Coste Mawélé Loudy

Sirikorn Chasvised

Clara Paybou

Cecile Courreges

Joachim Allouche

Hervé Martinez

Antoine Bousquet

Laurent Billon

Cécile Courrèges

Revealing surface functionalities via microwave for the para-fluoro-Thiol click reaction

Keywords: para-fluoro-thiol click reaction, surface segregation, diblock copolymer, microwave, gold nanoparticles

Introduction

The control of surface composition and properties, such as wettability, adhesion, biocompatibility, friction and wear, is crucial to develop applications in electronics, water-treatment, energy and biomedical industries. [START_REF] Nemani | Surface Modification of Polymers: Methods and Applications[END_REF][START_REF] Ikada | Surface modification of polymers for medical applications[END_REF][START_REF] Behl | Towards plastic electronics: Patterning semiconducting polymers by nanoimprint lithography[END_REF][START_REF] Goddard | Polymer surface modification for the attachment of bioactive compounds[END_REF][START_REF] Saqib | Membrane fouling and modification using surface treatment and layer-by-layer assembly of polyelectrolytes: State-of-the-art review[END_REF].

Efficient "click chemistry" reactions have been developed for 30 years to graft surfaces with molecules, macromolecules, metal or inorganic nanoparticles. [START_REF] Nandivada | Click chemistry: Versatility and control in the hands of materials scientists[END_REF] Among them, Huisgen cycloaddition [START_REF] Gehan | Thermo-induced electromagnetic coupling in gold/polymer hybrid plasmonic structures probed by surface-enhanced raman scattering[END_REF][START_REF] Díaz Arado | On-surface azide-alkyne cycloaddition on Au(111)[END_REF], thiol-ene reaction [START_REF] Shafagh | E-Beam Nanostructuring and Direct Click Biofunctionalization of Thiol-Ene Resist[END_REF], or Diels-Alder cycloadditions [START_REF] Li | Healable capacitive touch screen sensors based on transparent composite electrodes comprising silver nanowires and a furan/maleimide diels-Alder cycloaddition polymer[END_REF] are the most used. Recently, a new reaction has been investigated by the community: the nucleophilic aromatic substitution of para-fluorine atom of pentafluorophenyl moeities by a variety of nucleophiles, such as thiols, amines and alcohols. [START_REF] Delaittre | The para-fluoro-thiol reaction as an efficient tool in polymer chemistry[END_REF] The main limitation of these "click" methodologies is that the substrate must present surface reactive functions for the grafting to happen. Therefore, it is limited to a small range of materials.

Polymers surface modification is a powerful tool in order to allow cheap inert materials to gain reactive surface functionalities. Surface segregation, a spontaneous phenomenon based on thermodynamics, is a "soft" way of modifying the external properties of a materials blend. It is directed by the equilibrium between the decrease of surface tension and the energy cost of segregation from the bulk, as governed by Gibbs adsorption isotherm. [START_REF] Koberstein | Molecular design of functional polymer surfaces[END_REF][START_REF] Bousquet | Nanostructured interfaces by surface segregation of block copolymers[END_REF] Therefore, in a polymer blend, a "surface field" drives the migration of the material with the lowest surface tension to the air interface. As a consequence, the phenomenon leads to significant modifications between the surface and the bulk composition and properties. [START_REF] Genzer | Recent developments in superhydrophobic surfaces and their relevance to marine fouling: A review[END_REF][START_REF] Liu | Surface immobilization of polymer brushes onto porous poly(vinylidene fluoride) membrane by electron beam to improve the hydrophilicity and fouling resistance[END_REF][START_REF] Koberstein | Creating Smart Polymer Surfaces with Selective Adhesion Properties[END_REF] Surface segregation has been demonstrated in several polymeric systems [START_REF] Bousquet | Design of stimuliresponsive surfaces prepared by surface segregation of polypeptide-b-polystyrene diblock copolymers[END_REF][START_REF] Jalbert | End group effects on surface properties of polymers: Semiempirical calculations and comparison to experimental surface tensions for α,ω-functional poly(dimethylsiloxanes)[END_REF][START_REF] Hardman | Surface modification of polyethylene with multi-end-functional polyethylene additives[END_REF][START_REF] Bergius | Synthesis and characterisation of end-functionalised poly(N-vinylpyrrolidone) additives by reversible addition-fragmentation transfer polymerisation[END_REF][START_REF] Su | Adsorption of end-functionalized poly(ethylene oxide)s to the poly(ethylene oxide)-air interface[END_REF], either in flat [START_REF] Bousquet | Control of the surface properties in polymer blends[END_REF] or spherical [START_REF] Bousquet | Functional pH-responsive polystyrene microspheres prepared by surface segregation of diblock copolymers[END_REF] material and in dry (vacuum) or humid environment [START_REF] Bousquet | Structured assemblies of ferromagnetic particles through covalent immobilization on functionalized polymer surfaces obtained by surface segregation[END_REF].

Even if surface segregation is a spontaneous phenomenon, the thermic properties of the blends components have a huge influence on the process kinetics. Blends of polystyrene (PS) and end-functionalized polystyrene, which glass transition temperatures (Tg) are around 100°C, would reach thermal equilibrium in the time scale of weeks at room temperature. A thermal annealing above Tg is required to reduce the segregation time to half a day. [START_REF] Elman | A neutron reflectivity investigation of surface and interface segregation of polymer functional end groups[END_REF] Perhaps the most reported system is the blend of an end-fluorinated polystyrene additive (PS-F) in a PS matrix. [START_REF] Elman | A neutron reflectivity investigation of surface and interface segregation of polymer functional end groups[END_REF][START_REF] Affrossman | Surface segregation in blends of polystyrene and perfluorohexane double end capped polystyrene studied by static SIMS, ISS, and XPS[END_REF][START_REF] Affrossman | Surface Segregation in Blends of Hydrogenous Polystyrene and Perfluorohexane End-Capped Deuterated Polystyrene, Studied by SSIMS and XPS[END_REF][START_REF] Mason | Surface energy and surface composition of end-fluorinated polystyrene[END_REF][START_REF] Xie | Effect of low surface energy chain ends on the glass transition temperature of polymer thin films[END_REF] In the publications, the authors showed a strong fluorine surface enrichment and very hydrophobic films were produced. Indeed, the material surface energy is reduced by the segregation of fluorine atoms having a lower surface tension than the styrene repetitive units. In 1994, Affrossman et al. used PS-F/PS blend, they showed that an initial weight composition of 15/85, after a thermal annealing at 130°C for 24 hours, could lead to an enrichment in PS-F of 62 w%. Elman and coworkers proved by neutron reflectivity the segregation of deuterated PS-F in a hydrogenated polystyrene matrix. [START_REF] Elman | A neutron reflectivity investigation of surface and interface segregation of polymer functional end groups[END_REF] Other studies were published [START_REF] Affrossman | Surface segregation in blends of polystyrene and perfluorohexane double end capped polystyrene studied by static SIMS, ISS, and XPS[END_REF][START_REF] Mason | Surface energy and surface composition of end-fluorinated polystyrene[END_REF][START_REF] Xie | Effect of low surface energy chain ends on the glass transition temperature of polymer thin films[END_REF], confirming the segregation of fluorinated polymers after annealing above Tg (from 110°C to 165°C) in the time scale of days (from 12h to 72 hrs).

