squares: surface binding energy for reconstructed surface (silicon only); full black triangles: surface binding energy for disordered surface with random roughness. Error bars correspond to the sum of standard deviation of the data set and the systematic error, and describe the spread of the SBE values. Dashed lines are guides to the eye.

Figure 6 :

 6 Figure 6: Induced damage in collision cascade simulations of 5 keV Ga + ions in Si at 300 K. (a) perspective view and (b) projected view of a slice with a thickness of 4 nm located at the simulation box center, i.e. the highest concentration of incoming ions. (c) perspective view where atoms in a perfect cubic diamond structure environment (until the second neighbor) are hidden to highlight irradiation induced damage. Atoms colored according the diamond structure identification method implemented in Ovito (blue -cubic diamond, cyan/greencubic diamond 1st/2nd neighbor, white -non-diamond structure).

  ); joining the ZBL to the Pun potential doesn't change the trend of strain dependency, but strongly increases the TDE values. The TDE values computed with ZBL potential are twice the values of TDE without ZBL. An increase of the averaged TDE of Si and Al can have different origins. Both, an increased spread favoring higher values in the individual calculations, or a global shift of the TDE, might explain such increase of the averaged TDE. Looking at the distribution of the TDE over all spatial directions (Fig. 2a,b with boxplots) shows that the TDE distributions for SW and SW/ZBL mostly overlap, with a similar trend independent of the presence of the ZBL potential. Conversely, the TDE distribution is dramatically widened from Pun to Pun/ZBL, with the two central quartiles being 5 times larger in the Pun/ZBL case. The lowest values of the distribution are also strongly increased, being close the the median of the TDE for Pun. Thus, joining the ZBL to the Pun potential not only increases the averaged TDE of Al, but prevents low TDE values while strongly favoring TDE values higher than the most probable TDE for the Pun potential alone.The influence of adding the ZBL potential to the material specific potential can be assessed by calculating the cohesive energy as function of hydrostatic strain, see Figs.2c and d. Compared to the three-body potential for Si, the EAM potential for Al shows a significant increase of the cohesive energy for larger compressive applied strains through the addition of the ZBL potential.

Table 1 :

 1 Fraction of atoms belonging to irradiation induced damage as function of uniaxial applied strain along the [010] direction. Atoms in perfect cubic diamond structure environment are counted as Perfect atoms. Atoms removed by sputtering are counted as Sputtered atoms.

	Irradiated	no			yes
	Strain (%)	-	-4	-2	0	+2	+4
	Perfect atoms (#) 699,926 621,710 620,390 620,342 613,335 608,837
	Sputtered atoms (#)	0	2,350	348	308	366	369
	Defect atoms (#)	12,874	88,740	92,062	92,150	99,099 103,594
	Irradiation defect atoms (%)	0.0	11.0	11.2	11.2	12.2	12.8

Acknowledgments

This work was supported by the European Union, within the large collaborative project ISTRESS, Grant Agreement No. 604646. EB acknowledges the support of the Cluster of Excellence Engineering of Advanced Materials (EAM) and the Central Institute of Scientific Computing (ZISC). JG would like to thank J. Amodeo, Lyon, France and J. Godet, Poitiers, France for fruitful discussions.


François Touchaleaume
email: francoistouchaleaume@gmail.com

Romain Tessier

Rémi Auvergne

Sylvain Caillol

Sandrine Hoppe

Helene Angellier-Coussy

Sandrine Hoppé

Hélène Angellier-Coussy

Polyhydroxybutyrate/hemp biocomposite: tuning performances by process and compatibilisation

Keywords: A-Polymer-matrix composites, A-Natural fibres, B-Mechanical properties, E-Extrusion

come

Introduction

Biocomposites based on the combination of both bio-sourced and biodegradable polymer matrices and vegetal fillers have been extensively developed during the last decade in response to environmental concerns and/or to develop specific new functionalities. Among promising bioplastics, polyhydroxyalkanoates (PHAs), such as polyhydroxybutyrate (PHB), bacterial aliphatic copolyesters fully biodegradable materials [START_REF] Tokiwa | Degradation of microbial polyesters[END_REF][START_REF] Zaverl | Studies on recyclability of polyhydroxybutyrate-co-valerate bioplastic: Multiple melt processing and performance evaluations[END_REF] that can be produced from food industry by-products [START_REF] Serafim | Strategies for PHA production by mixed cultures and renewable waste materials[END_REF], agricultural or urban waste [START_REF] Bugnicourt | Polyhydroxyalkanoate (PHA): Review of synthesis, characteristics, processing and potential applications in packaging[END_REF][START_REF] Nielsen | Food waste conversion to microbial polyhydroxyalkanoates[END_REF]. Short lignocellulosic fibres stemming from jute [START_REF] Gunning | Mechanical and biodegradation performance of short natural fibre polyhydroxybutyrate composites[END_REF], hemp [START_REF] Gunning | Mechanical and biodegradation performance of short natural fibre polyhydroxybutyrate composites[END_REF][START_REF] Hermida | Transcrystallization kinetics at the poly(3hydroxybutyrate-co-3-hydroxyvalerate)/hemp fibre interface[END_REF], wheat straw fibres [START_REF] Berthet | Exploring the potentialities of using lignocellulosic fibres derived from three food by-products as constituents of biocomposites for food packaging[END_REF][START_REF] Berthet | Sustainable food packaging: Valorising wheat straw fibres for tuning PHBV-based composites properties[END_REF], olive pomace [START_REF] Berthet | Exploring the potentialities of using lignocellulosic fibres derived from three food by-products as constituents of biocomposites for food packaging[END_REF] , coffee waste [START_REF] Reis | Particles of Coffee Wastes as Reinforcement in Polyhydroxybutyrate (PHB) Based Composites[END_REF] or potato peel waste fermentation residues [START_REF] Wei | Thermophysical properties and biodegradation ior of green composites made from polyhydroxybutyrate and potato peel waste fermentation residue[END_REF] can be incorporated in such way as to decrease the overall cost of PHA-based materials and open their window of applications by modulating their functional properties.

