Donglou Ren

Zhuanghao Zheng

Meng Wei

Pengcheng Zhang

Michel Cathelinaud

Hongli Ma

Xianghua Zhang
email: xiang-hua.zhang@univ-rennes1.fr

Synthesis, structure and photoelectric properties of selenide composites with in situ constructed Sb 2 Se 3 /NaSbSe 2 heterojunction

Keywords: Selenide composites, Antimony selenide (Sb2Se3)-NaSbSe2 heterojunction, Impedance spectroscopy, Photo-electro-chemical (PEC) performance, Interface electric field

Inorganic semiconductor heterojunctions have attracted extensive attention for technological applications owing to interface phenomena. In this work, selenide composites with in situ constructed Sb2Se3/NaSbSe2 heterojunctions with similar band gap width have been synthesized by conventional melt-quenching method. The microstructure and photoelectric properties of the composites were investigated at J o u r n a l P r e -p r o o f different NaSbSe2 contents. The study revealed that NaSbSe2 content has direct influences on the photoelectric performance of the composites by modifying the heterojunction size and the grain boundary resistance, as evidenced by scanning electron microscopy and impedance spectroscopy, respectively. The photocurrent density of Sb2Se3 with 2.5 and 5 mol% NaSbSe2 was approximately 180 times larger than that of the pure Sb2Se3 at a bias voltage of -1.5 V and under an illumination of 7 mW/cm 2 , due to an effective separation of photogenerated carriers through the interface electric field. Additionally, the composites exhibited an excellent stability even in 0.5 M LiClO4 aqueous electrolyte.

Introduction

In recent years, orthorhombic antimony selenide (Sb2Se3) is actively considered for different applications such as solar cells, photodetectors, photoelectrochemical cells, and thermoelectric devices [START_REF] Messina | Antimony Selenide Absorber Thin Films in All-Chemically Deposited Solar Cells[END_REF][START_REF] Li | 9.2%-efficient core-shell structured antimony selenide nanorod array solar cells[END_REF][START_REF] Zhang | Alternative back contacts for Sb 2 Se 3 solar cells[END_REF][START_REF] Wang | Stable 6%-efficient Sb 2 Se 3 solar cells with a ZnO buffer layer[END_REF][START_REF] Choi | Diameter-Controlled and Surface-Modified Sb 2 Se 3 Nanowires and Their Photodetector Performance[END_REF][START_REF] Prabhakar | Photocorrosionresistant Sb 2 Se 3 photocathodes with earth abundant MoS x hydrogen evolution catalyst[END_REF][START_REF] Park | Efficient Solar-to-Hydrogen Conversion from Neutral Electrolytes using Morphology-Controlled Sb 2 Se 3 Light Absorbers[END_REF][START_REF] An | Low Thermal Conductivity and Optimized Thermoelectric Properties of p-Type Te-Sb 2 Se 3 : Synergistic Effect of Doping and Defect Engineering[END_REF]. This is because Sb2Se3 has some outstanding properties such as a narrow direct band gap (1.17 eV) [START_REF] Chen | Characterization of basic physical properties of Sb 2 Se 3 and its relevance for photovoltaics[END_REF], a high absorption coefficient (> 10 5 cm -1 ) [START_REF] Chen | Optical properties of amorphous and polycrystalline Sb 2 Se 3 thin films prepared by thermal evaporation[END_REF], a high Seebeck coefficient (1,800 μVK -1 ) [START_REF] Choi | Diameter-Controlled and Surface-Modified Sb 2 Se 3 Nanowires and Their Photodetector Performance[END_REF], and earth-abundant J o u r n a l P r e -p r o o f constituents [START_REF] Wen | Magnetron sputtered ZnO buffer layer for Sb 2 Se 3 thin film solar cells[END_REF]. However, application development of the Sb2Se3 based materials has been limited by its intrinsically high resistivity. One possibility to overcome this challenge is to dope this material with a low-valence metal cation [START_REF] Wu | Enhanced Broadband Responsivity of Ni-Doped Sb 2 Se 3 Nanorod Photodetector[END_REF][START_REF] Zhou | Buried homojunction in CdS/Sb 2 Se 3 thin film photovoltaics generated by interfacial diffusion[END_REF][START_REF] Li | Characterization of Mg and Fe doped Sb 2 Se 3 thin films for photovoltaic application[END_REF][START_REF] Choi | Magnetic and transport properties of Mn-doped Bi 2 Se 3 and Sb 2[END_REF][START_REF] Chen | Enhanced electrical conductivity and photoconductive properties of Sn-doped Sb 2 Se 3 crystals[END_REF]. The creation of internal heterojunctions seems to be an effective way to improve different photoelectric properties. For instance, Choi et al. [START_REF] Choi | Diameter-Controlled and Surface-Modified Sb 2 Se 3 Nanowires and Their Photodetector Performance[END_REF] fabricated Sb2Se3/Ag2Se heterojunction nanowire that possessed a much better dark current and photocurrent, as compared to that of the intrinsic Sb2Se3 nanowire, to approximately 50 and 7 times, respectively. Guijarro et al. [START_REF] Guijarro | Toward Antimony Selenide Sensitized Solar Cells: Efficient Charge Photogeneration at spiro-OMeTAD/Sb 2 Se 3 /Metal Oxide Heterojunctions[END_REF] constructed a Sb2Se3/TiO2 heterojunction that exhibited a 3-fold improvement in the overall yield of the charge separated state upon illumination. In our previous work [START_REF] Zhang | Enhancement of charge photo-generation and transport via an internal network of Sb 2 3 /Cu 2 GeSe 3 heterojunctions[END_REF], internal Sb2Se3/Cu2GeSe3 heterojunction enhanced the photocurrent (74 μA/cm 2 ) that was at least 100 times higher than any of these two crystals individually (Sb2Se3: ~ 0.6 μA/cm 2 , Cu2GeSe3: ~ 0.7 μA/cm 2 ). The enhanced photoelectric performance is attributed to the interface electric field that effectively promotes the separation and transport of photoinduced carriers.

Ternary semiconductors -the I-V-VI2 family, where I = Cu, Ag, or alkali metals; V = Bi, Sb; and VI = S, Se, Te, have attracted increasing attention in thermoelectric [START_REF] Guin | Promising thermoelectric performance in n-type AgBiSe 2 : effect of aliovalent anion doping[END_REF][START_REF] Xiao | High Thermoelectric and Reversible p-n-p Conduction Type Switching Integrated in Dimetal Chalcogenide[END_REF][START_REF] Guin | High thermoelectric performance in tellurium free p-type AgSbSe 2[END_REF] and solar cells [START_REF] Chou | Ag 3 SbS 3 Liquid-Junction Semiconductor-Sensitized Solar Cells[END_REF][START_REF] Liang | Homogenously hexagonal prismatic AgBiS 2 nanocrystals: controlled synthesis and application in quantum dot-sensitized solar cells[END_REF][START_REF] Liu | CuSbS 2 : a promising semiconductor photoabsorber material for quantum dot sensitized solar cells[END_REF][START_REF] Bernechea | Solutionprocessed solar cells based on environmentally friendly AgBiS 2 nanocrystals[END_REF][START_REF] Suriyawong | Ternary CuBiS 2 nanoparticles as a sensitizer for quantum dot solar cells[END_REF]. Among these materials, ternary chalcogenide semiconductor NaSbSe2 is another promising compound that is synthesized at high temperature with a NaCl-type structure and the lattice constant is 5.966(2) Å [START_REF] Salov | Phase diagram of the system A(I)-B(V)-C(VI). II. Ternary system Na-Sb-Se[END_REF][START_REF] Hoang | Atomic and electronic structures of I-V-VI 2 ternary chalcogenides[END_REF].

It has a narrow band gap of 1.1 eV [START_REF] Slade | High Thermoelectric Performance in PbSe-NaSbSe 2 Alloys from Valence Band Convergence and Low Thermal Conductivity[END_REF] and a high absorption coefficient of 10 5 cm -1 at λ = 600 nm [START_REF] Bazakutsa | Photoelectric and optical properties of thin films of ternary chalcogenides of the form Me I SbX VI 2[END_REF]. If Sb2Se3/NaSbSe2 heterojunction can be constructed, the influence of the interface between these two materials, with different structure but similar band gap, J o u r n a l P r e -p r o o f on the photoelectric performance will become very interesting. It is important to point out that the elements contained in the two materials are earth-abundant, low cost, nontoxic and environmentally friendly.

In the present work, the selenide composites with in situ synthesized Sb2Se3/NaSbSe2 heterojunction have been prepared by using Sb, Se and Na elements as starting materials and by using the conventional melt-quenching method of vacuumsealed silica tube to minimize the pollution. The influence of NaSbSe2 contents on the heterojunction size and the photoelectric performance of the composites has been investigated. Ultimately, the possible mechanism of property enhancement is proposed.

Experimental procedure

Materials preparation

The selenide composites with internal Sb2Se3/NaSbSe2 heterojunction were prepared by a conventional melt-quenching method. High-purity elements Sb shot (99.999%, 6 mm, Alfa Aesar), Se shot (99.999%), and Na ingot (99.95%) were used as raw materials. At first, all elements were weighted and mixed according to the appropriate stoichiometric ratio of each element (12 g mixture for each sample). The components are called SN-2.5%, SN-5%, SN-10% and SN-15%, S and N representing respectively Sb2Se3 and NaSbSe2, and the number corresponding to the molar fraction of NaSbSe2. The mixture was loaded into a carefully cleaned silica tube under protection of argon atmosphere in a glovebox. The tube has an inner diameter of 1 cm and an outer diameter 1.4 cm. Then, the tube containing all the starting elements was J o u r n a l P r e -p r o o f pumped to a vacuum of about 10 -5 mbar. The flame-sealed tube was placed at the center of a rocking furnace. The mixture was then heated to 700 °C with a 1.2 °C/min ramp, rocked at this temperature for 8 h to ensure a good homogenization of the melt. The tube was subsequently quenched in water to room temperature. Finally, the ingots were annealed at 350 °C for 3 h, for reducing the mechanical stress caused during the quenching process. The as-synthesized samples were then removed from the silica tube, cut and polished into 2-mm-thick discs for subsequent characterizations.