Nowadays, energy is a vital challenge for mankind and many research studies are devoted to reduce its consumption. In this report, a rapid method is described to perform the fluorine surface enrichment in sixty seconds, thus dividing the annealing time by 1440 (1 day/1minute). Microwave-induced annealing is used to allow the surface segregation of a fluorinated additive in a polystyrene matrix. Recently, high ordered nano-phase segregation of block copolymers (BCP) were obtained by microwave annealing. A few minutes of irradiation were sufficient to organize polystyrene or poly(methyl methacrylate) based copolymer in lamellae, cylinders or spheres. [START_REF] Zhang | Fast Assembly of Ordered Block Copolymer Nanostructures through Microwave Annealing[END_REF][START_REF] Mokarian-Tabari | Study of the Kinetics and Mechanism of Rapid Self-Assembly in Block Copolymer Thin Films during Solvo-Microwave Annealing[END_REF][START_REF] Toolan | Selective molecular annealing: in situ small angle X-ray scattering study of microwave-assisted annealing of block copolymers[END_REF][START_REF] Borah | Swift nanopattern formation of PS-b -PMMA and PS-b -PDMS block copolymer films using a microwave assisted technique[END_REF] Buriak et al. have proved that highly resistant silicon substrates (1-35 Ohms, doped by boron) can reach 200°C in a few seconds and serve as a hot pan to induce the nanosegregation of BCP. [START_REF] Jin | Deconvoluting the Mechanism of Microwave Annealing of Block Copolymer Thin Films[END_REF][START_REF] Benoot | Hierarchically organized honeycomb films through block copolymer directed self-assembly in "breath figure" templating and soft microwavetriggered annealing[END_REF] On the contrary, when glass substrates were used, no morphological modification was detected to a significant extent.

In this study, we used the ultra-fast annealing induced by the microwave irradiation to promote the surface segregation of a diblock copolymer, a polystyrene-block-poly(pentafluorostyrene) (PS-b-PFS) at the air/polymer interface (Scheme 1). The BCP additive, has been engineered to present a PS block compatible with the polystyrene matrix and a PFS block bearing 5 surface active fluorine atoms per repetitive monomer units, which can undergo the para-fluoro-thiol click reaction. To the best of our knowledge, nothing has been reported on the surface segregation of pentafluorostyrene-based copolymers. Contact angle (CA) measurement, X-ray photoelectron spectroscopy (XPS) and Time-of-Flight Secondary Ion Mass Spectrometry (ToF-SIMS) analyses were carried out to demonstrate that a 60 seconds annealing is enough to enrich the surface of the blends with the BCP additive. Finally, the surface functionalization with gold nanoparticles GNPs was performed in two steps. Indeed, the successful nucleophilic substitution of the para fluorine atom with the thiol function of cysteine allows the immobilization of anchoring groups for GNPs surface docking. This proves the efficiency of surface segregation to create a functional platform from an inert substrate in a very short period of time and low energy consuming.

Scheme 1. Overview of the system studied in this report.

Results and Discussion

PS-b-PFS copolymer synthesis

The polystyrene-block-poly(pentafluorostyrene) (PS-b-PFS) was synthesized by Nitroxide Mediated Polymerization (NMP), a controlled radical polymerization based on the reversible trap of growing chains by nitroxide molecules (see in supporting information Scheme SI1). [START_REF] Hawker | New polymer synthesis by nitroxide mediated living radical polymerizations[END_REF] The first step is the polymerization of styrene using the BlockBuilder ® MA. Size exclusion chromatography was used to measure the molar mass of the polymer, Mn = 12 000 g.mol -1 (using conventional calibration with polystyrene sample), the average degree of polymerization DPn = 115 and its dispersity, Ð = 1.27. After purification, the PS was used as macroinitiator to polymerize pentafluorostyrene and access the block copolymer additive. To ensure a sufficient mixing with the PS matrix and a high amount of fluorine moieties, we targeted a copolymer with a balanced composition, presenting the two blocks length equal. 1 H NMR was used to evaluate the ratio between PS and PFS molecular units and a DPn of 132 was calculated for the PFS block (Figure SI1). SEC analysis of the PS-b-PFS revealed a shift in the molar mass compared to the PS macroinitiator (Figure SI2), meaning the efficient chain extension of the PS first block with a PFS block. The copolymer dispersity Ð and molar mass Mn were calculated to be 1.15 and 38 000 g.mol -1 respectively. Literature has shown that the segregation was best occurring when the additive had a smaller molar mass than the matrix, therefore we followed this requirement (PS matrix molar mass is 300,000 g.mol -1 ). [START_REF] Bousquet | Control of the surface properties in polymer blends[END_REF][START_REF] Mason | Surface energy and surface composition of end-fluorinated polystyrene[END_REF] Differential Scanning Calorimetry was performed and only one glass transition temperature was detected at 107°C (Figure SI3) corresponding to the literature values of both PS and PFS homologue blocks. [START_REF] Fu | Nanoporous ultra-low-dielectric-constant fluoropolymer films via selective UV decomposition of poly(pentafluorostyrene)-block-poly(methyl methacrylate) copolymers prepared using atom transfer radical polymerization[END_REF] 2.2. Surface segregation 2.2.1. Determination of suitable annealing conditions. Films (thickness around 300 nm) were prepared onto silicon wafers by spin-coating from toluene solutions (4%) of a polymer blend composed of a PS matrix (Mn = 300 000 g.mol -1 , Ð = 1.2) and the PS-b-PFS additive with a mass ratio 90/10. This first ratio was chosen to keep the additive content low and based on literature, which reports efficient segregation and surface properties evolution at 10% of additive. [START_REF] Bousquet | Design of stimuliresponsive surfaces prepared by surface segregation of polypeptide-b-polystyrene diblock copolymers[END_REF][START_REF] Bousquet | Control of the surface properties in polymer blends[END_REF][START_REF] Affrossman | Surface segregation in blends of polystyrene and perfluorohexane double end capped polystyrene studied by static SIMS, ISS, and XPS[END_REF][START_REF] Affrossman | Surface Segregation in Blends of Hydrogenous Polystyrene and Perfluorohexane End-Capped Deuterated Polystyrene, Studied by SSIMS and XPS[END_REF] Such thick films were employed for two main reasons: 1) to avoid dewetting problems that appear in thin fluorine polymer films and 2) to separate the substrate/polymer and the polymer/air interfaces in order to reduce the number of competing interactions that can alter the surface segregation phenomenon. [START_REF] Bousquet | Nanostructured interfaces by surface segregation of block copolymers[END_REF] Then, the films were introduced in a pressure resistant glass vial with air atmosphere (Figure SI4) and placed in the microwave oven. The optimal annealing conditions were determined by applying different irradiation powers during different times. XPS was the technique of choice to investigate the presence and the amount of fluorine atoms at the surface of the polymer films. Figure 1 presents the Carbon spectra of the non-annealed film and films treated with microwave at various powers (10, 20, 30 and 40 Watts) during 60 seconds. Four major components are clearly observed: C=C from polystyrene rings (sp2, 284.5 eV), C-C from vinylic bonds of polystyrene (sp3, 285 eV), C-F from polypentafluorostyrene rings (288.5 eV) and the remaining 3 carbons of the pentafluorostyrene units 286.2 eV). [START_REF] Fu | Nanoporous ultra-low-dielectric-constant fluoropolymer films via selective UV decomposition of poly(pentafluorostyrene)-block-poly(methyl methacrylate) copolymers prepared using atom transfer radical polymerization[END_REF][START_REF] Han | Pulsed plasma polymerization of an aromatic perfluorocarbon monomer: Formation of low dielectric constant, high thermal stability films[END_REF] The π-π* shake-up transitions of both polystyrene and polypentafluorostyrene are also observed at As reported in Table 1, the intensity of fluorine increases along with the annealing power. A very significant increase is observed between the non-annealed sample (F: 3.8 %) and the sample annealed at 10 W, the minimum annealing power (F: 12.3 %). When the annealing power is increased from 10 W to 30 W, the intensity of the fluorine peak raises significantly to F: 26.8 % (Figure 1b-d). When the annealing power is increased beyond 30 W, no further rise of the fluorine is observed. Indeed, the amount of fluorine detected in the sample annealed at 40 W (F: 28.5 %, Figure 1e) is close to the one in the sample annealed at 30 W (Table 1). Also, when the samples are annealed with different power conditions, from 10 W to 40 W, no additional components are observed by XPS analysis. Only the intensities of the same former components change or increase. This suggests that there is no chemical degradation of the sample under those various conditions. In order to save energy, 30 W was set as the optimum power to use in this study and the surface composition was followed during the annealing time from 0 to 210 seconds. Table 2 reports the carbon and fluorine surface content as measured by XPS (carbon spectra in Figure SI5). From 0 to 60 seconds microwave treatment, the fluorine surface content increases from 3.8 to 26.8%, and then stays stable to 25.9% for 90 s. Finally, when the annealing is longer, 120 seconds, the fluorine content slightly decreases to 21.1%. Although we could not observe a variation in the peaks shape in XPS, this decrease could come from a slight thermal degradation of the labile para-fluorine atoms at the interface with air. [START_REF] Benoot | Hierarchically organized honeycomb films through block copolymer directed self-assembly in "breath figure" templating and soft microwavetriggered annealing[END_REF] This evolution in time corresponds to an increase of the temperature in the microwave vials. This leads consecutively to a more efficient surface segregation provided by a mobility rise and afterwards to a saturation at the surface. From these preliminaries experiments, a 60 s microwave treatment at 30 W was set for the rest of the study.