One of the main bottlenecks of PHB/lignocellulosic fibres biocomposites is the poor affinity between lignocellulosic fibres and PHB resulting in limited tensile properties. To overcome this problem, different strategies can be applied to improve wettability and intimate contact between lignocellulosic fibres and polymer matrices, i.e. the fibre surface modification to increase their surface free energy and particularly their hydrophobicity, the polymer matrix modification to increase its hydrophilicity, or the introduction of amphiphilic compatibilizers [START_REF] Bledzki | Composites reinforced with cellulose based fibres[END_REF][START_REF] Mohanty | Surface modifications of natural fibers and performance of the resulting biocomposites: An overview[END_REF][START_REF] Belgacem | The surface modification of cellulose fibres for use as reinforcing elements in composite materials[END_REF][START_REF] Gandini | Physical and chemical methods of fiber surface modification[END_REF]. If the incorporation of compatibilizers is widely reported in literature, particularly using melt extrusion [START_REF] Reddy | Renewable resources-based PTT poly(trimethylene terephthalate) /switchgrass fiber composites: The effect of compatibilization[END_REF], only a handful of papers depict the use of bio-based compatibilizers [START_REF] Yu | Polymer blends and composites from renewable resources[END_REF], while biosourcing plasticizers has become a common practice [START_REF] Bocque | Petro-Based and Bio-Based Plasticizers: Chemical Structures to Plasticizing Properties[END_REF]. A combination of biobased polyethylene-graft-maleic anhydride (PE-g-MA) with sepiolite was proposed by Samper-Madrigal et al. to manufacture films made of polyethylene and 30 wt% of thermoplastic starch (TPS) [START_REF] Samper-Madrigal | The effect of sepiolite on the compatibilization of polyethylene-thermoplastic starch blends for environmentally friendly films[END_REF]. Some authors proposed glycolysis of polylactide (PLA) with biobased polyols such as glycerol or sorbitol to yield compatibilizer oligomers to enhance compatibilization in PLA/starch composites [START_REF] Wu | Recycling PLA to multifunctional oligomeric compatibilizers for PLA/starch composites[END_REF]. Recently, Xiong et al. [START_REF] Xiong | Preparation of Biobased Monofunctional Compatibilizer from Cardanol To Fabricate Polylactide/Starch Blends with Superior Tensile Properties[END_REF] proposed the epoxidizization of biobased cardanol with epichlorohydrin to yield an effective bio-based compatibilizer for PLA/starch composites.

Our team proposes a new strategy to synthesize bio-based compatibilizers for PHB/hemp fibre composites. We intend to design oligo-PHB with aromatic groups, which could develop interactions with hemp fibres, by depolymerizing PHB with alcohol functions of biobased aromatic groups. Our team deeply studied cardanol [START_REF] Jaillet | Synthesis of cardanol oil building blocks for polymer synthesis[END_REF] or tannins [START_REF] Benyahya | Functionalized green tea tannins as phenolic prepolymers for bio-based epoxy resins[END_REF], which only bear phenol groups, and also lignin derivatives including vanillin and vanillin alcohol, which have a primary alcohol that could be a good candidate to depolymerize PHB. Indeed, vanillin and derivatives are especially interesting as vanillin is the only mono-aromatic compound currently industrially produced from lignin [START_REF] Benyahya | Functionalized green tea tannins as phenolic prepolymers for bio-based epoxy resins[END_REF][START_REF] Bjorsvik | Fine chemicals from lignosulfonates. 1. Synthesis of vanillin by oxidation of lignosulfonates[END_REF]. In a previous paper [START_REF] Fache | Vanillin, a promising biobased building-block for monomer synthesis[END_REF], our team investigated the functionalization of vanillin and its derivatives at different oxidation states.