Characterization

The phases in the as-synthesized samples were determined by X-ray diffraction (XRD) using a Bruker AXS D8 Advance X-ray diffractometer (Karlsruhe, Germany) coupled with Cu-Kα radiation (λ = 1.5406 Å) in a scanning rate of 0.02° s -1 . The X-ray tube was operated at 40 mA and 40 kV in locked coupled mode. Scanning electron microscopy (SEM) studies were carried out on a JEOL JSM-7100F thermal field emission electron microscopy equipped with an energy dispersive X-ray spectroscopy (EDS) at 20 kV. The impedance spectroscopy and temperature-dependent conductivity were measured on an Autolab PGSTAT302N (Metrohm, AUT85901, Switzerland) in the temperature range of 278-373 K covering a frequency of 10 6 -1 Hz with two stainless-steel plates as electrodes and heating sample holder. All measured samples have a diameter of 10 mm and a thickness of 2 mm. To improve the contact between the electrodes and the sample, the surface of the samples was covered with a layer of Au. Spectra analyses were performed by Zsimpwin impedance analysis software. The J o u r n a l P r e -p r o o f photo-electro-chemical (PEC) performance of as-synthesized samples was evaluated using a three-electrode configuration, where Ag/AgCl electrode was used as the reference electrode, Pt-wire as the counter electrode and our samples as the working electrode. For obtaining the working electrode, the fine polished sample with diameter of 1 cm was connected with a copper wire by using silver paint as the back contact.

Then, the sample was covered with a layer of epoxy resin for ensuring the isolation between electrode and electrolyte during the PEC measurement. The LiClO4 solution (0.5 mol/L) was used as electrolyte and a white light tungsten halogen lamp was used as light source. The stability and the response speed of the photocurrent in our samples were evaluated under chopped light irradiation using a mechanical chopper. The optical property was measured with a step size of 1 nm using diffuse reflectance spectroscopy (DRS) equipped with an integrating sphere at room temperature. DRS experiments were carried out in the wavelength range of 300-2500 nm that covers the absorption zones, due to electronic transition of the semiconductor materials. (220) peaks increases with increasing contents of NaSbSe2. The XRD patterns of powders are similar to the XRD patterns of bulks, suggesting the samples prepared by melt-quenching method are homogeneous. This phenomenon was already observed in our previous works due to the mode of liquid mass transfer [START_REF] Ren | Densification and mechanical J o u r n a l P r e -p r o o f properties of pulsed electric current sintered B 4 C with in situ synthesized Al 3 BC obtained by the molten-salt method[END_REF][START_REF] Ren | Synthesis and properties of conductive B 4 C ceramic composites with TiB 2 grain network[END_REF]. The grinding process destroyed the preferential orientation in the bulk samples, which caused some differences between the bulk and the powder in term of the relative intensity of peaks.

Results and discussion

Phase analysis and formation mechanism of composites

These results suggest that the Sb2Se3-NaSbSe2 composites were successfully prepared without impurity phase.

Because the materials were synthesized by melt-quenching method at 700 °C, the liquidus projection of the Na-Sb-Se system [START_REF] Salov | Phase diagram of the system A(I)-B(V)-C(VI). II. Ternary system Na-Sb-Se[END_REF] (Fig. 2) is useful for understanding the formation mechanism. It can be seen that the largest primary crystallization field (NaSbSe2) and the second-largest primary crystallization field (Na2Se) are located in the ternary system. In addition, there is a big immiscibility area marked by dashed black line in the system. The system consists of eight binary compounds, Na3Sb, NaSb, Sb2Se3, Na2Sex (x = 1, 2, 3, 4, 6), and the only ternary compound NaSbSe2. Although there exist many binary compounds in the Na-Sb-Se system, no one is detected by XRD in Fig. 1 except Sb2Se3. According to previous work [START_REF] Sangster | The Na-Se (Sodium-Selenium) System[END_REF], the Na2Se6, Na2Se4, Na2Se3, and Na2Se2 decomposed at 258 °C, 290 °C, 313 °C, and 435 °C, respectively. The low J o u r n a l P r e -p r o o f eutectic temperature of Na3Sb and NaSb is 437 °C [START_REF] Liu | Thermodynamic descriptions and phase diagrams for Sb-Na and Sb-K binary systems[END_REF]. These binary compounds may react with each other to generate NaSbSe2. Sb2Se3 has a negative Gibbs free energy (-38.1152 kJ mol -1 ) at 298 K [START_REF] Ghosh | The sb-se (antimony-selenium) system[END_REF][START_REF] Zhou | Solution-Processed Antimony Selenide Heterojunction Solar Cells[END_REF] and a low melting point of 610 °C. The local atomic arrangement in liquid is similar to that of crystalline state [START_REF] Satow | The structure analysis liquid Sb 2 Se 3 by neutron diffraction[END_REF]. Consequently, we have successfully prepared Sb2Se3-NaSbSe2 composites after quenching, as evidenced by Fig. 1.

Microstructural Characterization

The backscattered electron images and energy dispersive X-ray spectroscopy are essential for studying the distribution of phases and elements. The images of the SN-2.5% and SN-15% samples are shown in Fig. 3(a,b). It clearly illustrates that several phases are distributed in the Sb2Se3 matrix with different sizes. To further determine the composition of these phases, the EDS was used to measure the composition of the points 1, 2 and 3 in Fig. 3(b), as shown as Table 1. It suggests that the point 1 is Se, point 2 is NaSbSe2 and point 3 is Sb2Se3. It is observed that the Se is distributed around NaSbSe2. The residual Se may be due to the imbalance of local compositions in liquid during melting or quenching process. According to a previous report [START_REF] Ghosh | The sb-se (antimony-selenium) system[END_REF], the liquidus Se and Sb2Se3 have a strong tendency toward immiscibility in some range of Se atomic percent. Moreover, there is a big immiscibility area [START_REF] Salov | Phase diagram of the system A(I)-B(V)-C(VI). II. Ternary system Na-Sb-Se[END_REF] in Na-Sb-Se system (Fig. 2).

The existence of Se in the composites has not been detected in XRD patterns (Fig. 1) due to the low content. The EDS elemental mappings of the SN-15% sample further proves that the distribution of elements is globally homogenous except few selenium J o u r n a l P r e -p r o o f rich domains (Fig. 3(c-e)). The distribution of Na element is quite uniform (Fig. 3(e)), because of the globally low content level, leading to high noisy background.

In order to observe the grain size of composites, the surface of the SN-15% sample was etched with a solution of 1 mol/L NaOH at ambient temperature. As shown in Fig. 4, it can be seen that the sample consists of Sb2Se3 (Na-doped, white) and NaSbSe2 grains (gray) from the composition shown in Table 2 except the black holes. The average grain sizes of Sb2Se3 and NaSbSe2 are approximately 50 μm and 5 μm, respectively. The EDS elemental mapping further reveals that the NaSbSe2 has a homogeneous distribution in Sb2Se3. The formation mechanism of such microstructure can be explained as follows: in the liquidus, NaSbSe2 and Sb2Se3 are phase separated due to their immiscibility observed in Fig. 2. A small amount of NaSbSe2 phase precipitates firstly due to its higher melting point (740 °C) [START_REF] Salov | Phase diagram of the system A(I)-B(V)-C(VI). II. Ternary system Na-Sb-Se[END_REF] and the crystals are randomly distributed in liquid Sb2Se3 which will crystallize afterwards. The same phenomenon was observed in SN-5% and SN-10% samples (not shown). These results indicate that the Sb2Se3/NaSbSe2 heterojunctions were successfully in situ constructed by conventional melt-quenching method. It is generally observed that interface quality is often excellent when it is obtained by crystallization of liquid phases.

To further confirm the existence of heterojunctions inside the composites, the I-V curve of the SN-2.5% sample was characterized by using sputtered two gold contacts on the top and bottom surfaces (Fig. 5). The I-V curve displays a non-ohmic character, indicating that the SN-2.5% specimen contains internal heterojunctions, which is randomly distributed as shown in Fig. 3(a).

J o u r n a l P r e -p r o o f

UV-vis diffuse reflectance spectroscopy

The band gap of a semiconductor material is an important characteristic, which can be obtained by measuring the optical diffuse reflectance of the powders. The absorption spectra of all samples was converted from diffuse reflectance data by using the Kubelka-Munk and Tauc functions (Supporting Information). The band gap energy is then calculated by linear fit of the (F(R)•hν) 2 = B(hν -Eg) and the results are shown in Fig. 6 and Table 3 for all the samples. The band gap energy of pure NaSbSe 2 (1.21 eV) is higher than literature data (1.1 eV) [START_REF] Slade | High Thermoelectric Performance in PbSe-NaSbSe 2 Alloys from Valence Band Convergence and Low Thermal Conductivity[END_REF], which is related to intrinsic defects obtained by different synthesis methods and conditions [START_REF] Amoresi | Electrosteric colloidal stabilization for obtaining SrTiO 3 /TiO 2 heterojunction: Microstructural evolution in the interface and photonics properties[END_REF]. It can also be seen that the direct band gap of pure Sb 2 Se 3 sample is 1.15 eV in agreement with previous work [START_REF] Chen | Optical properties of amorphous and polycrystalline Sb 2 Se 3 thin films prepared by thermal evaporation[END_REF].

For the composites with internal Sb 2 Se 3 /NaSbSe 2 heterojunction, the direct band gaps are close to 1.17 eV. The narrow band gap energy would lead to a strong absorption of the solar spectrum.

Impedance spectroscopy

The electrical conductivity of different samples with a thickness of 2 mm and a diameter of 10 mm was measured by using impedance spectroscopy. Fig. 7 shows the variation of impedance real (Z′) part, impedance imaginary (Z″) part, and normalized Z″ with frequency at different temperatures for two representative samples SN-2.5% and SN-15%. It can be seen that the real part (Z′) of impedance decreases with increasing temperatures, corresponding to the behaviors of semiconductors [START_REF] Yang | Improvement of the Sintering and Dielectric Characteristics of Surface Barrier Layer Capacitors by CuO Addition[END_REF].

J o u r n a l P r e -p r o o f

According to previous works [START_REF] Dai | NaSbSe 2 as a promising lightabsorber semiconductor in solar cells: First-principles insights[END_REF][START_REF] Liu | Enhanced Sb 2 Se 3 solar cell performance through theory-guided defect control[END_REF], Sb2Se3 and NaSbSe2 have a large number of intrinsic defects, such as VSe, VNa, NaSb, SbSe. The space charge effect is a dominant process at low temperatures and high frequencies, and in contrast, the space charge polarization is positive at low frequencies and high temperatures in term of Z′ [START_REF] Kaushal | Impedance analysis of 0.5Ba(Zr 0.2 Ti 0.8 )O 3 -0.5(Ba 0.7 Ca 0.3 )TiO 3 ceramics consolidated from micro-granules[END_REF]. The Z′ drastically reduces with increasing frequency, suggesting the space charge polarization [START_REF] Jonscher | The 'universal' dielectric response[END_REF] exists in these samples. The variation of imaginary part of impedance (Z″) with frequency at different temperatures, can be used to evaluate the relaxation frequency. It can be seen that the Z″ has a maximum peak with frequency at different temperatures (Fig. 7(b,e)). This peak in Z″ shifts towards high frequencies with increasing temperature and NaSbSe2 content, which illustrates a decrease in the relaxation time and a thermally activated relaxation in the system [START_REF] Sinclair | Impedance and modulus spectroscopy of semiconducting BaTiO 3 showing positive temperature coefficient of resistance[END_REF]. A lower relaxation time implies faster movement of mobile charge carriers in the samples due to the existence of Sb2Se3/NaSbSe2 heterojunction. The peak broadening at high temperatures, suggests that the temperature dependent relaxation process exists in theses materials [START_REF] Jonscher | The 'universal' dielectric response[END_REF]. The asymmetric broadening of peaks also illustrates the presence of electrical processes in the material with a spread of relaxation time as indicated by changes in peak width [START_REF] Brahma | AC impedance analysis of LaLiMo 2 O 8 electroceramics[END_REF]. The relaxation may be caused by immobile species at low temperature and defects (vacancies, interstitials, and antisites) at higher temperature.