Variation of copolymer content in the blend

The blend composition was varied from 0 to 100 % of diblock copolymer to evaluate its influence on the surface wettability. Surface segregation was promoted via the microwave annealing and measurement of the contact angle with different liquids was performed to calculate the impact of the surface segregation on the surface tension values. In Figure 2a, the water contact angle is plotted against the copolymer content for the selected microwave treatment and, for comparison, the values of the non-annealed film are reported. First, the water contact angle raised when the copolymer content in the blend was increased, due to the augmentation of low surface energy fluorine atoms in the film. It is worth noting that the difference between the contact angles (CA) of a non-annealed pure PS film (90°) and the one of a pure PS-b-PFS film (101°C) is low. Nevertheless, after the microwave annealing, there is a clear increase in the water CA value for each composition of the blend except for the pure copolymer film. This is also in agreement with the surface segregation of the fluorinated segments observed by XPS. In the pure copolymer sample, the fluorine surface content before annealing must be sufficiently high to provide the surface with hydrophobic properties. The evolution of the contact angle with a non-polar solvent such as diiodomethane (Figure 2b) is more affected by the blend composition. Indeed, the difference between the pure polystyrene and the copolymer surface is 37° (respectively 29° and 66° after annealing). The same behavior has been observed between polyethylene and poly(tetrafluoroethylene) in which contact angle with diodomethane varied from 52 to 88°C when water contact angle changed only from 94 to 108°. [START_REF] Owens | Estimation of the surface free energy of polymers[END_REF] It can also be observed in Figure 2b that for every blend ratio above 5 % in additive, an increase of 20° is measured after the treatment of the film at 30 W during 60 seconds compared to the non-annealed sample. Oleophobic surfaces have largely been developed with polymer substrates and a common strategy is to functionalize micro-patterned surfaces with fluorine molecules. [START_REF] Yong | Superoleophobic surfaces[END_REF] Surface tension of the different polymer films was calculated by the OWRK method from the contact angle of three solvents, Water, Diiodomethane and Ethylene glycol (see experimental part and Table SI1 andSI2 In order to understand these changes of wettability, the surface composition of these blends was analyzed by XPS (carbon spectra in Figure SI6 and surface composition in Table SI3). Figure 3 presents the overlay of the surface fluorine content of polymer film before and after annealing, with the theoretical content in the blend calculated from the matrix/additive ratio (calculation described in SI). The first observation is that the value of the fluorine surface content just after spin-coating is higher that the theoretical one. This means that surface segregation happened even during the evaporation process. [START_REF] Chen | Solvent effects on polymer surface structure[END_REF] Indeed, the solvent allows chains to reorganize in order to minimize surface tension. This effect has already been observed by Affrossman et al. when they reported the study of a blend composed of a polystyrene matrix with a fluorine end-functional polystyrene. [START_REF] Affrossman | Surface Segregation in Blends of Hydrogenous Polystyrene and Perfluorohexane End-Capped Deuterated Polystyrene, Studied by SSIMS and XPS[END_REF] Secondly, for all the blend compositions, the fluorine surface content increases after the microwave annealing promoting the migration of the copolymer. For example, when a blend of 5 w% in copolymer is used, the fluorine surface content is 2.1 % before annealing, and reaches 14 % after the 60 seconds treatment. This value corresponds to a surface enrichment as high as 55 w% in block copolymer. From a blend composed of 10 % of copolymer, a fluorine surface content similar to the one of a pure copolymer film was reached after annealing (around 25 %).

Finally, the increase of the fluorine content for the pure PS-b-PFS film compared to the theory means that a reorganization in the upper layer occurs and leads to the surface orientation of the PFS block to the air.

Reversible segregation upon annealing in humid environment

Tanaka and Koberstein have shown in two different studies that immersing a polymer blend in a polar environment (water or ethylene glycol) could induce the adsorption of the more hydrophilic component at the surface. [START_REF] Koberstein | Molecular design of functional polymer surfaces[END_REF][START_REF] Tanaka | Surface segregation of chain ends in α,ωfluoroalkyl-terminated polystyrenes films[END_REF] Using a polystyrene terminated by a fluorinated group, they proved the surface depletion of fluorine atoms after an annealing in saturated water vapor at 55 °C during 48 hours, resulting in the increase of the surface hydrophilicity. Indeed, the styrene unit being less hydrophobic than the fluorinated group, it migrated at the water/polymer interface. It has to be underlined that surface reorganization occurred in this case even in the glassy state. Following this finding, a sample composed of 10 % of diblock was first subject to treatment in dry atmosphere at 30 W during 60 s and analyzed by XPS to monitor the evolution of the surface composition.

The fluorine surface content was around 30 % (see carbon spectra in Figure SI7 and surface composition in Table SI4). Then 0.5 mL of water was introduced at the bottom of the microwave vials, without changing the position of the samples (and the water does not touch the sample). Another annealing at 30W during 60 seconds was applied and some water vapor was observed in the vial at the end of the treatment. The fluorine surface content detected by XPS then decreased to 11%. The amount of fluorine for the sample annealed with water was still higher than before dry annealing (2.8 %) but lower than after the annealing in dry atmosphere (30 %). This strengthens previous findings in the literature in which research teams showed that annealing in water atmosphere could decrease the fluorine surface content of polystyrene blends. [START_REF] Koberstein | Molecular design of functional polymer surfaces[END_REF][START_REF] Tanaka | Surface segregation of chain ends in α,ωfluoroalkyl-terminated polystyrenes films[END_REF][START_REF] Wong | Surface dynamics of polymer glasses: Sub-T g surface reorganization in end-functional polymers[END_REF] Although the fluorine surface content didn't decrease to 0% after 60 seconds at 30 W, an appropriate annealing could lead to pure polystyrene surface. The objective of this study being surface functionalization from the fluorostyrene moieties, we did not further investigate this point.