In addition to this chemical strategy that reduces the lack of affinity between the components, it is necessary to homogeneously disperse the fibres within the polymer the matrix to fully benefit from the introduction of fibres. For that purpose, processing conditions need to be optimized as largely reported in the literature, whatever the fibre type [START_REF] Pickering | A review of recent developments in natural fibre composites and their mechanical performance[END_REF][START_REF] Faruk | Biocomposites reinforced with natural fibers: 2000-2010[END_REF][START_REF] Gamon | Twin-screw extrusion impact on natural fibre morphology and material properties in poly(lactic acid) based biocomposites[END_REF]. Ranganathan et al. recently reported that when manufacturing viscose fibre/PP composites at low shear, the fibre bundles retained in clusters, whereas higher shear conditions drove to homogenized fibre dispersion and higher mechanical performances. Further addition of dispersing agent improved the fibre dispersion along with the mechanical performance of the composites [START_REF] Ranganathan | Effect of long fiber thermoplastic extrusion process on fiber dispersion and mechanical properties of viscose fiber/polypropylene composites[END_REF]. Similarly, Kuroda and Scott performed basic experiments concerning the dispersion mechanism of glass fibre bundles and found that complete dispersion occurs above a critical shear stress [START_REF] Kuroda | Initial dispersion mechanisms of chopped glass fibers in polystyrene[END_REF].

The objective of the present work is to optimize the mechanical performance of PHB/hemp fibres biocomposites by investigating and combining two routes: 1/ extrusion processing conditions (screw profile and speed) and 2/ addition of bio-based compatibilizers produced by reactive melt extrusion from the depolymerization of PHB with vanillin alcohol. The impact of processing and formulation on mechanical properties, water vapour sensitivity and biodegradability has been assessed and discussed in relation to the structure of the materials.

Materials and methods

Raw materials

A commercial polyhydroxybutyrate (PHB) was purchased from Metabolix, Germany (P(3HBco-4HB) with 5% of 4-hydroxybutyrate, M2100 grade). Pellets were vacuum dried overnight at 60 ºC before processing. Hemp fibres (retted, carded, 4mm long) were provided by Chanvriers de l'Est (France). Zinc acetate dihydrate (ZnAc2, 99% of purity) and vanillic alcohol (VA, 98% of purity) were purchased from Sigma-Aldrich.

Synthesis of the compatibilizer

The compatibilizer was obtained by trans-esterification of PHB by VA in a batch-way. In a two-neck flask, PHB and VA were mechanically stirred and heated at 180°C with ZnAc2 as a trans-esterification catalyst (1w% relative to polymer) in order to obtain oligo-esters exhibiting a phenol end (Figure 1). Reagents were previously dried for one night at 45°C in a vacuum oven and three argon/vacuum cycles were applied to the flask prior to heating so as to remove residual oxygen. Reaction was maintained during 1.5 hour and the material was then put in a vacuum container during cooling and further hand-crushed in a mortar.

O H O O H R k + OH O CH 3 O H m O O CH 3 O H O H O R O H O O H R p +  cat. R= -CH 2 -CH 2 -CH 2 -, -CH 2 -CH- m,p<<k CH 3
Fig. 1 Trans-esterification of PHB by vanillic alcohol A masterbatch of the compatibilizer previously prepared was compounded in a Eurolab 16XL twin screw extruder (ThermoScientific). Pellets of compatibilizer and P(3HB-co-4HB) were previously dry mixed, the coupling agent standing for 30w% of the total throughput (2.86 kg.h - 1 ). Both components were dried before extrusion and screw speed was set at 500 rpm, leading to a residence time of 70-75 s. The temperature profile was a downstream gradient from 180°C at the feeder to 150°C at the die. The so prepared masterbatch was air dried and further pelletized.

Preparation of PHB/hemp fibres biocomposites

Pellets of virgin PHB and compatibilizer masterbatch were dried for one night in a vacuum oven at 45°C and mixed in a plastic can before processing. Biocomposites were prepared in a twin-screw extruder with a L/D ratio of 28 and a screw diameter of 24 mm (Haake Polylab, Thermo Scientific). Hemp fibres were dried at 80°C for 1 hour and added to the extruder by a lateral feeder directly into the polymer/masterbatch melt. The fibre content was set at 20%, the temperature was set at 180°C all along the screw and the total throughput was 4.5 kg.h -1 .

Three screw speeds were chosen (250, 500 and 750 rpm) and two screw profiles have been tested providing two different shear levels to the extruded material. The first screw profile was constituted by five distributions zones (made of mixing elements) and one single dispersion zone (made of mixing elements directly followed by an inverse screw thread) and was called "Low Shear profile". The second screw profile was constituted by five dispersion zones and one distribution zone and called "High Shear profile". Residence times for the Low Shear profile were 80 s, 50 s and 40 s at 250 rpm, 500 rpm and 750 rpm, respectively. When using the High Shear profile, the residence times were 115 s, 90 s and 80s when processing at 250 rpm, 500 rpm and 750 rpm, respectively.

Extruded composites were granulated, dried for one night in a vacuum oven at 45°C and further injected as dog-bone samples with the aid of a DSM MC15 microcompounder and a DSM IM12 injection moulding machine. Mould geometries were chosen according to ISO 572-2 standard specifications and injected samples were of 1B type. It is worth noting that unfilled materials could not be processed along with this last step as injection molding requires crystallizing kinetics that those compositions did not show since no crystallization agent was employed.

Samples were codified as follows: with compatibilizer: PHB-C-H; without: PHB-H. Processing conditions are precised detailed as follow: "LS" and "HS" referring to the materials elaborated with the low shear and the high shear profiles, respectively. The three digits' figure of the sample codification refer to the screw speed chosen during processing, in rpm.