The electrical conduction in the material is realized by hopping of electrons among the available localized sites [START_REF] Dai | NaSbSe 2 as a promising lightabsorber semiconductor in solar cells: First-principles insights[END_REF][START_REF] Liu | Enhanced Sb 2 Se 3 solar cell performance through theory-guided defect control[END_REF][START_REF] Kumar | Effect of strontium concentration on electrical conduction properties of Sr-modified BaSnO 3[END_REF][START_REF] Chakraborty | Magnetic and electric properties of antimony selenide (Sb 2 Se 3 ) crystals[END_REF]. The phenomenon was also observed in the normalized Z″ with frequency in Fig. 7(c,f). Moreover, the magnitude of Z″ declines with shifting peak frequency to high frequency direction with increase of NaSbSe2 J o u r n a l P r e -p r o o f content. This may be due to the accumulation of space charge in all materials in the high frequency zone. Similar result was also reported by other authors [START_REF] Kumar | Effect of strontium concentration on electrical conduction properties of Sr-modified BaSnO 3[END_REF].

The Nyquist plots and the variation of conductivity with temperature were shown in Fig. 8. The asymmetric semicircular arcs appear in the impedance plot (Fig. 8(a,b)).

The symmetry of semicircular arc depends on the nature of the material or its history [START_REF] Sahu | Inter-grain mediated intrinsic and extrinsic barrier layer network mechanism involved in Ca 1 Cu 3 Ti 4 O 12 bulk ceramic[END_REF]. The spectrum consists of single semicircular arc, which shrinks with increasing temperature. It further suggests that the all samples are semiconductors with a negative temperature coefficient of resistance. The bulk and grain boundaries effects exist in polycrystalline materials [START_REF] Macdonald | Impedance Spectroscopy: Emphasizing Solid-State Material and Systems[END_REF]. For selenide composites (SN-2.5% and SN-15%) with internal Sb2Se3/NaSbSe2 heterojunctions, the plots include two semicircular arcs whose center is located below the real axis. The plots display the phenomena of semi-circle decentralization in the composites, which is frequently observed [START_REF] Verma | Impedance spectroscopy and dielectric behavior in barium strontium J o u r n a l P r e -p r o o f titanate-nickel zinc ferrite composites[END_REF]. It can be seen that the electrical response is consisted of two overlapped semicircles. Due to the similar relaxation frequency, the high overlapping degree exists in the two semicircles.

The first relaxation reflects the grains or bulk at high frequency and the second relaxation corresponds to the grain boundaries at low frequency. In our impedance spectra, the lack of electrode effect (line tail) in the range of experimental temperature indicates that all samples are electronic conductors, rather than ionic conductors.

According to the Debye's model, a material should be an ideal semicircle with the center on the real axis because of a single relaxation time [START_REF] Rahaman | Ceramic Processing and Sintering[END_REF]. However, the relaxation process is non-Debye type in our materials [START_REF] Barick | Impedance and Raman spectroscopic studies of (Na 0.5 Bi 0.5 )TiO 3[END_REF], due to the grain size, grain boundaries, grain orientation, defect distribution, etc [START_REF] Sen | Impedance spectroscopy study of strontium modified lead zirconate titanate ceramics[END_REF]. In order to better understand the electrical J o u r n a l P r e -p r o o f response in materials, an equivalent circuit is necessary for fitting the measured data.

The electrical properties are well illustrated by two parallel elements (RbCb-RgbCgb) and R0 in series for these composites at 25 °C in Fig. 8(c), where Cb = bulk capacitance; Cgb = grain boundaries capacitance; Rb = bulk resistance; and Rgb = grain boundary resistance. The equivalent circuits of pure Sb2Se3 and NaSbSe2 can be found in Fig. S4 (Supporting Information). R0 corresponds to the high frequency intersection (R0 = 0 for pure compounds), which is related to pores, capillary cavities, micro-cracks and even external contacts resistance [START_REF] Song | Equivalent circuit model for AC electrochemical impedance spectroscopy of concrete[END_REF][START_REF] Srinivas | Impedance spectroscopy study of polycrystalline Bi 6 Fe 2 Ti 3 O 18[END_REF][START_REF] Ângelo | Characterization of TiO 2 -based semiconductors for photocatalysis by electrochemical impedance spectroscopy[END_REF]. It can be observed that these materials have a strong temperature dependence of conductivity (Fig. 8(d)). The curve was fitted by Arrhenius relation and activation energy for electrical conduction was obtained from the slope of the fitted lines. The equivalent circuit best fitted to measured data and the values of R0, Rb, and Rgb, resistivity at 25 °C, and activation energy are shown in Table 4. The NaSbSe2 has a bulk resistance of 8.63×10 3 Ω and a much higher grain boundary resistance of 1.44×10 6 Ω. However, the grain boundary resistance (2.60 × 10 5 Ω) is close to the bulk resistance (4.02 × 10 5 Ω) for Sb2Se3. This may relate to the crystalline structure of Sb2Se3 composed of intrinsic one dimensional (Sb4Se6)n ribbons with no dangling bonds at the edge, corresponding to grain boundaries [START_REF] Zhou | Thin-film Sb 2 Se 3 photovoltaics with oriented one-dimensional ribbons and benign grain boundaries[END_REF]. However, NaSbSe2 has a NaCl-type three-dimensional structure [START_REF] Guin | Temperature driven p-n-p type conduction switching materials: current trends and future directions[END_REF] that has an isotropic carrier transport and dangling bonds at grain boundaries. The dangling bonds typically act as recombination centers in three-dimensional crystal structure, such as Si, GaAs, CdTe, InP, and Cu(In,Ga)Se2 (CIGS), which can be minimized by using different techniques including chemical surface/defect passivation and appropriate thermal processing [59-J o u r n a l P r e -p r o o f 61]. Further, the concentration, the type and the distribution of defects in grain boundary and bulk/grain may be another reason for the difference in bulk and grain boundary resistance. The resistivity of Sb2Se3 and NaSbSe2 is 2.14×10 6 Ω•cm and 8.87×10 5 Ω•cm, respectively. For the composites with internal Sb2Se3/NaSbSe2 heterojunctions, the resistivity is reduced with increasing NaSbSe2 contents, which is related to the interface defects. Similar work was also reported by O. Dier et al [START_REF] Dier | Reduction of hetero-interface resistivity in n-type AlAsSb/GaSb distributed Bragg reflectors[END_REF].

The activation energy, reflecting the energy for the hopping of electrons, of all Sb2Se3/NaSbSe2 composites is between the quite similar values for pure Sb2Se3 and NaSbSe2 (between 0.45 -0.61 eV). It means that the activation energy is mainly governed by the hoping of electrons inside Sb2Se3 or NaSbSe2. Therefore, the grain boundaries and the Sb2Se3/NaSbSe2 interfaces are not difficult barriers for electrons to cross.

Photo-electro-chemical (PEC) performance

In order to explore the influence of heterojunction interface on the PEC performance of composites, the three-electrode configuration (Inset in Fig. 9) was used at ambient temperature. As shown in Fig. 9, all samples show cathodic photocurrents and their photocurrent density increases with increasing cathodic potential, indicating these materials are p-type semiconductors. The difference between dark and light current represents the photocurrent density. The photocurrent densities of pure Sb2Se3 and NaSbSe2 are very weak (less than 1 μA/cm 2 ) (Fig. S5, Supporting Information), due to the absence of internal heterojunction that could effectively separate J o u r n a l P r e -p r o o f photogenerated carriers based on the interface electric field. Similar results can also be obtained in our previous works [START_REF] Chen | Enhanced electrical conductivity and photoconductive properties of Sn-doped Sb 2 Se 3 crystals[END_REF][START_REF] Zhang | Enhancement of charge photo-generation and transport via an internal network of Sb 2 3 /Cu 2 GeSe 3 heterojunctions[END_REF]. However, very important increase of photocurrent density has been observed in composites with internal heterojunctions.

The values of photocurrent density (SN-2.5%: -139.87 μA/cm 2 , SN-5%: -134.37 μA/cm 2 , SN-10%: -44.26 μA/cm 2 , and SN-15%: -72.47 μA/cm 2 ) at a bias voltage of -1.5 V are first reduced and then increased with increasing NaSbSe2 contents. It can be explained as follows: Firstly, the internal heterojunctions could promote the separation of photogenerated electron-hole pairs, thanks to the interface electric field, and therefore prolong the carrier lifetime, resulting in higher photocurrent density when NaSbSe2 content was low. The photocurrent densities of SN-2.5% and SN-5% samples are 139.87 μA/cm 2 and 134.37 μA/cm 2 , respectively, which are approximately 180 times larger than that of pure Sb2Se3 (less than 1 μA/cm 2 ). Secondly, the number of NaSbSe2/NaSbSe2 grain boundaries increased with increasing NaSbSe2 contents, resulting in fewer Sb2Se3/NaSbSe2 interface. Meanwhile, the NaSbSe2/NaSbSe2 grain boundaries could cause higher recombination due to the three-dimensional structure and the dangling bonds at grain boundaries. This is illustrated by the recombination resistance [START_REF] Kim | Hybrid-Type Quantum-Dot Cosensitized ZnO Nanowire Solar Cell with Enhanced Visible-Light Harvesting[END_REF] (grain boundary resistance) in Table 4. A larger recombination resistance suggests a lower rate of recombination [START_REF] Basu | A type-II semiconductor (ZnO/CuS heterostructure) for visible light photocatalysis[END_REF]. The grain boundary resistance decreased with increasing NaSbSe2 content for SN-10% sample, which caused the decreases of photocurrent density due to increased recombination of photogenerated carriers. Finally, the grain size of NaSbSe2 is increased in SN-15% sample with increasing NaSbSe2 content (Fig. 3), accompanied by increased area of Sb2Se3/NaSbSe2 heterojunction J o u r n a l P r e -p r o o f interface. Compared with the reduced number of Sb2Se3/NaSbSe2 interfaces, the increased area will become the dominant factor affecting the photocurrent density.