Fluorine Depth Profile

In order to obtain more informations on the in-depth spatial distribution of fluorine within the copolymer film depending on the annealing conditions, ToF-SIMS depth profiles experiments (series of 30 cycles "analysis/sputtering" with 10 sec of etching per cycle) were performed on three different samples: a) the nonannealed film, b) the one after the microwave annealing in dry atmosphere (30W 60s) and c) the film after two consecutive annealings, one in dry atmosphere followed by one in water vapor (2 times (30W, 60s)). Figure 4 presents the concentration depth-profile of C2 -(in blue, representing the PS polymer matrix) and F -(in green, representing the PFS block of the BCP additive) secondary ions over 220 seconds etching time obtained in negative polarity for the samples a), b) and c). The signal intensities were normalized relative to the total ion counts and adjusted to allow a better comparison between the three systems. In all cases, the C2 -concentration increases with the etching while the F -one decreases. However, for the annealing in dry atmosphere, the F -signal decreases quickly at the beginning of the etching (the normalized intensity is equal to 0.07 after 5 cycles / 50 sec), while the F -signal intensity remains much higher through all the sputtering for the non-annealing sample (the normalized intensity is equal to 0.48 after 50 sec and close to 0.4 at the end of the etching). For the sample c) with two consecutive annealing (one in dry atmosphere and one in water vapor), the fluorine signal mainly decreases during the five first cycles (the normalized intensity is equal to 0.16 after 50 sec) but with a lower slope comparing to sample b). Afterwards the intensity remains stable between 70 sec and 140 sec and then slightly increases to 0.2 until the end of the sputtering. A 3D image can be reconstructed for each system from the related depth profiles where the signal intensities of the considered secondary ions C2 -and F -are plotted over the analyzed area (600µm . 600µm = x and y dimensions) versus the etching time (the z axis, 220s). For a better visibility, the z axis is over-dimensioned compared to the other axes. Each species has a 3D distribution over the analyzed volume with one specific color (blue for C2 -and green for F -). The final 3D map corresponds to the overlay of the two species 3D distributions, to which a transparency factor is applied so that the two colors can be seen (the light blue color corresponds to areas where both ions C2 -and F -are present). When a color (corresponding to one species) is not appearing anymore on the image, it means the intensity of the related peak on the mass spectrum is too low to be plotted. Note that the sputtered depth has not been determined here; references samples of each polymer with precise thickness should have been analyzed using the same etching conditions to determine the sputtering ion yield of each compound. The 3D image related to the annealing in dry atmosphere b) clearly shows that fluorine species, characteristic of the PFS block, are mainly located at the upper part of the sample, which confirms the enrichment of the surface blend by the BCP additive and the depletion of the inner layers (bulk).

For the non-annealed film a), even if the proportion of F -is higher at the top surface than in the inner part of the blend, fluorine species are observed all over the analyzed volume, which confirms that BCP additive is present everywhere in the blend before annealing. Regarding the sample c), fluorine species are mainly located at the surface of the blend but also over the entire analyzed volume, which reveals a fluorine migration from the top to the inner part of the blend induced by the second annealing in wet atmosphere. This preliminary experiment highlights the reversibility of the segregation process by changing the conditions of annealing. and studied its modification with thiols in water. [START_REF] Turgut | The para-fluoro-thiol ligation in water[END_REF] Following their experimental procedure, we studied the surface functionalization of the polystyrene film. For that purpose, a polymer blend composed of 10 w% of PS-b-PFS was submitted to the microwave annealing to reveal the pentafluorostyrene moieties at the surface. Then, cysteine was grafted via thiol nucleophilic substitution of the para-fluorine atoms (Figure 5). XPS analysis of the annealed film grafted with cysteine revealed the presence of the anchored molecule at the surface of the sample, with nitrogen and sulfur atoms detection. The amount of fluorine measured by XPS after the modification decreased significantly (17.1 %, Table SI5) as compared with the film before the cysteine grafting (29.8 %). This is mainly due to the nucleophilic substitution of the para-fluorine atom. However, if only one fluorine (in para position) out of five in the repetitive unit is substituted by cysteine, then 24 % out of the initial 30 % of fluorine must remain at the surface. The extra 7 % (from 24 to 17 %) can either come from the presence of additional chemical elements at the surface of the film (sulfur, nitrogen) that naturally decreases the atomic composition of all element, or from a possible slight reorganization of the surface during the grafting reaction occurring in water (at room temperature), leading to a decrease in the PSF surface content. Therefore, it was not possible to investigate precisely the amount of fluorine that reacted with cysteine.

After the immobilization of gold nanoparticles via the cysteine anchors, no changes were observed by XPS in the chemical environments of the various elements. Only the grafted GNPs were clearly detected with a significant atomic contribution of 1.1 % (Table SI5).

Figure 5: Gold nanoparticles grafting onto the pentafluorostyrene platform revealed by surface segregation Atomic force microscopy was also used to assess the changes of the surface morphology before and after microwave annealing but also after GNPs grafting. In the PS-b-PFS block copolymer, the PS volume fraction is 0.4 and the AFM analysis of the pure diblock showed a nano-phase segregation with a mixture of in-plane and out of plane PS cylinders in a PFS matrix (see Figure SI8a). Figure 6a shows the image of the polymer blend with 10% of diblock before microwave treatment. The surface is mainly covered by polystyrene (in yellow) with small copolymer domains (corresponding to black domains). After microwave annealing, the surface covered by the copolymer largely increased and 200 nm domains appeared in which an out-of-plane cylindrical nano-structure can be observed (Figure 6b). Around these large domains, the homopolystyrene matrix is pierced by smaller copolymers areas. Obviously, the PS matrix does not swell the PS domain of the diblock due to its high molar mass (≈300 000 g.mol -1 ) but there is a good compatibility between the macromolecules since no microphase segregation was observed. After the GNPs grafting, the films were imaged by AFM and SEM (Figure 6c and 6d respectively). With both techniques, a non-uniform gold pattern is observed, with a structure corresponding to the PS-b-PFS initial domains. Indeed, the PS phases being insensitive to nucleophilic substitution, the nanoparticles cannot be immobilized in these areas. It has to be underlined here, that the geometry of the grafting area (cylinders) is dependent of the diblock composition and therefore can be tuned by appropriate synthesis conditions. The average diameter of gold nanoparticles measured from AFM images (Figure 6-c) is 25 nm in good correlation with the UV-visible absorbance spectrum of the unbound particles showing a maximum at 523 nm (figure SI15).

Conclusion

In summary, we demonstrated the efficiency of a microwave annealing to promote the surface segregation of a fluorinated additive, the PS-b-PFS, in a PS matrix. In 60 seconds, at a power of 30 W, the block copolymer enriches the surface and increases the hydrophobicity and oleophobicity of the film, without degradation of the matrix material. A blend of 10 w% in additive can lead to a surface composed of more than 20 % of fluorine atoms. ToF-SIMS, used to follow the in-depth spatial distribution of fluorine within the film, clearly showed that the surface was enriched in copolymer compared to the bulk of the film. This surface segregation phenomenon is reversible. Indeed, when the same microwave annealing is performed under water vapor atmosphere, the low surface energy fluorine atoms hide in the bulk and a polystyrene surface is restored. Finally, it was proved that this time and energy reducing methodology is an efficient way to provide a functional platform for the immobilization of materials at the surface of, at the beginning, inert (PS) materials. Indeed, the PFS moieties can undergo nucleophilic substitution with thiol and have been used in this study to immobilize GNPs in the block copolymer domains. This methodology could be applied to a wide range of applications such as supported catalysis or bioadhesion.