Characterization of PHB/hem fibres biocomposites

Scanning Electron Microscopy.

Scanning electron microscopy (SEM) observations were performed using a scanning electron microscope (SEM S-4500, Hitachi, Japan) with an acceleration voltage of 2 kV and a detector for secondary electrons. Prior to observation, the injection molded samples were frozen under liquid nitrogen, then fractured, mounted and coated with gold on an ion sputter coater.

Molecular weight analysis.

The weight-average molecular weights (Mw) were determined by gel permeation chromatography (GPC) on a Waters HPLC system equipped with a Waters 410 differential refractive-index detector, a 600 mm column PL gel MixC 5µm. The mobile phase was CHCl3, its flow rate set at 0.8ml/min at 30°C and toluene used as flowmarker. The samples were prepared as 10mg/ml solutions and when containing fibres, were filtered on a 45 µm-pores filter (VWR, filter paper, qualitative 413). Then, all samples were filtered using 0.2µm PTFE filters.

A sample injection volume of 200 µL was used in the GPC analysis and the calibration was performed with PS standards.

Differential Scanning Calorimetry.

Differential Scanning Calorimetry (DSC) measurements were performed with a calorimetric NETZSCH DSC 200 F3 calibrated with an indium standard. Samples of 10 ± 2 mg were placed in the measurement heating cell and were heated under inert atmosphere from -50 to 200 °C at a heating rate of 20 °C/min. Two heating runs and a cooling one were recorded and the glass transition temperature (Tg) values were measured during the second run. Tgs were calculated at the mild point of the heat capacity jump. The crystallinity degree was obtained from the DSC curve using the following equation:

∆𝐻 𝑚 -∆𝐻 𝑐𝑐 ∆𝐻 𝑚100% × (1 -𝛼)
where ∆𝐻 𝑚 is the measured melting enthalpy for a given sample, ∆𝐻 𝑐𝑐 the cold crystallization enthalpy, , ∆𝐻 𝑚100% the melting enthalpy of 100% crystallized PHB (144 J/g) [START_REF] Cong | A study on properties of poly(3-hydroxylbutyrate-co-4hydroxylbutyrate) with various 4HB contents and triethyl citrate plasticization[END_REF] and (1 -α) is the weight fraction of polymer in the material.

Thermal stability. ATG

Thermogravimetric analyses (TGA) were performed on a Q50 from TA Instrument. 10 mg of sample were displayed in an aluminum pan and heated from RT to 550°C under a nitrogen flow (60 mL/min). The experiments were carried out at a heating rate of 10°C/min.

Tensile tests.

Mechanical tensile tests were performed on a Zwick metrology Z010 apparatus owing to NF EN ISO 527-1 standard in order to determine mechanical properties of materials. The apparatus is equipped with pneumatic grips, with 100 mm spacing, a sensor of 500 N or 5 kN depending on the tested materials. Traction speed is 10mm/min, controlled by position regulation, with a preload of 2 N before measurement. Results are an average of measurements performed on at least five samples.

Water sorption kinetics.

Moisture sorption isotherms were determined with the aid of a precision scale. The experiments were carried out on end-parts of dog-bone injection molded samples. The samples were dried at 40 •C in a vacuum oven for 24 hours and then let to equilibrate at 0% relative humidity (RH) for one week before measurement. The sorption curves were conducted at 25°C with 96 RH%.

The moisture uptake M(t) was calculated using the following equation:

𝑀(𝑡) = 𝑤 𝑚𝑜𝑖𝑠𝑡 (𝑡) -𝑤 𝑑𝑟𝑦 𝑤 𝑑𝑟𝑦 × 100
where 𝑤 𝑚𝑜𝑖𝑠𝑡 (𝑡) is the sample weight exposed to 96 RH% for a time 𝑡 and 𝑤 𝑑𝑟𝑦 is the dry weight of the sample at 0 RH%. Numerous models have been developed to properly describe the moisture contamination of composite materials [START_REF] Wolf | Water vapor sorption and diffusion in wheat straw particles and their impact on the mass transfer properties of biocomposites[END_REF][START_REF] Miguel | Water transport properties in poly(3-hydroxybutyrate) and poly(3-hydroxybutyrate-co-3-hydroxyvalerate) biopolymers[END_REF]. As indicated in the ASTM standard for water diffusion in thin plates of fibre-reinforced polymers [START_REF] Astm | Standard Test Method for Moisture Absorption Properties and Equilibrium Conditioning of Polymer Matrix Composite Materials[END_REF], this process can be adequately described by the one dimensional Fick's second law:

𝜕𝑐 𝜕𝑡 = 𝐷 𝜕²𝑐 𝑑𝑥²
where c is the moisture concentration, D is the diffusion coefficient, t is the time and x is the position through the thickness. A useful closed-form approximate solution is given as [START_REF] Shen | MOISTURE ABSORPTION AND DESORPTION OF COMPOSITE-MATERIALS[END_REF]:

𝑀(𝑡) 𝑀𝑠 ≈ 1 -𝑒𝑥𝑝 [-7.3 ( 𝐷𝑡 ℎ² ) 0.75 ]
where M(t) is the evolution of the water absorbed, Ms the water content at saturation and h the thickness of the plate. The curve were fitted thanks to a Levenberg-Marquardt algorithm applied on the asymptotic model performed on OriginPro 2017 software. All the coefficentscoefficients of determination (r²) were higher than 0.993.