Consequently, the photocurrent density of this sample is higher than that of SN-10% due to the effective separation of photogenerated carriers [START_REF] Tayebi | The effect of silver doping on photoelectrochemical (PEC) properties of bismuth vanadate for hydrogen production[END_REF][START_REF] Chen | Construction of titania-ceria nanostructured composites with tailored heterojunction for photocurrent enhancement[END_REF]. These results illustrate that the photoelectric properties of selenide composites are significantly enhanced through interface electric field of Sb2Se3/NaSbSe2 heterojunction.

Furthermore, the cyclic photoresponse of the pure Sb2Se3 and selenide composites was characterized (Fig. 10(a)). When the light is turned on, the current densities quickly increase from -1.27 μA/cm 2 (dark) to -1.35 μA/cm 2 (light) for Sb2Se3 at a bias of -0.7 V. In contrast to Sb2Se3, the SN-5% sample has a much higher current density that increases from -4.56 μA/cm 2 (dark) to -10.93 μA/cm 2 (light) due to the interface electric field of heterojunction. Additionally, the current density drops once light is switched off. Sb2Se3 shows a sharp decrease with a recovery time (τoff) of 0.029 s, whereas all composites both show a slower decay such as SN-5% sample with τoff of 0.076 s (Fig. S8, Supporting Information). This slow decay could be associated with the presence of charge trap centers and other defect states in composites, as already found in previous reports [START_REF] Diliegros-Godines | Effect of Ag doping on structural, optical and electrical properties of antimony sulfide thin films[END_REF][START_REF] Liu | Facile microwave-assisted synthesis of uniform Sb 2 Se 3 nanowires for high performance photodetectors[END_REF][START_REF] Sablon | High-response hybrid quantum dots-2D conductor phototransistors: recent progress and perspectives[END_REF]. The photoresponse has not significant difference during at least 10 cycles, revealing the excellent stability of the selenide composites with internal heterojunctions. The speed of rise and fall for photocurrent is a good indicator of the photosensitivity for a material. Moreover, the photosensitivity (Sph) of Sb2Se3 and composites was calculated by the following formula: Sph = (IL -ID)/ID = (Jph -Jd)/Jd [START_REF] Diliegros-Godines | Effect of Ag doping on structural, optical and electrical properties of antimony sulfide thin films[END_REF],

where IL, ID, Jph, and Jd represent illuminated current, dark current, photocurrent density, J o u r n a l P r e -p r o o f and dark current density, respectively. The Sph values are 0.049, 1.638, 2.102, 2.000, and 1.870 for pure Sb2Se3, SN-2.5%, SN-5%, SN-10%, and SN-15% samples, respectively. It is obvious that the Sph value of pure Sb2Se3 is much lower than that of the composites. It further proved that the composites with internal heterojunctions have much better photosensitivity, resulting in the higher photocurrent density (approximately 180 times) as compared to Sb2Se3. where Jph is the photocurrent density, P is the power density of the incident light, and θ is an exponent [START_REF] Chen | Enhanced electrical conductivity and photoconductive properties of Sn-doped Sb 2 Se 3 crystals[END_REF]. The θ value was obtained by linear fitting in the form of double log-plot. All θ values are smaller than that of low trap state (θ = 1), which can be attributed to the complex process of carriers generation, trapping and recombination in composites [START_REF] Li | Self-powered, high-speed Sb 2 Se 3 /Si heterojunction photodetector with close spaced sublimation processed Sb 2 Se 3 layer[END_REF].

Mechanism of the enhanced PEC performance

On the basis of the above results, the possible mechanism of the enhanced PEC performance of composites is proposed (Fig. 11). The valence band (VB) and the conduction band (CB) potential of Sb2Se3 and NaSbSe2 can be calculated by the following empirical formulae [START_REF] Cao | Novel heterostructured Bi 2 S 3 /BiOI photocatalyst: facile preparation, characterization and visible light photocatalytic performance[END_REF][START_REF] Feng | The highly improved visible light photocatalytic activity of BiOI through fabricating a novel p-n heterojunction BiOI/WO 3 nanocomposite[END_REF]: EVB = X -E e + 0.5 Eg and ECB = EVB -Eg, where EVB is the VB edge potential, ECB is the CB edge potential, Eg is the band gap energy of the semiconductor, X is the electronegativity of the semiconductor, and the values of Sb2Se3 and NaSbSe2 were calculated according to the electronegativity of the constitute J o u r n a l P r e -p r o o f atoms [START_REF] Lagunin | QSAR Modelling of Rat Acute Toxicity on the Basis of PASS Prediction[END_REF]. E e is the energy of free electrons on the hydrogen scale (~ 4.5 eV). As a result, the X values for Sb2Se3 and NaSbSe2 are 5.41 eV and 4.66 eV, respectively. The VB and CB of Sb2Se3 were separately calculated to be 1.48 eV and 0.34 eV. Similarly, the VB and CB of NaSbSe2 correspond to 0.76 eV and -0.44 eV, respectively. The Fermi level of NaSbSe2 is pinned at 0.45 eV above VB from the early report [START_REF] Dai | NaSbSe 2 as a promising lightabsorber semiconductor in solar cells: First-principles insights[END_REF]. The Fermi level in Sb2Se3 laid in the middle of CB and VB [START_REF] Liu | Thermal Evaporation and Characterization of Sb 2 Se 3 Thin Film for Substrate Sb 2 Se 3 /CdS Solar Cells[END_REF] that located at 0.91 eV, which helps us to draw the band diagram. When Sb2Se3 and NaSbSe2 contact with each other, the heterojunction interface is formed with an electric field. Both of Sb2Se3 and NaSbSe2 can be easily excited and produce electron-hole pairs under visible light illumination due to their narrow direct band gaps. The photoinduced electrons could more easily transfer from the CB bottom of NaSbSe2 to that of Sb2Se3 under the effect of interface electric field, while the holes left on the VB top of Sb2Se3 moved in the opposite direction to VB top of NaSbSe2. Therefore, the heterojunction interface, not only improves the separation efficiency of the photogenerated electrons and holes, but also prolong the lifetime of photoinduced carriers, leading to higher photocurrent density.

Conclusion

Selenide composites with in situ synthesized Sb2Se3/NaSbSe2 heterojunctions based on two materials having close band gap energy were successfully prepared via the reaction among Sb, Se and Na by using conventional melt-quenching method, which is favourable for forming a high-quality solid-solid interface without pollution.

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The impedance spectroscopy shows that the composites are electronic conductors and the photo-electro-chemical measurement reveals that the composites have a p-type conducting characteristics. The photocurrent density of composites is firstly reduced and then increased with increasing NaSbSe2 contents, which is related to the decreased grain boundary resistance and increased heterojunction size. The interface electric field of the Sb2Se3/NaSbSe2 heterojunctions helped effectively the separation of the photogenerated electron-hole pairs. The photocurrent density of Sb2Se3 with 2.5 and 5 mol% NaSbSe2 contents was approximately 180 times larger than that of the pure Sb2Se3 at a bias voltage of -1.5 V and under an illumination of 7 mW/cm 2 . Additionally, the composites exhibited an excellent stability even in 0.5 M LiClO4 aqueous electrolyte. Considering the enhanced photocurrent density and the excellent stability, the selenide composite with internal Sb2Se3/NaSbSe2 heterojunctions can be considered as a promising candidate for PEC water splitting and photocatalysis.

Figure captions

Fig. 1

 1 Fig.1shows the XRD patterns of as-prepared selenide composites, obtained on

Fig. 10 (

 10 Fig. 10(b) displays the relationship between the incident light intensity and the

Fig. 1 .

 1 Fig. 1. XRD patterns taken from the pure Sb2Se3, SN-2.5%, SN-5%, SN-10% and SN-

Fig. 2 .

 2 Fig. 2. The liquids projection of Na-Sb-Se system [27].

Fig. 3 .

 3 Fig. 3. Backscattered electron images of (a) SN-2.5% and (b) SN-15%. (c-e) the X-ray

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Fig. 4 .

 4 Fig. 4. Backscattered electron micrograph of etched surface of SN-15% sample and the

Fig. 5 .

 5 Fig. 5. The I-V curve of SN-2.5% sample in the voltage range of -0.8 to 0.8 V. Inset is

Fig. 6 .

 6 Fig. 6. Tauc plot of pure Sb2Se3, NaSbSe2, SN-2.5%, SN-5%, SN-10% and SN-15%

Fig. 7 .

 7 Fig. 7. The frequency dependence of impedance real (Z′) part, impedance imaginary

Fig. 8 .

 8 Fig. 8. Complex impedance plots of Z' versus Z″ (Nyquist plot) at different

Fig. 9 .

 9 Fig. 9. Photoelectrochemical response of pure Sb2Se3, SN-2.5%, SN-5%, SN-10% and

Fig. 10 .

 10 Fig. 10. (a) Time-resolved PEC photoresponse of pure Sb2Se3 and composites at light

Fig. 11 .

 11 Fig. 11. Schematic illustration for the separation and transfer of photogenerated charges

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J o u r

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Table captions Table 1 .

 captions1 The compositions of points 1, 2 and 3 in SN-15% sample.

	Point	Composition (at.%)
		Na	Sb	Se
	1 2 3 J o u r n a l P r e -p r o o f 0 2.48 97.52 24.6 25.3 50.1 0.22 39.34 60.44

Table 2 .

 2 After NaOH (1 M) etching, the compositions of white and gray areas in SN-

	15% sample.
	Area	Composition (at.%)
		Na	Sb	Se
	white	0.55	39.34	60.11
	gray	15.01	29.94	55.05

Table 3 .

 3 The energy gap values of all compounds.

	Sample	Sb2Se3 NaSbSe2 SN-2.5% SN-5% SN-10% SN-15%
	Energy gap (eV) 1.15	1.21	1.18	1.16	1.17	1.17

Table 4 .

 4 Values of Rgb, Rb, R0, resistivity at 25 °C, and activation energy of Sb2Se3,

	NaSbSe2, and composites.
	Sample	Rgb (Ω)	Rb (Ω)	R0 (Ω) Resistivity	Activation energy
					(Ω•cm)	(eV)
	Sb2Se3	2.60×10 5	4.02×10 5	-	2.14×10 6	0.61
	NaSbSe2 1.44×10 6	8.63×10 3	-	8.87×10 5	0.45
	SN-2.5% 1.55×10 4	4.07×10 3	3.70×10 3	1.48×10 4	0.45
	SN-5%	4.66×10 3	1.85×10 3	3.14×10 3	1.20×10 4	0.55
	SN-10% 2.36×10 3	1.55×10 3	3.35×10 3	9.71×10 3	0.60
	SN-15% 3.09×10 3	2.08×10 3	3.39×10 3	2.67×10 3	0.58

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Acknowledgements

This research was supported by CNRS and Université de Rennes 1. We gratefully acknowledge the Chinese Scholarship Council of PR China for providing financial support (201804910786) for D.R. to stay at the ISCR.