METHODS

Experimental

Synthesis

PS-b-PFS diblock copolymer was synthesized in two steps using Nitroxide-Mediated Polymerization (NMP) as reported in supporting information (Scheme SI1). In the first step, styrene (120 mmol), the Blocbuilder® alkoxyamine (0.5 mmol) and the nitroxide radical (SG1 solution, 0.07 mmol, 15%) were added to a round bottom flask of 50 mL. The flask was sealed with a septum, put in an ice bath, degazed for fifteen minutes with nitrogen and immersed in an oil bath at 115 °C for 5h to reach 50 % of conversion (determined by 1 H NMR).

The resulting viscous mixture of polystyrene (PS) and the styrene were precipitated twice in methanol to remove the remaining monomer, filtered and dried at room temperature under vacuum. In the last step, 300 mg of the dried powder of PS (0.025 mmol) were dissolved in 5 mL of dimethylformamide (DMF) overnight. After solubilizing PS-macroinitiator, the 50 mL round bottom flask was put in an ice bath. Then pentafluorostyrene (PFS) (7.5 mmol) and nitroxide radical (SG1 solution, 0.003 mmol, 15%) were added, the flask was sealed with a septum and the mixture was degassed for 15 minutes with nitrogen and immersed in an oil bath at 115 °C. After 3h, the reaction was stopped and the resulting block copolymer was precipitated twice in methanol, filtered, and dried at room temperature under vacuum. The resulting block copolymer (PS-b-PFS) was analyzed by 1 H NMR and size exclusion chromatography (SEC).

The homopolystyrene matrix is a commercial product from PSS-Polymer with a molar mass of Mn = 300

Figure 1 .

 1 Figure 1. XPS carbon spectra of the a) non-annealed film and films treated with microwave at various powers:

Figure 2 .

 2 Figure 2. Evolution of the a) Water contact angle, b) Diiodomethane contact angle and c) surface tension of

Figure 3 .

 3 Figure 3. Comparison of the surface fluorine content determined by XPS before and after annealing for different

Figure 4 . 2 . 3 .

 423 Figure 4. TOF-SIMS depth-profile experiments over 220s etching time of C2 -(in blue) and F -(in green)

Figure 6 .

 6 Figure 6. Images of the surface of a blend composed of 10% PS-b-PFS a) before any modification (AFM), b)

Table 1 .

 1 XPS quantification and characterization of the film components in function of the power (annealing time = 60 s).

	Components	Position (eV)	FWHM (eV)	0 W a (%At.)	10 W (%At.)	20 W (%At.)	30 W (%At.)	40 W (%At.)
	C=C	284.5	0.9	66.1	46.4	45.2	18.7	15.2
	C-C	285	0.9	22.2	17.6	13.9	8.4	6.8
	C-CF	286.2	1	2.1	8.7	8.9	16.7	17.8
	C-F	288.5	0.9	3.2	11.9	14.9	25.6	28.8
	π-π*	292	1.2	2.6	3.1	2	3.8	2.9
	F-C	688.7	1.4	3.8	12.3	15.1	26.8	28.5

a Non-annealed sample

Table 2 .

 2 XPS

	Components	Position (eV)	FWHM (eV)	0 second (% At.)	30 s (% At.)	60 s (% At.)	90 s (% At.)	120 s (% At.)

quantification and characterization of the film components in function of the annealing time (power = 30 W). a Non-annealed sample

Acknowledgements

We acknowledge the government of Thailand and Doctoral School ED211 for PhD funding. ARKEMA is thanked for providing BlockBuider MA.

Surface attachment of gold nanoparticles

The attachment of gold nanoparticles at the surface of the polymer blend with 10 % of diblock after microwave treatment was done through a nucleophilic substitution of the pentafluorostyrene with thiol groups from the cysteine. A 4 % toluene solution of polymer blend was spun cast on a silicon wafer substrate and annealed at 30 W during 60 s to allow the migration of the fluorine atoms at the surface of the film. The substrate was then dipped into 25 mL of a buffered solution (pH 12: NaOH: 35 mg + Na2HPO4:115.4 mg) containing cysteine (0.01M) for 7 hours at room temperature to allow the grafting of cysteine via thiol nucleophilic substitution of the para-fluorine atoms. Afterwards the film was thoroughly washed several times in buffered solutions (pH 12) to remove unbound cysteine, and finally washed twice in water to remove and avoid the formation of salt crystals during the drying process. During all these steps, we didn't observe any degradation of delamination of the films.

The film was dried and analysis by XPS to observe the attachment of cysteine at the surface of the annealed film.

A decrease was also observed in the water contact angle value of the film, from 98° to 72° before and after cysteine grafting respectively. In the last step, the cysteine-grafted film was dipped again into 25 mL of a buffered solution containing cysteine (0.01 M). Next 0.5 mL of a 50 mM of HAuCl4 solution was added and mixed for 15 minutes before adding 2.5 mL of a NaBH4 solution (0.01 M). After 2 hours, the color of the mixture became red due to the formation of gold nanoparticles stabilized by the fixation of cysteine at the surface of gold. This fixation occurs not only in solution but also at the film surface where cysteine molecules grafted on the film bound the surface of gold during the formation of the nanoparticles. The reaction was left over night at room temperature to complete the fixation of gold nanoparticles at the surface of the film. The film was washed successively in a buffered solution (pH 12) and in water several times to remove unbound nanoparticles and avoid the formation of salt crystals.

Thin films preparation

Toluene solutions of polymer blend were prepared at 4w% and spin-coated onto boron doped silicon substrates (TED PELLA -prod. n°16010, Orientation: <100>, Resistance: 1-30 Ohms Type: P (Boron doped)) at 1000 rpm to reach a thickness around 300 nm (measured by ellipsometry).

Microwave annealing

A CEM microwave was used on fixed mode at several powers for a controlled time. Microwave heating films were cast on substrate with a surface of 0,7 x 0,7 cm². The set-up used to submit the wafers to the microwave irradiation is described in supporting information (SI1). For the experiments in humid atmosphere, 0.5 mL of water is added in the microwave tube at the bottom without any contact with the film.

Characterization Techniques

All details about the characterization techniques can be found in supporting information.

Associated content

Supporting Information. Experimental details and additional characterization data. This material is available free of charge via the Internet at http://pubs.acs.org.

Author information

Corresponding author: antoine.bousquet@univ-pau.fr


Maximin Varnier

Nicolas Sauvat

Laurent Ulmet

Cédric Montero

Frédéric Dubois

Joseph Gril

Influence of temperature in a mass transfer simulation: application to wood

Keywords: Heat and mass transfer, timber elements, temperature and moisture content coupling, analytical model

come

List of symbols

Latin symbols

A , B ,  :

Fitting parameters of water capacity, dimensionless For both economic and environmental reasons, the use of wood in construction is of considerable interest. Due to its biological origin, timber is sensitive to external conditions. This dependence, known as hygroscopicity, induces internal moisture content by virtue of outdoor variables, including air temperature and relative humidity. Variation of mechanical properties according to moisture content is well documented for a long time. This is roughly considered in timber structures standards, with global modification factors of strength or stiffness, in supposed service classes, mostly dependent on relative humidity hypothesis. If this assumption is acceptable for new construction, a better knowledge of moisture content profiles in service environment is necessary for in situ assessment of existing structures. In outdoor conditions, diagnosis of structures has to balance between accuracy of prediction, and amount of data. In this paper, the specific influence of temperature on moisture transfer is studied as a guide to estimate the impact of temperature on the various steps of the hygroscopic equilibrium calculation. Prioritization and ranking of effects on a finite element model is proposed.

Comparison of idealized data is provided to evaluate if the modelling is physically consistent, free from measured effects that would be difficult to model (wind-oriented airflow, enclosed fan flow, fluid/sample interactions, …).