Biodegradation.

Respirometric tests were conducted in compost medium at 58°C to evaluate the biodegradability of the materials. The method was adapted from the US standard ASTM D5988-03 to determine the Aerobic Biodegradation of Plastic Materials After Composting. The released CO2 being proportional to the percentage of biodegraded substrate, CO2 evolution quantifies the ultimate degradation step (i.e. mineralization) during which a substance is broken down to its final products [START_REF] Lucas | Polymer biodegradation: Mechanisms and estimation techniques[END_REF]. Beforehand, materials were cut into 1-2mm bits and carbon contents were measured with an elementary analyseranalyzer (ThermoQuest NA 2500) in order to precisely set the material dose to 50 mg of carbon into 3g of compost. Biodegradation tests were carried out in real and mature compost. Distilled water was initially added to the solid media and then regularly added all along the experiment to maintain the moisture content of the medium around 80-100%.

Results and discussion

3.1. Multi-scale structure of PHB/hemp fibres biocomposites

Morphology of composite samples

The morphology of PHB-based composites was assessed by SEM observations of cryofractured surfaces of injected samples (figure 2). Such observations gave information on two aspects of the impact of the elaboration conditions on the microstructure of the prepared composites. The first one was the dispersion state of the fibres which is mainly influenced by the shear applied to the melt during extrusion and which could be assessed at low magnification (figures 2a and 2b). Dispersion of the hemp fibres within the PHB matrix appeared homogeneous. The absence of fibre cluster was an encouraging indicator for favored interactions between the matrix and the fibres. However, no significant impact of the processing conditions was picked up. Indeed, the composite prepared under the most severe conditions, i.e. using the high-shear profile at 750 rpm (figure 2a) exhibited a fibre dispersion as uniform as the one prepared under the softest conditions, i.e. the low-shear profile at 250 rpm (figure 2b), indicating that the shearing forces induced by all the chosen processing conditions were sufficient enough to homogenously dispersed hemp fibres within the polymer matrix.

The second investigated characteristic of the microstructure was the level of interfacial adhesion between the matrix and the fibres, usually influenced by the chemistry of the environment. This was qualitatively assessed by high magnification observations of the filler/matrix interface. Figures 2c and2d exhibit pictures of two composites elaborated with similar processing conditions (high-shear profile, 250 rpm), leading to the highest residence time of the various processing conditions. The reported pictures revealed dissimilar fibre/matrix adhesion levels whether a compatibilizer had been added or not. The composite prepared with a compatibilizer (figure 2d) exhibited an interphase between the fibre and the polymer, while gaps could be noticed between the hemp fibres and the matrix when no compatibilizer was employed (figure 2c). This improvement of the interface revealed that this residence time (115 s) was long enough to develop an interphase, confirming thus the efficiency of the compatibilizer. However, all the compatibilized materials (PHB-C-H) exhibited quite similar dispersion states and interphases, whatever the residence time, i.e. whatever the processing conditions employed. Nevertheless, even if those various materials could not be discriminated by SEM analyses, their performances could also be linked to their macromolecular structure and molar masses.

Polymer molar mass

Molar mass analyses have been performed on the injection-molded biocomposites prepared under various processing conditions and with various compositions (Table 1). The pristine PHB matrix displayed a molar mass (Mw) of 150,700 g.mol -1 . In comparison with this reference value, all samples underwent a common reduction of the molar mass when the material was submitted to an extra processing step (Table 1). This reduction was comprised between -13%