J o u r n a l P r e -p r o o f

Declaration of interests

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

J o u r n a l P r e -p r o o f


N Reuge
email: reuge@free.fr

F Collet

S Pretot

S Moissette

M Bart

C Lanos

Modeling of hygrothermal transfers through a bio-based multilayered wall tested in a bi-climatic room

Keywords: Bio-based building materials, Local kinetics, Sorption, Moisture buffering, Hygrothermal transfer, Modeling

A bio-based multilayered wall has been developed in the framework of the European ISOBIO project.

A key point was to be able to perform proper simulations of the hygrothermal transfers occurring through the wall: local predictions are of first importance to characterize the behavior of the wall and thereafter its ability to ensure comfortable hygrothermal conditions inside buildings. A previous study proved that the conventional assumption of an instantaneous equilibrium between local relative humidity and water content according to the sorption isotherm is not relevant for bio-based porous materials, where in practice slow sorption kinetics occur. In the present study, an improved expression of the local kinetics is proposed and validated by sorption experiments. Then, Moisture Buffer Value tests are performed (Nordtest project's protocol). The simulations are adjusted to these measurements by using the inverse method in order to refine the knowledge of some critical parameters. Depending on the studied materials, the local kinetics constants are between 0.15 and 14 day -1 /(kg.m -3 ). Finally, the ISOBIO wall is studied in a bi-climate room under a wide range of operating conditions. Simulations carried out with the conventional approach (TMC) and the local kinetics approach (TMCKIN) are compared to measurements: this clearly shows that the latter is able to predict well the relative humidity dynamics while the former underestimates it by a factor up to 66%. These results highlight the relevance of the new expression of the local kinetics and its ability to describe well the local hygric dynamics is certainly an achievement.

Introduction

In the framework of the European ISOBIO project (featuring the slogan "naturally high-performance insulation"), a multilayered wall made of bio-based materials involving very low carbon footprints and high insulating properties has been developed. One of the key points of this project was to be able to perform reliable simulations of the hygrothermal transfers occurring inside this ISOBIO reference wall. The main difficulty with such simulations is to correctly describe hygric phenomena in bio-based materials. Reuge et al. work on this subject and several studies are already available [START_REF] Reuge | A local kinetics of sorption model: theoretical background and application to the simulation of an ISOBIO demonstrator[END_REF][START_REF] Reuge | Hygrothermal effects and moisture kinetics in a bio-based multi-layered wall: Experimental and numerical studies[END_REF].

Besides their good insulating properties, bio-based materials are usually excellent moisture regulators [START_REF] Douzane | Hygrothermal performance of a straw bale building: In situ and laboratory investigations[END_REF][START_REF] Dhakal | Hygrothermal performance of hempcrete for Ontario (Canada) buildings[END_REF]. In their experimental and modeling study, Mnasri et al. [START_REF] Mnasri | Building incorporated biobased materials: Experimental and numerical study[END_REF] demonstrated the potential of bio-based materials (and more particularly a wood-cement composite) to improve hygrothermal comfort and buildings energy consumption.

Water sorption in porous media involves various phenomena: the transport is ruled by vapor / liquid water diffusion and the water sorption by the equilibrium isotherms of adsorption / desorption coupled with hysteretic phenomena. The diffusivities can be measured by permeability tests (i.e. "wet cup method" [START_REF] Kumaran | Interlaboratory Comparison of the ASTM Standard Test Methods for Water Vapor Transmission of Materials (E 96-95)[END_REF]). The main equilibrium isotherms of sorption also known as "water storage functions" can be measured by gravimetric methods [START_REF] Iglesias | Handbook of Food Isotherms: Water Sorption Parameters for Food and Food Components[END_REF]. The actual water content evolves between the main adsorption and desorption isotherms as a function of the relative humidity along hysteretic paths as described by some rather complex models such as the Carmeliet model [START_REF] Carmeliet | Hysteresis and moisture buffering of wood[END_REF] and the Huang model [START_REF] Huang | A novel hysteresis model in unsaturated soil[END_REF]. They consider local memory effects depending on the full hygroscopic history of the studied materials.

However, the aforementioned models are not sufficient to provide a good description of the hygric state in these porous media. Actually, conventional simulations greatly underestimate the time required for the water content to reach the equilibrium. This was shown for bio-based materials: in [START_REF] Nyman | A numerical method for the evaluation of non-linear transient moisture flow in cellulosic materials[END_REF] for cellulosic materials, in [START_REF] Frandsen | A revised multi-Fickian moisture transport model to describe non-Fickian effects in wood[END_REF] and [START_REF] Eitelberger | The sorption behavior of wood studied by means of an improved cup method[END_REF] for wood, in [START_REF] Alexandersson | Triphasic model of heat and moisture transport with internal mass exchange in paperboard[END_REF] for paperboard, by Reuge et al. in [START_REF] Reuge | A local kinetics of sorption model: theoretical background and application to the simulation of an ISOBIO demonstrator[END_REF] and [START_REF] Reuge | Hygrothermal effects and moisture kinetics in a bio-based multi-layered wall: Experimental and numerical studies[END_REF] for ISOBIO materials and in [START_REF] Reuge | Modèle de cinétique locale de sorption couplé au phénomène d'hystérésis pour les matériaux biosourcés[END_REF] and [START_REF] Reuge | Water transport in bio-based porous materials: A model of local kinetics of sorption-Application to tree hemp concretes[END_REF] for various hemp-lime concretes, but also for more classic compounds such as cements [START_REF] Johannesson | A numerical approach for non-linear moisture flow in porous materials with account to sorption hysteresis[END_REF][START_REF] Janssen | Experimental study of dynamic effects in moisture transfer in building materials[END_REF]. These deviations obtained from conventional models are of particular concern when hygric transfers are subject to permanent fluctuations of relative humidity (RH) such as in building envelope materials, food materials or soils. Several expressions for the local kinetics of sorption can be found in the aforementioned references. A kinetics is usually expressed as a kinetic constant multiplied by a driving force. In most of the aforementioned studies, the authors have proposed to express the driving force as a function of local relative humidities with more or less success. The problem is that they consider an equilibrium relative humidity which is a priori not known for a local approach and / or they have to change the value of the kinetics constant according the operating conditions. Actually, it seems more natural to express the driving force as a function of the local water content, as done by Nyman et al. [START_REF] Nyman | A numerical method for the evaluation of non-linear transient moisture flow in cellulosic materials[END_REF] and Johannesson and Nyman [START_REF] Johannesson | A numerical approach for non-linear moisture flow in porous materials with account to sorption hysteresis[END_REF]. This will be detailed in section 4.1.

Thus, conventional approaches describing hygrothermal transfers in building materials are based on the assumption that for a given local relative humidity ϕ, the corresponding equilibrium local water content w is reached instantaneously (Künzel approach [START_REF] Künzel | Simultaneous Heat and Moisture Transport in Building Components -One-and Two-Dimensional Calculation Using Simple Parameters[END_REF]). In our previous studies [START_REF] Reuge | A local kinetics of sorption model: theoretical background and application to the simulation of an ISOBIO demonstrator[END_REF][START_REF] Reuge | Hygrothermal effects and moisture kinetics in a bio-based multi-layered wall: Experimental and numerical studies[END_REF][START_REF] Reuge | Modèle de cinétique locale de sorption couplé au phénomène d'hystérésis pour les matériaux biosourcés[END_REF][START_REF] Reuge | Water transport in bio-based porous materials: A model of local kinetics of sorption-Application to tree hemp concretes[END_REF], various bio-based materials were studied and it was demonstrated that such an assumption led to patent inconsistencies such as a water vapor / liquid water equilibrium reached too fast at the local scale and at the sample scale and / or underestimation of the local RH dynamics. Thus, as reported in the aforementioned literature, our previous studies have established that a local kinetics of sorption exists (from water vapor to liquid water and inversely) which can be slow compared to the diffusive phenomena.

In this study, an improved expression of the local kinetics of sorption is proposed and validated by experimental results allowing to obtain better results from the simulations for small time scales (from seconds to a few hours).

To our knowledge, this is the first modeling work studying a fully bio-based multilayered wall in the controlled conditions of a bi-climatic room while various studies have already been carried out considering only one bio-based layer. Moujalled et al. [START_REF] Moujalled | Experimental and numerical evaluation of the hygrothermal performance of a hemp lime concrete building: A long term case study[END_REF] have studied the effect of real climatic conditions (Périgueux, FR) on a bio-based building with a wall of three layers: a hemp-lime concrete but with classic internal and external renders. Their results of the simulations were broadly in good agreements with the measurements but the small time scale (on a few hours) RH dynamics was very notably underestimated. Piot et al. [START_REF] Piot | Hygrothermal behaviour of a hemp concrete wall: experimental and numerical study of coating[END_REF] have also studied a three-layered wall (Savoie, FR) in real climatic conditions: a hemp concrete wall but also with classic internal and external renders. Again, the calculated small time scale RH dynamics was very notably underestimated compared to the measurements. In the studies of Lelievre et al. [START_REF] Lelievre | Hygrothermal behavior of bio-based building materials including hysteresis effects: Experimental and numerical analyses[END_REF], Colinart et al. [START_REF] Colinart | Experimental and numerical analysis of the transient hygrothermal behavior of multilayered hemp concrete wall[END_REF][START_REF] Colinart | Temperature dependence of sorption isotherm of hygroscopic building materials. Part 2: Influence on hygrothermal behavior of hemp concrete[END_REF], Rahim et al. [START_REF] Rahim | Numerical investigation of the effect of non-isotherm sorption characteristics on hygrothermal behavior of two bio-based building walls[END_REF], Fabbri and McGregor [START_REF] Fabbri | Impact of the determination of the sorption-desorption curves on the prediction of the hemp concrete hygrothermal behaviour[END_REF] and Seng and al. [START_REF] Seng | Scale analysis of heat and moisture transfer through bio-based materials -Application to hemp concrete[END_REF], the authors have studied the response of hemp concrete panels to controlled indoor and outdoor conditions. Even in these controlled operating conditions, most of these studies led to simulation results that underestimate clearly the small time scale RH dynamics. From that point of view, some studies seem to obtain better results playing on the temperature dependence of the sorption isotherms [START_REF] Colinart | Temperature dependence of sorption isotherm of hygroscopic building materials. Part 2: Influence on hygrothermal behavior of hemp concrete[END_REF][START_REF] Rahim | Numerical investigation of the effect of non-isotherm sorption characteristics on hygrothermal behavior of two bio-based building walls[END_REF] or on the slope of the sorption curve [START_REF] Fabbri | Impact of the determination of the sorption-desorption curves on the prediction of the hemp concrete hygrothermal behaviour[END_REF] or on some parameters which have an effect on the hysteretic behavior of the sorption phenomena such as the initial water content (which is usually unknown) and / or on the considered hysteretic model [START_REF] Lelievre | Hygrothermal behavior of bio-based building materials including hysteresis effects: Experimental and numerical analyses[END_REF].