Two transfer laws are necessary to model the equilibrium state: Fourier's law for heat transfer, and Fick's law for moisture transfer. In addition, coupling parameters are needed to consider the thermo-migration of bound water and its dual effect. For a one-dimensional problem, these two transfer equations are as follows [START_REF] Luikov | Theory of Energy and Mass Transfer[END_REF][START_REF] Philip | Moisture movement in porous materials under temperature gradients[END_REF]:

    T Tw T grad D grad T D grad w t         (1)     w wT w grad D grad w D grad T t         (2)
with T D and w D respectively representing the heat and moisture transfer tensor, and w the bound water content, such that:

w anh m w m  (3)
with w m and anh m , respectively, the wet and dry mass.

wT D denotes the Soret effect [START_REF] Li | Nonisothermal moisture movement in wood[END_REF][START_REF] Siau | Flow in wood[END_REF]Siau and Jin, 1985a). It is used herein to model the capacity of the temperature pattern to generate a water flow. The mutual effect is represented by the parameter Tw D . While methods are indeed available to successfully measure the thermal properties of materials, determining water diffusion parameters does however remain a scientific obstacle. This determination is typically achieved using conditioning chambers so as to identify adsorption and desorption kinetics during the transitional phase. Yet as an initial constraint, this is a time-consuming method and, secondly, the application of isothermal conditions does not lead to characterizing the various thermo-hydric couplings. Tests conducted in climatic chambers also provide sorption isotherms for modeling convective transfers between air vapor and bound water on the surface of samples. Most of these isotherms are defined for a given temperature; hence, they are not directly relevant for the thermo-hydric simulation of timber structures under outdoor conditions.

The first section presents the coupled heat and mass transfer model. The coupling is proposed through Fick's and Fourier's Laws, by means of introducing internal sources led by latent heat transfers, as a result of the adsorption and desorption of bound water via a thermodynamic state change. With vapor pressure being considered as a potential activator, the equivalent relative humidity and apparent permeability are inserted into Fick's Law, as proposed by Künzel [START_REF] Künzel | Simultaneous heat and moisture transport in building components : Oneand two dimensional calculation using simple parameters[END_REF].

The second section studies the sorption isotherms occurring in the moisture convection process both at the surface and between the inner moisture and equivalent relative humidity. Coupling with temperature is performed through saturation moisture and a thermodynamic sorption model.

Lastly, a parametric study is provided by way of a finite element simulation. Its objective is to display the influence of studied phenomena on the water balance and long-term trends.

2 Coupled heat and mass transfer model

Constitutive law for heat transfer

In wood, water can migrate under three different states [START_REF] Stamm | Wood and cellulose science[END_REF], see Figure 1:

 Vapor in lumens,
 Bound water in the cell wall,  Free water over the Fiber Saturation Point.

Below the saturation point, the first two modes can coexist (Figure 1). The driving force is thus the vapor pressure gradient. An instant equilibrium between the relative humidity of air in lumens and the water bound in cells is assumed at every point of the material. This assumption neglects any convective effect on the surface of cells. However, convective effects can decelerate bound water and heat transfers between the lumens and cells. This effect will may be integrated into the characterization of the permeability coefficients.

          h h s vs T C w T H RH p t               (4)
Equation ( 4) now presents a generalized form of heat transfer, in which h  and h C are the density and thermal capacity, respectively, of the homogenized material composed of dry wood and bound water. According to the mixing principle, h  and h C are defined by the following expressions:

  h anh 1w      (5)
H L H    (7)
Moreover, [START_REF] Merakeb | Couplage hygromécanique dans le processus de diffusion dans le bois[END_REF] proposed the following expression to relate the dependence of moisture content on sorption enthalpy:

s s w H A ln w       (8)
s w indicates the moisture content when fibers are saturated by bound water for a relative humidity close to 100%.

A is an intrinsic parameter related to each wood species; its value depends on the sorption direction, with two distinct values a A and d A for the adsorption and desorption phases, respectively [START_REF] Rawat | Enthalpy-entropy compensation during sorption of water in wood[END_REF][START_REF] Merakeb | Modeling of the sorption hysteresis for wood[END_REF]. Equation ( 8) shows that as w tends toward s w , the correction s H  approaches 0. Under these conditions and according to Equation ( 7), the latent heat of adsorption converges to the free water latent heat.

Constitutive laws of mass transfer

Equation ( 2) can be replaced by the following expression in substituting

w for RH :     anh vs vs w RH p RH RH p RH t                    (9) anh 
is the anhydrous density of the material.   denotes the apparent permeability, which integrates the permeability vapor and a correction dependent on moisture content. [START_REF] Choong | Movement of moisture through a softwood in the hygroscopic range[END_REF], [START_REF] Kulasinski | Physical and mechanical aspects of moisture adsorption in wood biopolymers investigated with atomisitic simulations[END_REF], [START_REF] Rosen | Exponential dependency of moisture diffusion coefficient[END_REF] and [START_REF] Stamm | Bound water diffusion into wood in the fiber direction[END_REF][START_REF] Stamm | Wood and cellulose science[END_REF] have all observed that the permeability coefficient is an increasing function with respect to temperature. They have proposed correlating this increase via an Arrhenius Law, which typically describes the influence of temperature on chemical reaction kinetics according to both the activation energy and the ideal gas law constant. In our case, the Arrhenius Law can be used to express permeability in the following form:

a o E exp RT           ( 10
)
o  is a virtual permeability value which can be defined as a fitting parameter. T is the temperature given in Kelvin, R the ideal gas constant, and a E the activation energy. According to [START_REF] Nelson | Diffusion of bound water in wood-part 3-A model for nonisothermal diffusion[END_REF][START_REF] Nelson | Heats of transfer and activation energy for bound water diffusion in wood[END_REF], Siau (1985b) and [START_REF] Skaar | Wood water relations[END_REF], the activation energy a E depends on both sorption latent heat and the specific heat capacity of vapor p v C , such that:

  a s p v E H C T    (11)
In considering Equation ( 11), the apparent permeability   , as defined in Equation ( 10), becomes:

  sp v o H C T exp RT             (12)

Boundary conditions

Heat and mass transfer must be completed by heat and water transfers at the surface. Such transports are expressed by the following differential equations:

  T amb surf T h T T x        (13)   w amb surf Rh h RH RH x        (14)
where



Sorption isotherms

As regards model implementation in the context of structural timber behavior, the three difficulties yet to be overcome consist of: the isotherm envelope, partial hysteresis, and temperature dependence.

Isotherm envelopes

Hygroscopic materials can adsorb or desorb water molecules when placed in wet or dry environments, resulting in transports between bound water and water vapor present in the surrounding air. On the material surface, this process acts as the engine of convective transfers. Moreover, in the material, it characterizes the transport of water molecules between porosities and sorption sites, thus inducing energy transfers due to the creation or rupture of hydrogen bonds between bound water and material fibers. Several models have been proposed in the literature. While most have been developed on the basis of phenomenological hypotheses [START_REF] Brunauer | Adsorption of gases in multimolecular layers[END_REF][START_REF] Dent | A sorption theory for gas mixtures[END_REF][START_REF] Hartley | Analysis of the wood sorption isotherm using clustering theory[END_REF][START_REF] Stamm | Wood and cellulose science[END_REF], others are based on thermodynamic approaches. Among this latter category, [START_REF] Merakeb | Couplage hygromécanique dans le processus de diffusion dans le bois[END_REF] interpreted hygroscopic balance as a thermodynamic property of bound water. By analogy with the latent heat of free water vaporization, the following form has been proposed:

      v vs 22 s ln p ln p ln RH H R T R T T T T                 (15)
In considering Equations ( 8) and ( 15), Merakeb developed a logarithmic relationship of the following general form between water content and relative humidity: Buildings exposed to outdoor conditions are not subjected to total moisture cycles from 0% to 100% RH. Sorption hysteresis must therefore be replaced by partial isotherms. Carsten-Rode-Pedersen (1990), [START_REF] Kulasinski | Physical and mechanical aspects of moisture adsorption in wood biopolymers investigated with atomisitic simulations[END_REF] and [START_REF] Merakeb | Couplage hygromécanique dans le processus de diffusion dans le bois[END_REF]

    ii s w ln ln RH exp RH w          (
w 27%  a 0.99   d 0.73   a 1.52   d 1.39   RH (%) (%) Moisture content (%)       bb i a d d i a d da w w D w w ww             (18)
and

      bb i a d d i a a da A w w w w ww             (19)
Equations ( 18) and ( 19) have been integrated into an explicit incremental algorithm in order to calculate the equilibrium humidity for relative humidity A , D and  are three phenomenological parameters. Hence, by applying Equations ( 18) and ( 19), an update of internal humidity