for the virgin PHB extruded under the softest conditions (LS250) down to -71% for the PHB-C-H extruded under the most severe processing conditions (HS750). More precisely, when comparing the two screw profiles at a similar screw speed, the Mw drop was stronger for the material processed with the high shear profile with the low shear one (table 1). For instance, the two PHB-H materials processed at 250 rpm reveal Mw equal to 122,200 g.mol -1 and 72,200 g.mol -1 with the low-shear and the high-shear profiles respectively, corresponding to a 19% reduction for the low-shear processed material and to a 49% reduction for the high-shear processed one, in comparison with pristine PHB. Those Mw reductions were even more pronounced when the screw speed increased (in spite of reduced residence times). Indeed, the molar mass decreased from 122,200 g.mol -1 for the PHB-H processed with the low-shear profile down to 63,700 g.mol -1 when the screw speed was increased from 250 rpm up to 750 rpm. This sensitivity to mechanical stresses exhibited by polyester-based materials has already been widely studied [START_REF] Carrasco | Processing of poly(lactic acid): Characterization of chemical structure, thermal stability and mechanical properties[END_REF][START_REF] Pachekoski | The Influence of the Industrial Processing on the Degradation of Poly(hidroxybutyrate) -PHB[END_REF][START_REF] Montano-Herrera | In-line monitoring of thermal degradation of PHA during melt-processing by Near-Infrared spectroscopy[END_REF][START_REF] Larsson | Melt processability and thermomechanical properties of blends based on polyhydroxyalkanoates and poly(butylene adipate-co-terephthalate)[END_REF]. Literature also reports a decisive role played by moisture during extrusion, inducing hydrolysis reactions [START_REF] Pachekoski | The Influence of the Industrial Processing on the Degradation of Poly(hidroxybutyrate) -PHB[END_REF]. When adding fibres, two phenomena contributed to worsen this Mw drop: 1/ PHB hydrolysis was favored by the presence of water, alcohols and/or acids produced during biomass thermal degradation [START_REF] Berthet | Exploring the potentialities of using lignocellulosic fibres derived from three food by-products as constituents of biocomposites for food packaging[END_REF][START_REF] Spitalsky | Controlled degradation of polyhydroxybutyrate via alcoholysis with ethylene glycol or glycerol[END_REF], 2/ melt shear viscosity was higher than without fibre, increasing then the internal warming during the process of thermally sensitive PHB. When the compatibilizer was introduced, PHB-C-H exhibited slightly lower Mw than the corresponding PHB-H. For instance, the composites processed at 250 rpm under low-shear exhibit a molar mass of 122,200 g.mol -1 without compatibilizer and 106,500 g.mol -1 when 2.4 wt% compatibilizer was added, indicating a 18.9% reduction for PHB-H and 29.3% reduction for PHB-C-H. This increase of degradation level induced by the presence of the compatibilizer was expected as the composite processing conditions were similar to those of the compatibilizer synthesis (transesterification in reactive extrusion with catalyzer still in media). The required experimental conditions being fulfilled, the transesterification reaction occurred during the compounding process, thus favoring an extra reduction of the PHB molar mass.

Thermal and crystallization behaviour

DSC analyses revealed that introducing hemp fibres drove to two concomitant effects on the crystallization behaviour of the matrix polymer (Table 1). First, a plasticizing effect was noticed by a reduced glass transition (Tg) for PHB-H in comparison with PHB. This Tg reduction was limited (-4°C was the largest Tg shift) and attributed to the production of PHB oligomers during processing. Indeed, the already reported strong diminution of mass-average molar mass indicated a shift of the molar mass distribution towards lower values and the apparition of PHB oligomers which acted as plasticizers of the PHB matrix. The second effect induced by the introduction of hemp fibres was a strong nucleating effect. Crystallinities of the unfilled extruded matrices were rather low (table1) while the biocomposites exhibited much higher Xc values, around 40%. An another clear evidence of the nucleation effect is the Tc shift towards high temperatures (table 1). Besides, DSC cooling curves of the unfilled materials hardly exhibited crystallization regions, between 50°C and 0°C in comparison with the biocomposites which presented clear crystallization peaks around 75°C. On heating DSC curves, unfilled materials exhibited cold crystallization peaks, which disappeared totally for the fibres-filled materials. This nucleating effect was already noticed visually during the biocomposites elaboration. At the extruder die, the melt material exhibited some rigidity whereas the unfilled material flew out of the extruder as a liquid. When the compatibilizer was used, the previously detailed plasticizing effect was slightly compensated by a reduction of the macromolecular mobility induced by improved fibre/matrix interactions and/or a better fibre dispersion (Table 1).

Concerning the thermal stability of the materials, the effect of the process was clear, as revealed by the degradation onset (T-5%) provided in Table 1. The raw PHB pellets exhibited a degradation onset of 279°C which was slightly reduced down to 274°C after one extra extrusion step (high shear process). The drop was even higher for the low shear process (T-5% = 265 °C).

This sensitization provides from the extrusion step which led to random chain scissions [START_REF] Nguyen | Thermal degradation of poly(3hydroxyalkanoates): Preparation of well-defined oligomers[END_REF] and creation of crotonate-ending PHB oligomers and crotonic acid [START_REF] Morikawa | PYROLYSIS OF BACTERIAL POLYALKANOATES[END_REF]. Such reactions, confirmed by Mw measurements, contributed to reduce the thermal stability of the material.

However, the difference observed between the two extruded polymers may be linked to their crystalline content (16.9% for the high-shear extruded and 9.6% for the low-shear one). Indeed, in the highly ordered state exhibited by crystalline phases, it is less possible for macromolecules to move one relatively to another as additional forces must be overcome in the transformation to the unordered fluid state [START_REF] Beyler | Thermal Decomposition of Polymers[END_REF]. This energy difference was maintained after the polymer melting and appeared as a difference among degradation onsets. For the fibrescontaining materials, the T-5% reduction was higher than the unfilled extruded PHB. Such results confirmed the fibre-induced sensitization previously discussed when detailing Mw results, the hemp fibres favoring the PHB hydrolysis and intensifying the internal warming of the matrix by increasing the melt-shear viscosity.

Mechanical properties

Given the concomitant reductions of both Mw and thermal performances of the biocomposites when a compatibilizer was introduced and/or when high shear rates were applied during processing, the mechanical performances of the so-prepared materials were expected to be negatively impacted by these two processing parameters.