The first part of this study is a summary of the classic hygric and thermal properties measured on samples of ISOBIO wall materials. Some classic models are used and adjusted to describe these properties evolutions as a function of water content or relative humidity. Then, the governing equations describing the hygrothermal transfers are given. In the following part, the expression of the sorption rate previously defined is recalled and a fine modeling of the global kinetics of the sorption measurements is used to define the improved expression of the sorption rate. This allows better predictions at the beginning of the sorption process. Then, MBV tests are simulated and adjusted to measurements by the inverse method: these adjustments allow refining the knowledge of some critical parameters. Finally, a hygrothermal study is performed at the wall scale. Experiments are carried out on the ISOBIO test wall under controlled climatic conditions of a bi-climatic room. This provides experimental data to be compared to the simulations based on the classical approach and to the simulations carried out with the new kinetic model, these two approaches leading to different predictions of the local relative humidity dynamics.

ISOBIO materials and hygrothermal properties

Reference ISOBIO wall

The reference ISOBIO wall is made of the layering of several materials / panels: a BCB TM lime-hemp render (BCB), a CAVAC TM Rigid insulation panel made of hemp shiv and an organic binder (CAV), a Biofib Trio flexible insulation panel from CAVAC TM made of hemp flax and cotton (BIO1), an OSB3 panel, a Proclima TM INTELLO membrane (INT), a second Biofib Trio flexible insulation panel (BIO2), a Lignicell CSB TM panel made of compressed straw (CSB) and a CLAYTEC TM clay-hemp plaster (CLA). Note although a timber frame supports this wall, this will be ignored in the simulations. This ISOBIO reference wall and the layers thicknesses are shown in Figure 1.

Hygrothermal properties

This section summarizes the values of the properties needed to perform the simulations, i.e. the materials densities ρ 0 , porosities ε 0 , vapor diffusion resistance factors μ 0 , thermal conductivities λ 0 and specific heat capacities Cp 0 : they are reported in Table 1. While most of them come from [START_REF] Collet | Hygric properties of materials used for ISOBIO wall solution for new buildings[END_REF] where experimental methods and measurement are provided, a few others come from trustable technical sheets.

The isotherms of adsorption of representative samples of ISOBIO materials (CAV, BIO, OSB3 and CSB) have been determined in [START_REF] Collet | Hygric properties of materials used for ISOBIO wall solution for new buildings[END_REF]. The moisture storage functions of the other ISOBIO materials come from technical sheets and / or Fraunhofer Institute for Building Physics (F-IBP) databases (BCB, INT and CLA).

Models of properties

The appropriate models of properties needed for the simulations have been studied in [START_REF] Reuge | Hygrothermal effects and moisture kinetics in a bio-based multi-layered wall: Experimental and numerical studies[END_REF]. For the isotherms of adsorption, the Van Genuchten model (VG) [START_REF] Van Genuchten | A closed-form equation for predicting the hydraulic conductivity of unsatured soils[END_REF] has been used. It is claimed valid even near the liquid water saturation state and is expressed as follow:

( ) ( ) ( ) 1 1 1 ln η η -   = + -   eq sat W RH W h RH (1)
where W eq is the sample water content at equilibrium, W sat is the maximum water content in the sample, h and η are adjustment coefficients. The values of these adjustment coefficients are given in Table 2 and the experimental and modeled isotherms of adsorption of CAV and CSB are shown in Figure 2.

Figure 2

The hygric dependence of the vapor diffusion resistance factors µ has been neglected except for the Proclima INTELLO because this is a hygrovariable membrane evolving very significantly as a function of the moisture content (from 550 at 100% RH to 136400 at 0% RH). The data provided by Proclima / F-IBP have been fitted by a logistic power law [START_REF] Reuge | A local kinetics of sorption model: theoretical background and application to the simulation of an ISOBIO demonstrator[END_REF][START_REF] Reuge | Hygrothermal effects and moisture kinetics in a bio-based multi-layered wall: Experimental and numerical studies[END_REF] (because of its great values, this parameter must be carefully modeled):

( )

1 . c µ a b RH = +
, with: a = 7.3310 -6 , b = 1.8.10 -3 and c = 7.644.

Finally, the hygric dependence of the thermal conductivities has been described by the selfconsistent scheme [START_REF] Collet | Thermal conductivity of hemp concretes: Variation with formulation, density and water content[END_REF], which takes the following expression:

( ) ( ) ( )( ) ( ) { ( ) ( )( ) ( ) ( ) ( ) 0 0 0 1 1 0 1 1 3 3 1000 1 3 1 1000 1 2 1 λ λ ε ε ε λ λ λ λ ε λ λ λ λ - -  = + - + + -    ⋅ -- - +     s a w a s a w w s W W W (2)
where λ a (0.025 W.m -1 .K -1 ) is the air thermal conductivity and λ w (0.6 W.m -1 .K -1 ) is the liquid water thermal conductivity. The coefficient λ s has been adjusted such as λ(W=0) equals λ 0 . The values of λ s are given in Table 2.

Note that the expressions (1) and ( 2) are written at the sample scale but they remain valid at the local scale replacing RH by the local relative humidity ϕ and W by the local water content w.

Table 2:

Adjustment coefficients for the VG model (h and η) and the self-consistent scheme (λ s )

3 Mathematical modeling

Mass transport governing equations

As classically assumed, (i) air transport is ignored. In the porous materials, water is present as water vapor and liquid. Thus, two mass balance equations have to be considered. Assuming that (ii) the convective transport is negligible, they are given by (cf. [START_REF] Reuge | A local kinetics of sorption model: theoretical background and application to the simulation of an ISOBIO demonstrator[END_REF][START_REF] Reuge | Hygrothermal effects and moisture kinetics in a bio-based multi-layered wall: Experimental and numerical studies[END_REF][START_REF] Reuge | Water transport in bio-based porous materials: A model of local kinetics of sorption-Application to tree hemp concretes[END_REF]):

( ) ( ) ( ) , , sat v p sat s w w p l s P RT RT P R t M M w D w R t ϕ δ ϕ ∂   -∇ ⋅ ∇ = -     ∂    ∂  -∇ ⋅ ∇ =  ∂  (3,4)
where the porous media vapor permeability is given by: ,

v p v v w D M RT δ δ µ µ = =
and the water vapor diffusion resistance factor by:

, , v v p v p v D D µ δ δ = =
, D p,v and D p , l being the water vapor and liquid water diffusivities in the porous media respectively.

The sorption rate R s will be detailed in section 4. It is commonly assumed that R s is very fast compared to the vapor diffusive flux. This is not the case for the bio-based materials studied here. Note that according to this common assumption, the following single governing equation can be obtained:

, , 0 v p sat p l T T w w P D t ϕ δ ϕ ϕ ϕ     ∂ ∂ ∂ -∇ ⋅ + ∇ =     ∂ ∂ ∂       (5)
Equation ( 5) is the so-called Künzel mass transfer equation [START_REF] Künzel | Simultaneous Heat and Moisture Transport in Building Components -One-and Two-Dimensional Calculation Using Simple Parameters[END_REF].

The classic heat transport governing equation is not given here but it is obviously taken into account considering latent heat of vaporization.

Boundary conditions

At the wall or sample edge edg i , the local relative humidity is given by:

W sat (kg.m -3 ) h (-) η (-) λ s (W.m -1 .K -
, i i v p edg edg m RH h δ ϕ ϕ = - ⋅∇ (6)
where h m is the mass transfer coefficient. The local water content gradient is given by:

i i edg edg T w w β ϕ ϕ ∂ ∇ = ∇ ∂ (7)
where β is in the range of 0 to 1 and dynamically depends on the sorption rate R s . Its value will be considered as a constant value of 1. It was shown in [START_REF] Reuge | A local kinetics of sorption model: theoretical background and application to the simulation of an ISOBIO demonstrator[END_REF][START_REF] Reuge | Water transport in bio-based porous materials: A model of local kinetics of sorption-Application to tree hemp concretes[END_REF] that its value (0 or 1) does not impact the simulation results.

Improvement and validation of the local kinetic model of sorption 4.1 State of the art

In their studies, Nyman et al. [START_REF] Nyman | A numerical method for the evaluation of non-linear transient moisture flow in cellulosic materials[END_REF] and Johannesson and Nyman [START_REF] Johannesson | A numerical approach for non-linear moisture flow in porous materials with account to sorption hysteresis[END_REF] have proposed the following expression for the sorption rate:

( ) ( ) 0 ϕ = - s eq R k w w (8)
where k 0 is the local kinetic constant of sorption (adsorption or desorption) and w eq is the equilibrium local water content given by the sorption isotherm at a local relative humidity ϕ.

Independently, our very first investigations have led to establish the same expression. However, the value of the kinetic constant k 0 still has to be adjusted as a function of the operating conditions: this was not really satisfactory, the local kinetic constant should only depend on the porous materials and not on the hygric conditions, at least as long as the hygric state is far from saturation.

From Reuge et al. [START_REF] Reuge | Modèle de cinétique locale de sorption couplé au phénomène d'hystérésis pour les matériaux biosourcés[END_REF][START_REF] Reuge | Water transport in bio-based porous materials: A model of local kinetics of sorption-Application to tree hemp concretes[END_REF], the sorption rate R s is preferably expressed as follow:

( ) ( )

2 0 ϕ = ± - s eq R k w w (9)
where k 0 (day -1 /(kg.m -3 )) is a kinetic constant of a second order kinetics. The sign in front of k 0 is the same as the sign of ( ) ( ) ϕeq w w , i.e. plus for adsorption, minus for desorption. Using this second order local kinetics, k 0 can be kept constant for a wide range of RH, at least between 30% and 70% RH [START_REF] Reuge | Modèle de cinétique locale de sorption couplé au phénomène d'hystérésis pour les matériaux biosourcés[END_REF][START_REF] Reuge | Water transport in bio-based porous materials: A model of local kinetics of sorption-Application to tree hemp concretes[END_REF].