1 i RH    1 ii RH RH RH     . In this case,
1 i w  is expressed as follows: i 1 a,d i w RH w       (20)
To illustrate this approach, the model response is compared to Merakeb's experimental results.

In his work, Merakeb proposed a cyclic sorption test with a decreasing amplitude centered at: 50% RH (0%-100%, 100%-20%, 20%-80%, 80%-30%, 30%-70%, 70%-40%, 40%-60%, 60%-50%, Figure 3).

(%) (%) (%) (%) (%) (%) (%) (%) Moisture content (%) Moisture content (%) Moisture content (%) Moisture content (%)
The simulation was performed with an increment of 1% relative humidity according to the following parameter values: A 0.4  , D 0.06  and 1.5  A good fit has been obtained between the model and experimental test results, with a slightly increasing relative error, yet not exceeding a least square error of 1.8% for the last cycle.

Temperature dependence

In the literature, many studies on sorption isotherms have been carried out under isothermal conditions. Nonetheless, it is accepted that the water balance is conditioned by the ambient temperature. Some authors [START_REF] Merakeb | Modeling of the sorption hysteresis for wood[END_REF][START_REF] Perré | A Numerical Drying Model That Accounts for the Coupling Between Transfers and Solid Mechanics. Case of Highly Deformable Products[END_REF] have proposed an initial correction that strongly affects the moisture content at 100% relative humidity, the fiber saturation point s w . From a phenomenological standpoint, a linear dependence on temperature is proposed, i.e.:

In agreement with [START_REF] Frandsen | Selected constitutive models for simulating the hygromechanical response of wood[END_REF], this question is being raised here from the perspective of thermodynamic transfers, whose temperature constitutes a catalyst according to Le Chatelier's principle. Let's consider a temperature increase T  . The induced heat variation is given by:

hh dE m C dT    (22)
where h m is the homogenized mass sample, composed of dry mass anh m and bound water mass w m , whereby:

h anh w m m m  (23)
This heat variation is balanced with the sorption process. Equations ( 7), ( 8) and ( 23) can now be used to write the following at the saturation point   s ww  :

  anh anh w w w m C m C dT L dm        (24)
In considering Equation (3), Equation ( 24) is laid out as a first-order differential equation:

s w anh s dw C C w dT L L     (25)
Heat capacity of bound water can change, as recently described in [START_REF] Zhang | Moisture-induced crossover in the thermodynamic and mechanical response of hydrophilic biopolymer[END_REF]. For a civil engineering application, for moisture and thermal ranges, the heat capacities anh C and w C as well as latent water vaporization heat L are assumed as invariant relative to ambient temperature. An analytical form of saturation humidity as a function of temperature is thus derived by solving Equation (25), i.e.:

    o anh w anh ss ww C C C w T w exp T 273 C L C              (26)
where o s w is the saturation moisture at 273K. The proposed analytical model has been compared to the data stemming from both the hygroscopic equilibrium abacus of Eurocode 5 (AFNOR, 2010) and the linearized function proposed by Perré, (see Equation ( 21)), yielding a very good correlation (Fig. 4) with the following thermodynamic parameters:

Simulation and discussion

In order to estimate the thermo-hydric coupling and hysteresis effects on heat and mass transfer, a parametric study will be proposed in this section. The moisture diffusion direction is confined to the grain's direction when considering a 3D model whose general algorithm is implemented in the finite element code CASTEM. The wood species studied is a Douglas fir, i.e.

Pseudotsuga menziesii.

Geometry and boundary conditions

The geometry and boundary conditions of this study are described in Figure 5. Four sides are moisture-proof while being permeable to heat flow. Only the two faces perpendicular to fibers are conducive to heat and moisture convective transfers. The mesh discretizes the 8 th volume.

According to Equations ( 13) and ( 14), the convection process is driven by t h and w h . Heat flow is assumed to be isotropic. For forced convection conditions, these values are fixed to: For an initial conditioning with a temperature of 20°C and relative humidity of 60%, the initial and homogeneous internal moisture has been calculated at 11.7%. In order to simulate an average European oceanic climate, an annual climate is created. This input is closed to exterior recording. Reproduced fifty times, its periodicity assists comparison between simulations options. Temperature and relative humidity functions, representing seasonal changes (over 360 days), anticyclonic effects (15 days) and daily variations (1 day) in both temperature and relative humidity, have been assigned as follows:

  3 Rh ii i i1 2 RH t MIN 1 ; RH RH sin t P                 (27)   3 T ii i i1 2 T t MAX 0 ; T T sin t P                 (28)
The climatic amplitudes are specified in Table 1. The temporal evolution of the relative humidity is in phase opposition with temperature for the annual, sequential and daily periods (i.e. RH T ii



    ). While the sequential and daily phase shifts are zero in temperature, the annual temperature phase shift corresponds to the first day of simulation positioned during the year. Moreover, the evolution of the relative humidity is limited between 0% and 100% RH, and temperature is limited to positive values.

Diffusion properties and isotherms

According to the previous description, experimental identification of parameters on Douglas fir is presented in [START_REF] Varnier | Adaptation of Eurocode 5 standard to French hardwoods -Proposal of new hygroscopic equilibrium charts[END_REF]. The diffusion properties are specified in The parameters of the total and partial adsorption and desorption isotherms are presented in Table 3.

Table 2. The parameters of the total and partial adsorption and desorption isotherms are presented in Table 3. The average inner moisture evolution over 5 years is presented in Figure 7 for these 8 combinations. The difference between results can now be analyzed from several standpoints.

• Deviation from a reference Setting as a reference the variant with the most temperature-dependent parameters (case 8), the evolution of differences between the other 7 cases and the reference is plotted in Figure 8: An initial conclusion can be drawn from the influence of the three phenomena on the average moisture content. Except for case 6, the other cases have all overestimated this influence. The variation compared to case 3 indicates the greatest overestimation, i.e. up to 4.5% of moisture content.

This general overview however is too broad to isolate the impact of each individual parameter, whose impact on inner moisture will now be analyzed.

 Influence of hysteresis

The influence of hysteresis is visible in Figure 9 by comparing models 1/2, 3/4, 5/6 and 7/8 in pairs. These differences reveal a 5-year equilibrium between 0.5% and 2% moisture content. Thus, neglecting the effect of hysteresis induces an overestimation of the water balance.

Moreover, the representation Δ1-2 and Δ5-6 highlights the influence of hysteresis on diffusion kinetics. Indeed, the hygroscopic equilibrium is reached more quickly on those models that do not take the influence of temperature on permeability into account. The dependence of temperature on s w is exposed by comparing models 2/4, 6/8, 1/3 and 5/7 two-by-two (Figure 10): Couples 2-4 and 6-8 also highlight the influence the role of temperature dependence in the relationship between apparent permeability and hygroscopic equilibrium.