The effects induced by the processing conditions (screw speed and profile) were rather weak regarding the Young's modulus. Indeed, the stiffnesses of the various biocomposites prepared without compatibilizer (PHB-H) ranged between 304 and 336 MPa, without significant differences (figure 3). However, the processing conditions had a much clearer impact onto the ultimate properties and notably onto stress at break, which frankly decreased when the screw speed increased, from 33.9 MPa for PHB-H LS250 down to 29.5 MPa for PHB-H LS750. This drop was even higher for the material processed with the high-shear profile. The stress at break was reduced by 49% when the screw speed increased from 250 rpm to 750 rpm for PHB-H under high shear. Concomitantly the ductility of the materials was significantly reduced. Such a trend can be explained when the processing conditions became more severe antagonist phenomena occurred on fibre dispersion (positive), possible degradation of fibres (negative)

and degradation of polymers (negative).

The introduction of compatibilizer significantly increased the materials' stiffness, and this loadtransfer was more noticeable for the materials that stayed in the melt state for a longer time. For instance, the Young's modulus increased by 19%, 50% and 40% respectively when compatibilizer was added to PHB-H LS250, PHB-H LS500 and PHB-H LS750 respectively.

The higher residence time induced by the low-shear process improved the transfer of the compatibilizer towards the fibre/matrix interface and finally drove to better compatibilization mechanisms, as observed when the materials underwent short strain levels. For higher strain levels, the addition of compatibilizer had fewer effect. Indeed, the stress at break was only slightly impacted, thus indicating that the fibre/matrix interfacial adhesion could still be improved.

Contrary to the clear trends observed for the low-shear processed materials, where coupling the fibres and the matrix was an efficient way to tune the mechanical performances, the results reported for the high-shear processed materials were unpredictable. This absence of correlation was attributed to the severe degradation mechanisms induced by the process, which deleted the influence of the compatibilizer.

Water sensitivity

In addition to the mechanical performances, an extra aspect of the elaborated biocomposites was investigated, being a key property for the targeted packaging application. Transfer properties have been assessed by evaluating the water vapour permeation of the biocomposites (figure 4) and by modelling the of the materials, the water vapour sorption parameters were obtained (table 2). The moisture content adsorbed by the materials at equilibrium was around 2 and 3% for all the composites, whatever the processing conditions and the composition. Similar results were provided by Stubar et al. [START_REF] Srubar | Modeling the kinetics of water transport and hydroexpansion in a lignocellulose-reinforced bacterial copolyester[END_REF] who reported that compatibilizing a PHB matrix with lignocellulosic fibres slowed moisture transport into the composites without modifying the equilibrium moisture content. The present equilibrium was linked to the hemp fibres (20 wt% content) which were much more sensitive to water vapour than the PHB matrix, which was reported to sorb at equilibrium less than 0.4 wt% moisture in similar conditions [START_REF] Miguel | Water transport properties in poly(3-hydroxybutyrate) and poly(3-hydroxybutyrate-co-3-hydroxyvalerate) biopolymers[END_REF].

Moreover Christian and Billington [START_REF] Srubar | Modeling the kinetics of water transport and hydroexpansion in a lignocellulose-reinforced bacterial copolyester[END_REF] reported moisture contents at equilibrium for PHB/hemp biocomposites of 6.8 to 8.1% with 40 wt% fibre content, which is consistent with the values of the present work. In addition to the fibre content, the matrix degradation state and the presence of compatibilizer are considered as secondary parameters influencing the final moisture content. Despite the similar equilibrium observed, the kinetics observed to reach it, assessed by the water vapour diffusivity (D), highly depended on the process used to elaborate the material. And similarly to what has been observed for the mechanical properties, the water vapour sorption highly depended on the screw profile used for the elaboration. Notably, when the low shear profile was used, the influences of the screw speed and the composition were clear. Indeed, by improving the dispersion (through higher screw speed and the recourse to compatibilization) and the interphase quality (by adding a compatibilizer), the fibres were less percolating and better coated, which limited he diffusion of water vapour among the material. This reduction of the D value observed when a compatibilizer was introduced into the composition (table 2) was higher for the materials elaborated at low screw speed, i.e. with higher residence time enabling better compatibilization processes. For the composites elaborated under low shear, the D value reduced by 66% at 250 rpm, 40% at 500 rpm and 17% at 750 rpm when a compatibilizer was introduced. For the composites elaborated under high shear, the water vapour diffusions were much than when the low shear profile was used during the elaboration process. The whole resulting D values obtained by the various processing routes ranged from 1.4 to 11.6 10 -13 m²s -1 enabling the application as packaging materials to various food products.

The pure PHB material degraded faster than the reference (cellulose). Indeed, after a 27 days incubation, PHB exhibited around 80% of biodegradation while the reference underwent only 60% of biodegradation. Moreover, the addition of fibres did not impact negatively this high biodegradability, as indicated by the slightly higher biodegradation level exhibited by PHB-H after 92 incubation days (figure 5). This result is consistent with the literature [START_REF] Muniyasamy | Biodegradability and Compostability of Lignocellulosic Based Composite Materials[END_REF] which reveals that the biodegradation of biocomposites containing lignocellulosic fibres is mainly driven by the ability of the matrix to biodegrade. As far as polyhydroxylkanoates are concerned, the introduction of natural fibres was reported to improve the biodegradability of the composite in comparison with the pure matrix [START_REF] Gunning | Mechanical and biodegradation performance of short natural fibre polyhydroxybutyrate composites[END_REF] by creating additional pathways for moisture, enzymatic, and microbial ingress leading to fibre swelling, increased damage at the fibrematrix interface, and cracking, further accelerating degradation [START_REF] Ryan | Biocomposite Fiber-Matrix Treatments that Enhance In-Service Performance Can Also Accelerate End-of-Life Fragmentation and Anaerobic Biodegradation to Methane[END_REF].