Sorption experiments and improvement of the sorption rate expression

Figure 3 shows the kinetics of water adsorption of a CAV sample [START_REF] Collet | Hygric properties of materials used for ISOBIO wall solution for new buildings[END_REF]. The sample had been initially stabilized at a given RH and suddenly submitted to a greater ambient RH (0-30% RH, 30-50% RH and 50-65% RH). For the 0-30% RH and 50-65% RH steps, the sample has been weighted continuously whereas for the 30-50% RH step, only discontinuously values are available due to a computer failure. In Fig. 3, the measurements and the results of the simulations of these tests are compared. As an illustration, a simulation has been carried out using the Künzel approach for the 30-50% RH step: the stabilization is predicted after two days while it takes weeks according to the measurements (Fig. 3). Then, simulations have been carried out using expression [START_REF] Huang | A novel hysteresis model in unsaturated soil[END_REF] for the sorption rate with the kinetic constant k 0 as adjustment parameter. Broadly, the adjustments are good but if the comparison is focused at the very beginning of the process, it appears that the adjustments are not so good, this is particularly noticeable within the first day: the simulations tend to underpredict the adsorption rate. Thus, the following new expression is proposed for the sorption rate: [START_REF] Nyman | A numerical method for the evaluation of non-linear transient moisture flow in cellulosic materials[END_REF] where k 01 (day -1 /(kg.m -3 )) and k 02 (m 3 .kg -1 ) are kinetic constants. As shown in Figure 3, very good adjustments are obtained using k 01 equal to 0.75k 0 (k 0 = 0.56 day - 1 /(kg.m -3 ) for 0-30% RH step and k 0 = 0.3 day -1 /(kg.m -3 ) for 30-50% RH and 50-65% RH steps) and values of k 02 equal to 0.5.10 5 m 3 .kg -1 for the 0-30% RH step and 3.10 5 m 3 .kg -1 for the 30-50% RH and 50-65% RH steps. Considering the first two days of the 0-30% RH step, the correlations coefficients r between the measurements and the simulations carried out using the kinetics model ( 9) and ( 10) are of 0.997 and 0.999 respectively. Considering the first two days of the 50-65% RH step, the correlations coefficients r between the measurements and the simulations carried out using the kinetics model ( 9) and ( 10) are of 0.994 and 0.999 respectively. They are clearly in favor of the kinetics model [START_REF] Nyman | A numerical method for the evaluation of non-linear transient moisture flow in cellulosic materials[END_REF].

( ) ( ) 2 01 02 ϕ ϕ ∂   = ± + -   ∂   s eq R k k w w t
For standard operating conditions (RH > 30%), the following expression of the sorption rate can be deduced:

( ) ( ) 2 6 0 0.75 10 ϕ ϕ ∂   = ± + -   ∂   s eq R k w w t (11)
There is no guarantee that this expression is valid whatever the bio-based material but it will be assumed to be so. However, note that this expression allows to carry out sorption simulations that are in agreement with the measurements for all the studied ISOBIO materials and also for the hemp concretes studied in [START_REF] Reuge | Water transport in bio-based porous materials: A model of local kinetics of sorption-Application to tree hemp concretes[END_REF].

From [START_REF] Reuge | Hygrothermal effects and moisture kinetics in a bio-based multi-layered wall: Experimental and numerical studies[END_REF], the values of the kinetic constant k 0 are given in Table 3. Its values for OSB3, INT and CLA remain unknown. Figure 3 Table 3: ISOBIO materials kinetic constants k 0 obtained by adjusting simulations to sorption measurements [START_REF] Reuge | Hygrothermal effects and moisture kinetics in a bio-based multi-layered wall: Experimental and numerical studies[END_REF] k 0 (day -1 /(kg.m -3 )) BCB 0.005 CAV 0.3 BIO 14 CSB 0.25

MBV tests: measurements and simulations

Measurements

Representative samples of ISOBIO materials have been subject to standard Moisture Buffer Value (MBV) tests according to the Nordtest project's protocol [START_REF] Collet | Hygric properties of materials used for ISOBIO wall solution for new buildings[END_REF]. It relates the amount of moisture uptake / release to the exchange area and to the relative humidity step during daily cyclic variations (8 hours at ≈75% RH, and 16 hours at ≈33% RH). The recorded ambient RH is shown in Figure 4 (smoothed curve). Note that the last cycle is uncomplete due to technical issues.

The obtained MBV values have been reported in [START_REF] Collet | Hygric properties of materials used for ISOBIO wall solution for new buildings[END_REF], they are of 1.7, 0.77, 1 and 0.53 g/(m².%RH) for CAV, CSB, BCB and OSB3 respectively. For the present study, it is interesting to consider the temporal evolution of the relative water mass Δm w of the samples during the tests. The results of these measurements are presented in Figures 5 (CAV), 6 (CSB), 7 (BCB) and 8 (OSB3).

Simulations

Then, simulations have been carried out with home-made 1D Cartesian tools, TMC based on the Künzel approach ( 5) and TMCKIN based on the kinetics approach [START_REF] Douzane | Hygrothermal performance of a straw bale building: In situ and laboratory investigations[END_REF][START_REF] Dhakal | Hygrothermal performance of hempcrete for Ontario (Canada) buildings[END_REF][START_REF] Frandsen | A revised multi-Fickian moisture transport model to describe non-Fickian effects in wood[END_REF]. Initially, the samples had been stabilized at 50% RH at a temperature of 22.6°C, these initial conditions have been used for the simulations. The mass transfer coefficient h m at the exposed samples surface has been considered equal to 4.10 -8 kg.m -2 .Pa -1 .s -1 [START_REF] Mortensen | Effect of airflow velocity on moisture exchange at surfaces[END_REF][START_REF] Talev | Measurement of the convective moisture transfer coefficient from porous building material surfaces applying a wind tunnel method[END_REF].

The right amplitudes of the W variations have been obtained by adjusting the water vapor diffusion resistance factor µ to a value between µ 0 (25% RH) and the lower µ humid (70.5% RH, see [START_REF] Collet | Hygric properties of materials used for ISOBIO wall solution for new buildings[END_REF]) for each material: this is consistent with the actual water content of the materials.

As shown in Figures 5 (CAV) and 6 (CSB), the results of the simulations are in good agreements with the measurements but the results obtained with TMCKIN appear significantly better than those obtained with TMC. The simulations named "TMC bis" are carried out with TMC using the values of µ obtained from the adjustments of TMCKIN simulations. Note that with TMC, the adjustment for CSB was not possible with µ between µ humid and µ 0 , a greater value than µ 0 had to be considered. Regarding BCB (Fig. 7), results are not good at all with TMC, no adjustment could be done since µ 0 and µ humid have the same value of 9 (from measurements performed at University of Bath) ; in order to obtain a decent adjustment with TMCKIN, a value of k 0 of 0.15 day -1 /(kg.m -3 ) has to be considered instead of the previous value of 0.005 day -1 /(kg.m -3 ) given in Table 3: this is not surprising since the data used in [START_REF] Reuge | Hygrothermal effects and moisture kinetics in a bio-based multi-layered wall: Experimental and numerical studies[END_REF] to determine this kinetic constant were not appropriate (i.e. desorptions from 100% RH, far beyond the common range of RH).

Finally, as shown in Figure 8 for OSB3, the adjustment with TMCKIN has allowed to determine a value of k 0 for this material, which is 0.4 day -1 /(kg.m -3 ).

According to these results, some values of k 0 can be updated as shown in Table 4. The values of µ used for the adjustments and the correlation coefficients between measurements and simulations are also reported in this table. Note that the correlations coefficients are not always better with TMCKIN than with TMC: this is due to the fact that the adjustments have been carried out considering the minimum and maximum points of the measurements whereas the correlation coefficients have been calculated with respect to all the experimental points. It is also important to note that some tries have been carried out using the old expression ( 9) of the kinetics model but it was quite impossible to obtain as good adjustments as with the new expression [START_REF] Frandsen | A revised multi-Fickian moisture transport model to describe non-Fickian effects in wood[END_REF]: the amplitudes of the W variations were systematically underestimated; The only solution to obtain descent adjustments with ( 9) was to consider greater k 0 , typically by one order a magnitude: this is obviously not satisfactory and support the relevancy of the model [START_REF] Frandsen | A revised multi-Fickian moisture transport model to describe non-Fickian effects in wood[END_REF].

For the CAV material, Figure 9 shows full hygric cycles (w, ϕ) obtained with TMC and TMCKIN between t = 48 h and t = 72 h at 2 mm and 2 cm depths. According to the TMC simulation results, (w, ϕ) logically moves along the adsorption isotherm whereas the TMCKIN simulation leads to (w, ϕ)

moving around this adsorption isotherm.

Still for the CAV material, Figure 10 shows the water content profiles and the relative water content distributions referring to the initial water content W eq (50% RH) as a function of sample depth at t = 48 h and t = 56 h obtained with (a) TMC and (b) TMCKIN. Regarding the water content distributions, mean values corresponding to slices of 1 cm depth are estimated integrating the calculated local water contents.

Note that the MBV measurements [START_REF] Collet | Hygric properties of materials used for ISOBIO wall solution for new buildings[END_REF] have been carried out on a 5 cm deepness sample of this material, i.e. exactly the deepness of the CAV panel in the ISOBIO reference wall.

Figure 10 The water content variations predicted by TMC between 3 cm and 4 cm (Fig. 10a) and by TMCKIN between 4 cm and 5 cm (Fig. 10b) are so low that the MBV values are very slightly affected by these slices; Thus, the penetration depth is slightly greater according to TMCKIN simulation than according to TMC simulation. From TMC and TMCKIN simulations, minimum sample depths of 4 cm and 5 cm are respectively required to ensure a very reliable MBV determination for the CAV sample. 6 Study of the ISOBIO wall in a bi-climatic room

k 0 (day -1 /(kg.m -3 )) µ (TMC)

Experimental setup

The ISOBIO reference wall has been studied in the controlled environments of a bi-climatic room (Figure 11). The walls of the bi-climatic room are made of rigid insulation panels covered with steel sheets and the floor is a concrete slab, meaning the humidity or thermal exchanges between indoor and outdoor remain low. The ISOBIO wall (surface of about 1.2 m 2 ) acted as separation between the two climatic rooms. Temperature and relative humidity have been measured thanks to 41 sensors (SHT35 Sensirion sensors) placed at different depths inside the wall and additional sensors were placed on the wall surfaces and in ambient environments.

Operating conditions

The measurements performed can be divided in three main period, 1, 2 and 3. The boundary conditions applied (i.e. T and RH at the wall surfaces) are shown in Figures 12a&b,12c&d, 12e&f for the periods 1 (1128 h), 2 (340 h) and 3 (148 h) respectively. The room contiguous to the BCB render is called "outdoor" while the room contiguous with the CLA plaster is called "indoor".

Initially, before period 1, the wall has been stabilized at 50% RH, 23°C but some chamber regulation tests performed just before period 1 may have result in a loss of the wall stabilization. During period 1, some monitoring issues had occurred around a time of 400 h, during this interval, RH and T setpoints are considered as boundary conditions (i.e. flat part). Period 2 is consecutive to period 1. Period 3 is not consecutive to period 2 but the wall has been stabilized again at 50% RH, 23°C before this last period.