 Influence of temperature on permeability

The four differences all generally exhibit the same behavior, which suggests that the temperature dependence of permeability exerts the greatest impact on the evolution of w . Moreover, neglecting the influence of temperature on the apparent permeability yields an overestimation of average humidity by 2-2.5%. The average moisture differences for the 8 cases during the first and last weeks of simulation are presented in Figure 12.

Cases 3 and 7 are the only ones to show average moisture changes over a daily period. These variations are on the order of 0.75% water content. Hence, the other six cases are only sensitive to sequential trends. After 5 years, the hygroscopic equilibrium of all 8 cases varies over an interval ranging from 8.75% to 12.25% water content. The final approach applied herein consists of analyzing stabilization trends over the 5-year simulation period.

For each year, the peak values of moisture content ( max min / ww ) and the average moisture content (wmean) for each case have been determined. These quantities were then compared with the initial water content i w of the test piece. Figure 11 depicts for all 8 cases the three criteria for each year. It should be noted that cases 2 and 4 reveal a different trend over the first year compared to the four following cases. This result is due to the hypothesis of a homogeneous initial moisture field.

A first analysis on 𝑤 𝑚𝑒𝑎𝑛 /𝑤 𝑖 provides us with the following conclusions on moisture trends:

 Cases 1, 3 and 4 tend to humidify the specimen.

 Cases 2, 5, 6, 7 and 8 tend to dry the specimen.

A second analysis of max / i ww and min / i ww makes it possible to draw conclusions on the established regimes:

 Cases 1, 2 and 5 reach a steady state as of the 3 rd year.

 Cases 3, 4, 6, 7 and 8 reach a steady state after the 4 th , if not the 5 th , year.

These two approaches display the influence of the three phenomena on the long-term equilibrium value, as well as on the speed with which the established regime is attained.

Conclusion

This work has focused on mass transfer processes coupled with heat transfer, and particularly on the temperature dependence involved in moisture transfer. In order to model wood element behavior in non-isothermal climates, e.g. timber structures, a strong coupling has been developed. Nevertheless, no phenomenological coupling coefficients could be proposed, as experimental characterization continues to pose a scientific challenge to this day.

Based on a thermodynamic approach, the permeability properties of the material and sorption characteristics have been corrected in accordance with a variable temperature.

The temperature impact on both the average evolution of humidity and the induced water profiles could then be obtained through implementation in a finite element code, namely CASTEM. The mass transfer in a structural element has successfully been modeled without significantly increasing the number of parameters needing to be characterized.

  vapor permeability, in kg.s -1 .m -1 .Pa -1 o  :Vapor permeability fitting parameter, in kg.s -1 .m -1 .Pa -1  w  :Thermal conductivity of the wet material, in W.m -1 .K -1

Figure 1 :

 1 Figure 1: Three modes of water diffusion in wood Transfer equations use two potentials, temperature T and relative humidity RH, in conjunction with Fourier's and Fick's Laws, respectively. To introduce vapor pressure, Equation (1) is changed as shown below:

  designates permeability. The values ( amb T , mean temperature and relative humidity of ambient air and sample surface, respectively. The heat and water flows are thus proportional to the coefficients of surface heat and water transfers, T h and w h .

  to translate the hysteretic effects discussed byChen et al. (2018) about the hysteresis mechanism connected with the different hydrogen bond network. The relevance of the model compared to gravimetric tests conducted at 23°C for Douglas fir wood is highlighted Figure2, as proposed in[START_REF] Merakeb | Couplage hygromécanique dans le processus de diffusion dans le bois[END_REF].

Figure 2 :

 2 Figure 2: Sorption hysteresis, model vs. experimental results for Douglas fir wood 3.2 Partial isotherms

  of the isotherm envelope calculated by derivation of Equation (16).

Figure 3 :

 3 Figure 3: Partial isotherms, model vs. experimental results

Figure 4 :

 4 Figure 4: Saturation moisture content as a function of temperature

Figure 5 :

 5 Figure 5: Geometry sample, finite element mesh and boundary conditions 4.2 Climate stressors

  average values of the cycles are RH 65%  and T 13.3 C  . An example is provided in Figure6, showing the annual change in temperature and humidity with an origin in mid-season before the hot dry period ( T 1    ). This simulation begins at a time when the external conditions are close to the internal equilibrium value.

Figure 6 :

 6 Figure 6: Temporal evolution of temperature and humidity over one year

Figure 7 :

 7 Figure 7: Average inner moisture evolution

Figure 8 :

 8 Figure 8: Evolution of deviations from the reference case (i.e. case 8)

Figure 9 :

 9 Figure 9: Differences between cases in which hysteresis is considered or not  Influence of temperature on s w

Figure 10 :

 10 Figure 10: Differences between cases in which ws is dependent or not on temperature

Figure 11 :

 11 Figure 11: Differences between cases where the influence of temperature on permeability is taken into consideration or not

Figure 12 :

 12 Figure 12: Evolution in inner moisture for the first and last weeks of the 5-year simulation period

Figure 14 :

 14 Figure 14: Trend in stabilization levels of the studied cases over 5 years

  denote the intrinsic density and heat capacity, respectively, of dry wood.Heat transfer is governed by two thermodynamic forces: 1) the temperature gradient, with  as the thermal conductivity; and 2) the vapor pressure gradient associated with the latent heat of sorption

			C	h		C	anh 1w w C  	w	, with	C	w		11 4.18 kJ kg K   	(6)
	where anh 	and anh C
	Heat sorption	H is determined from the latent heat of free water vaporization	L corrected by
			s
	the heat released by the fixation of water molecules bound onto fibers	H  , such that:
													s
									ss
							vapor free water
												bound water

s H . Vapor pressure is calculated using the saturation vapor pressure vs p and relative humidity RH of the inner air of lumens. Heat flow is proportional to vapor permeability  .

  suggested a model that takes into account water capacity  , as defined by:

			x : Experimental points		: Model
		28%
		24%					s
	content	16% 20%
	Moisture	12%
		8%
		4%
		0%
		0%	20%	40%	60%	80%	100%
					Rh
						w RH  	(17)
	Under these conditions, with	w being the initial water content for relative humidity	RH , two
				i			i
	water capacities can be defined as follows:

Table 1 :

 1 Climatic amplitudes

	Annual Sequential	Daily

Table 2 :

 2 Diffusion properties in the longitudinal direction (Douglas fir)

		o		anh 	C	anh		  w		a A	d A
	15 10  	4	450	1.6	0.17 w 0.28 		0.36		0.58

Table 3 :

 3 Partial and total isotherms parameters (Douglas fir)In order to highlight the contributions of the proposed model compared to more typical approaches, eight simulation variants have been assessed.The following parameters vary over the 8 studied combinations (Table4): Influence of temperature on apparent permeability according to Arrhenius' Law  Influence of temperature on the saturation water content according to Le Chatelier's principle  Influence of sorption hysteresis through partial isotherms according to Pedersen's model. If hysteresis is neglected, then the median sorption curve is used.

	 w T 0 C s 		a 	d 		a		d	A	D	
	29.4%		0.82	0.76	1.44	0.99	0.4	0.06	1.5
	4.4 Calculation hypotheses

nicolas.sauvat@unilim.fr

(%RH)

Acknowledgements

This work has been realised in the French National Research Agency (ANR) through EFEUR5 project (ANR-15-CE08-0027) concerning Structural behavior of French Hardwood for better optimization with Eurocodes 5. The authors would like to express their appreciation towards the ANR financial support.