The introduction of compatibilizer drove to the highest biodegradation pattern (figure 5), even if not statistically different from the two other PHB-based materials. Introducing fibres and compatibilizer into the PHB matrix drove to the most severe Mw reduction and lead to the highest biodegradation level. This was highly consistent with the results provided by Hong et al. who reported that the presence of PHB oligomers increased the biodegradation rate of PHB [START_REF] Hong | Thermal properties and applications of low molecular weight polyhydroxybutyrate[END_REF]. All in all, whatever the composition and processing conditions, the biodegradation of the PHB-based biocomposites was revealed to be fast and high.

Conclusion

Polyhyroxyalkanoates/hemp fibres biocomposites have been successfully prepared by reactive extrusion with various processing conditions, i.e variable shear rates (screw profile and speed) applied during the extrusion step and variable formulation (possible use of a compatibilizer).

Structural analyses revealed homogeneous fibres dispersion states and the development of an interphase when a compatibilizer was introduced. Introducing fibres drove to two main effects concerning the processed matrix. First, the crystallization kinetics of the polymer strongly improved and made it unnecessary the usual recourse to nucleating agents. Second, the polymer matrix underwent some thermal sensitization. Indeed, in the case of severe processing conditions, the fibre dispersion state was improved but severe degradation reactions occurred at the same time, then hindering the possible improvement provided by the compatibilizer. For the materials processed under low-shear rate, mechanical performances were preserved and even improved when the compatibilizer was added. All in all, the whole materials prepared under various processing routes presented a wide range of transfer properties and remained quickly and fully biodegradable. The original compatibilization route proposed here was confirmed and offers new opportunities to design biocomposites with tuned perfomances, reduced cost and low environmental impact.

Fig. 2 .

 2 Fig. 2. SEM pictures of fibres composites elaborated under extreme shears (a: PHB-H HS750; b: PHB-H LS250) and with the highest residence time (c: PHB-H HS250; d: PHB-C-H HS250)

Figure 3 .

 3 Figure 3. Tensile properties of PHB-based

Figure 5 .

 5 Figure 5. Biodegradation pattern of PHB-based materials in compost conditions

Table 1 .

 1 Thermal

		(Tg: glass transition; Tm: melting temperature; Tc: crystallization
	temperature; T-5%: degradation onset) and molecular (Mw: mass-average molar mass; Xc:
		crystallinity) properties of PHB-based materials.
	Screw	Screw speed	Sample	Mw	Tg (°C)	Tm(°C)	Xc(%)	Tc(°C) T-5% (°C)
	profile			(kg/mol)
	-	-	PHB as received	150.7	4	174	3.6	ind.	280
		250 rpm	PHB	130.7	3	171	9.6	0-50°C	265
		250 rpm	PHB-H	122.2	0	171	41.8	78	258
	Low Shear	500 rpm	PHB-H	90.0	1	170	37.2	76	258
	Profile	750 rpm	PHB-H	63.7	-1	167	37.8	76	254
		250 rpm	PHB-C-H	106.5	1	171	40.7	76	258
		500 rpm	PHB-C-H	80.6	3	170	40.0	74	259
		750 rpm	PHB-C-H	69.2	2	171	41.0	77	259
		250 rpm	PHB	115.6	3	171	16.9	0-50°C	274
		250 rpm	PHB-H	77.2	3	172	40.0	76	261
	High Shear	500 rpm	PHB-H	59.9	-1	169	40.9	75	264
	Profile	750 rpm	PHB-H	47.7	2	173	39.7	70	262
		250 rpm	PHB-C-H	74.9	3	168	39.6	76	259
		500 rpm	PHB-C-H	52.9	2	168	39.5	75	258
		750 rpm	PHB-C-H	43.4	1	165	40.5	74	257

Table 2 .

 2 Water vapour sorption fitted parameters obtained at 25°C

			D x 10 13 (m²s -1 )	moisture uptake at equilibrium (percentage of initial weight)
			PHB-H	PHB-C-H	PHB-H	PHB-C-H
		250 rpm	4,0	1,4	2,7	2,9
	Low shear rate	500 rpm	3,8	2,3	2,9	2,2
		750 rpm	3,3	2,8	3,5	2,0
		250 rpm	3,9	3,7	3,1	2,8
	High shear rate	500 rpm	11,3	4,5	2,6	2,9
		750 rpm	11,6	5,3	2,2	3,1

Acknowledgements

The authors thank Carnot Institutes Carnot 3BCAR, Chimie Balard and ICEE for funding the present MACOBIO project under grant agreement number XXXXX.