6.3 Comparison of measurements and simulations

Assumptions

Simulations have been carried out with TMC and TMCKIN, assumptions are given in sections 3 and 4.

Regarding TMCKIN simulations, expression [START_REF] Frandsen | A revised multi-Fickian moisture transport model to describe non-Fickian effects in wood[END_REF] of the sorption rate have been considered. ISOBIO materials kinetic constants k 0 given in Table 4 have been used. For INT and CLA layers, the associated k 0 are unknown but a median value of 0.25 day -1 /(kg.m -3 ) has been considered. No hysteric effect has been considered for the sorption mechanism. For the materials BCB, CAV, OSB3 and CSB, the values of µ obtained from the adjustments (TMC & TMCKIN) in the previous section (Table 4) have been considered. For BIO and CLA, µ 0 has been considered (cf. Table 1). For INT, the logistic power law of µ has been used (cf. section 1).

At the beginning of period 1 and period 3, the wall is assumed stabilized at 50% RH, 23°C. The initial conditions of period 2 are the final conditions of period 1. Lastly, RH and T have been measured at the wall surfaces (Fig. 12) and therefore are considered as Dirichlet boundary conditions for the simulations.

Results and discussion

The results (measurements and simulations) are analyzed at these positions equipped with (RH-T) sensors:

-position 1, CAV / BIO1 interface (8 cm depth), -position 2, BIO1 / OSB3 interface (22.5 cm depth), -and position 3, INT / BIO2 interface (23.75 cm depth).

As shown in Figure 13a, temporal evolutions of RH obtained by TMCKIN fit more closely the measurements than those obtained by TMC, at position 1 during period 1. At positions 2 and 3 (Fig 13b and13c), TMC and TMCKIN simulations are very close but underpredict RH (by 5% at most) likely due to inadequate initial conditions: technical issues have indeed disturbed the hygric stabilization prior to period 1 resulting in somewhat imperfect knowledge of initial hygric state and hygric history of the wall and then in the simulations offsets. In Figure 13b, TMC simulation underestimates the RH fluctuation by 18.5% while TMCKIN simulation underestimates it by only 11%.

As shown in Figure 14a, i.e. at position 1 during period 2, TMC simulation underpredicts the amplitude of the RH variations by 30% whereas TMCKIN results overpredict them by 40%. A position 2 (Fig. 14b), TMC simulation largely underpredicts the RH variations by 66%, TMCKIN simulation is much closer to the measurements even if it still underpredicts the RH variations by 12%. At position 3 (Fig. 14c), TMCKIN simulation still leads to better results than TMC predicting exactly the amplitude of the RH variations. Overall, discrepancies that still persists between TMCKIN simulation and measurements can be imputed to not taking into account the hysteretic phenomena (note that this would demand a perfect knowledge of the whole hygric history of the wall).

As shown in Figure 15a and 15b, i.e. at position 1 & 2 during period 3, TMCKIN simulation better predicts the RH variations than TMC simulation. At position 2, this is more clearly illustrated in Figure 16 where the TMC & TMCKIN RH curves has been raised by a value of +2%RH to compensate the offsets: the correlation coefficients between measurements / TMC simulation and measurements / TMCKIN simulation are of 0.824 and 0.896 respectively. In other words, with TMCKIN, the RH dynamics is better predicted. This is obviously an effect of the sorption kinetics model. Note that the temperatures evolutions predicted by the simulations are not presented here but they are in perfect accordance with the measurements. Finally, TMCKIN simulations are overall in significantly better agreement with the measurements than TMC simulations. It clearly shows the benefit of using the sorption kinetics model [START_REF] Frandsen | A revised multi-Fickian moisture transport model to describe non-Fickian effects in wood[END_REF] on the RH dynamics prediction.

Conclusions

The huge campaign of characterization and testing of the ISOBIO materials has allowed to carry out hygrothermal transfers simulations.

It has been shown that the expression of the local sorption rate used in previous studies could be improved to better describe the early beginning of the sorption process. The global sorption measurements performed at the scale of a large sample have allowed to validate the new expression of this model: this is the first step forward brought by this study.

Then, the simulations carried out with TMC (based on Künzel approach) and TMCKIN (based on the kinetics of sorption model) have been adjusted on some Moisture Buffer Value measurements. The results obtained with TMCKIN are in good agreement with measurements. It is worth noting that TMCKIN predicts slightly deeper moisture penetration depths than TMC. These results can be of some interest to guide the experimenters in performing Moisture Buffer Value measurements: this is the second step forward brought by this study.

Finally, the ISOBIO reference wall has been studied in a bi-climatic room with in-situ RH measurements: this is an unprecedented experimental work for a multilayered fully bio-based wall. This wall was submitted to various hygrothermal conditions. Simulations have been carried out and compared to the measurements. It has been shown that TMCKIN led to better results than TMC predicting more realistic relative humidity dynamics. It shows the pertinence of the new sorption kinetics model, this is an achievement in the considered field. The underestimation of the relative humidity dynamics by the conventional model would lead to erroneous prediction of hygric conditions inside rooms for future whole building simulations, this is why the new approach presented in this study should be considered.

Future investigations possibly lead to even better results trying to take into account the hygric history of the wall more precisely.

Nomenclature

Latin symbols

Cp 0 Specific heat capacity at dry state (J.kg -1 .K -1 )

D v

Vapor diffusivity in air (m 2 .s -1 )

D p,v

Vapor diffusivity in a porous medium (m 2 .s -1 )

D p,l

Liquid water diffusivity in a porous medium (m 2 .s -1 ) h Adjustment coefficient according to eq. ( 1)

h m Mass transfer coefficient (kg.m -2 .Pa -1 .s -1 )
k 0 Local kinetic constant defined in eq. ( 5) (day -1 /(kg.m -3 ))

k 01
Local kinetic constant defined in eq. ( 9) (day -1 /(kg.m -3 ))

k 02
Local kinetic constant defined in eq. ( 9) (m.kg -3 )

M w

Water molar mass (kg.mol -1 )

P sat Saturation vapor pressure in air (Pa) r Correlation coefficient (-) R Gas constant (J.mol -1 .K -1 )

R s

Sorption rate (kg.m -3 .s -1 )

RH

W (kg.m -3 )

Künzel approach (k0 = ∞)

Figure 16

Time (h) RH (%)

Figure 1

 1 Figure 1

  slow diffusion of bound water molecules in the biological cells as explained in[START_REF] Reuge | Water transport in bio-based porous materials: A model of local kinetics of sorption-Application to tree hemp concretes[END_REF], the new term 02 sudden capillary sorption of water in the macropores due to the Kelvin effect[START_REF] Collet | Porous structure and water vapour sorption of hemp-based materials[END_REF] occurring immediately during a sudden variation of local relative humidity ϕ. This new expression has the advantage to complexify the previous expression of the sorption rate (9) without denaturing its physical sense, expression(10) tends towards expression (9) in the absence of stiff variation of ϕ.

Figure 7

 7 Figure 7

Figure 8

 8 Figure 8

Figure 14 Figure 15

 1415 Figure 14Figure15

Figure 16

 16 Figure 16

wβFigure 1 :Figure 2 :Figure 3 :

 123 Figures captions

Figure 4 :Figure 5 :Figure 6 :Figure 7 :Figure 8 :Figure 9 :

 456789 Figure 4: MBV test (Nordtest project's protocol) -Smoothed curve of the ambient RH Figure 5: Temporal evolution of relative water mass in the CAV sample -Measurements, TMC & TMCKIN simulations Figure 6: Temporal evolution of relative water mass in the CSB sample -Measurements, TMC & TMCKIN simulations Figure 7: Temporal evolution of relative water mass in the BCB sample -Measurements, TMC & TMCKIN simulations Figure 8: Temporal evolution of relative water mass in the OSB3 sample -Measurements, TMC & TMCKIN simulations Figure 9: CAV sample submitted to hygric cycles, results between t = 48 h and t = 72 h, local results from TMC & TMCKIN simulations at 2 mm and 2 cm depths

Figure 10 :Figure 11 :Figure 12 :Figure 13 :Figure 14 :Figure 15 :Figure 16 :

 10111213141516 Figure 10: CAV sample -Water content profiles and relative water content distributions by slices of 1 cm compared to initial water content W eq (50% RH) as a function of sample depth at t = 48 h (black) and t = 56 h (red) -TMC (a) & TMCKIN (b) simulations Figure 11: General view of the bi-climatic room used for this study, monitoring systemFigure 12: RH and T measured at the wall surfaces during period 1, (a) and (b), period 2, (c) and (d), and period 3, (e) and (f) Figure 13: Temporal evolution of RH at positions 1 (a), 2 (b) and 3 (c) -Period 1 -Measurements, TMC & TMCKIN simulations Figure 14: Temporal evolution of RH at positions 1 (a), 2 (b) and 3 (c) -Period 2 -Measurements, TMC & TMCKIN simulations Figure 15: Temporal evolution of RH at positions 1 (a), 2 (b) and 3 (c) -Period 3 -Measurements, TMC & TMCKIN simulationsFigure 16: Temporal evolution of RH at positions 2 -Period 3 -Measurements, TMC results +2%RH & TMCKIN results +2%RH

Figures 1 and 4

 4

2 - 15 Figure 1 CAVAC

 2151 Figure 1

Figure 11 Figure 12 RH

 1112 Figure 4

Table 1 :

 1 ISOBIO materials properties at dry state at T = 23°C with margins of error

		ρ 0	ε 0	µ 0	λ 0	Cp 0
		±5%	±5%	±10%	±5%	±10%
		(kg.m -3 )	(-)	(-)	(W.m -1 .K -1 )	(J.kg -1 .K -1 )
	BCB	530	0.546	9	0.13	1006
	CAV	190	0.874	11	0.07	2100
	BIO	26.5	0.98	3.6	0.039	1800
	OSB3	551	0.609	138	0.13	1600
	INT	85	0.085	1.364.10 5	2.4	2500
	CSB	449	0.72	27	0.10	1700
	CLA	1392	0.294	10	0.62	1040

Table 4 :

 4 ISOBIO materials kinetic constants k 0 updated, values of µ obtained from adjustments of TMC and TMCKIN on MBV tests and correlation coefficients r Note that the adjusted values of µ are lower with TMCKIN than with TMC (and then closer to µ humid ).

Acknowledgments

This work has been performed and funded in the framework of the European project ISOBIO -(http://isobioproject.com) within the scope the of the research and innovation program Horizon 2020 (agreement No. 636835). This work has also been supported by the French region Bretagne Loire (UBL). Article highlights -Improvement of the local kinetics of sorption model -Comparisons of measurements / simulations of Moisture Buffer Value tests according to the Nordtest project's protocol -One of the first comparisons of measurements / simulations of a fully bio-based porous wall in the controlled environment of a bi-climatic chamber

Declaration of interest:

None