Florence Collet
email: florence.collet@univ-rennes1.fr

Julien Chamoin
email: julien.chamoin@univ-rennes1.fr

Sylvie Pretot
email: sylvie.pretot@univ-rennes1.fr

Christophe Lanos
email: christophe.lanos@univ-rennes1.fr

Comparison of the hygric behaviour of three hemp concretes

Hemp concrete is a bio-based building material the main qualities of which are its low environmental impact and its hygrothermal behaviour. Even for one kind of application (for example: wall), several compositions and manufacturing methods are encountered in the market. This study compares the hygroscopic behaviour of three hemp concretes used for building walls to identify whether composition and manufacturing have an impact on hygric properties. The investigations are based on the measurement of the sorption curve, of the water vapour permeability versus humidity and of the moisture buffer value. Moisture diffusivity is calculated from the sorption curve and from the water vapour permeability. The results underline the high transfer and storage capacities of these materials; they are classified as excellent (or nearly excellent) hygric regulators. A slight effect of porosity, connected with composition and manufacturing method, is observed.

Introduction

The hygrothermal behaviour of building envelopes impacts on energy needs, indoor comfort and indoor air quality. This behaviour depends on thermal and hygric properties of building materials like thermal conductivity, heat capacity, sorption curve and water vapour permeability. The use of hygroscopic materials appears as a good solution to reduce energy needs while maintaining high indoor comfort [START_REF] Cerolini | Moisture buffering capacity of highly absorbing materials[END_REF][START_REF] Simonson | Heat and mass transfer between indoor air and a permeable and hygroscopic building envelope: part 1 -field measurements[END_REF][START_REF] Simonson | Heat and mass transfer between indoor air and a permeable and hygroscopic building envelope: part 2 -verification and numerical studies[END_REF][START_REF] Osanyintola | Moisture buffering capacity of hygroscopic building materials: experimental facilities and energy impact[END_REF]. In order to understand and predict the hygrothermal behaviour of a building envelope implemented with such materials, numerical studies can be made. These studies are generally based on experimental data of sorption curve and water vapour permeability; and it was shown that, for hygroscopic materials, the uncertainty on this kind of data hampers reliable simulation of hygroscopic buffering [START_REF] Roels | Reliability of material data measurements for hygroscopic buffering[END_REF]. In order to characterise the moisture buffering capacity of hygroscopic materials, dynamic experimental methods have thus been developed during the last 10 years [START_REF] Rode | Moisture buffer value of materials in buildings[END_REF][7][8][START_REF] Osanyintola | Effect of initial conditions, boundary conditions and thickness on the moisture buffering capacity of spruce plywood[END_REF]. In this study, we focus on the case of hemp concrete and we use several experimental methods to identify its hygrothermal behaviour.

Hemp concrete is a bio-based building material that was rediscovered at the end of the 20th century and has been improved over the last 20 years. Its main qualities are its low environmental impact due to bio-sourced components [START_REF] Boutin | Etude des caractéristiques environnementales du chanvre par l'analyse de son cycle de vie[END_REF][START_REF] Garnier | Life assessment of hemp concrete wall manufactured by spraying, in: 2nd International conference on building energy and environment[END_REF] and its hygrothermal behaviour. This material is made of hemp shiv mixed with a mineral binder. According to its composition, it can be used for several applications: wall, floor and roof. Moreover, even for one kind of application, several compositions and manufacturing methods are encountered on the market. Hemp concrete shows low compressive strength [START_REF] Elfordy | Mechanical and thermal properties of lime and hemp concrete ("hempcrete") manufactured by projection process[END_REF][START_REF] Arnaud | Experimental study of parameters influencing mechanical properties[END_REF][START_REF] De Bruijn | Mechanical properties of lime-hemp concrete containing shives and fibres[END_REF] so, it is used as filling material associated with a wooden frame. From a thermal point of view, hemp concrete shows a low thermal conductivity (about 0.1 W/m/K [START_REF] Arnaud | Mechanical and thermal properties of hemp mortars and wools: experimental and theoretical approaches[END_REF][START_REF] Pretot | Variation des propriétés thermiques de bétons de chanvre en fonction de la formulation[END_REF]), so it is a good insulator that can be used without an added insulation layer. From a hygric point of view, hemp concrete was characterised with steady-state methods (sorption curve, water vapour permeability). It was shown that hemp concrete has high moisture transfer and storage capacities [START_REF] Collet | Porous structure and water vapour sorption of hemp-based materials[END_REF][START_REF] Evrard | Hygrothermal performance of lime-hemp wall assemblies[END_REF]. Recently, hemp concrete was also characterised with a dynamic method; it was emphasised that this material is an excellent hygric regulator [START_REF] Collet | Experimental investigation of moisture buffering capacity of sprayed hemp concrete[END_REF]. Finally, the hygrothermal behaviour of hemp concrete was studied at full-scale. Pretot and Collet [START_REF] Pretot | Experimental Study of Hygrothermal Behavior of a Hemp Concrete Wall (Without and With Coating)[END_REF] have shown that simultaneous heat and moisture flows can lead to huge vapour pressure variations in the wall linked with sorption phenomena. Shea et al. [START_REF] Shea | Hygrothermal performance of an experimental hemp-lime building[END_REF] have shown that the energy performance of an experimental hemp-lime building was higher than predicted from SAP rating and U-value calculations. It was emphasised that relative humidity influences the dynamic behaviour of hemp concrete. Numerical studies have shown that the transient hygrothermal behaviour of hemp concrete can reduce the energy demand of a building while maintaining indoor relative humidity [START_REF] Evrard | Hygrothermal performance of lime-hemp wall assemblies[END_REF][START_REF] Tran Le | Transient hygrothermal behavior of a hemp concrete building envelope[END_REF].

This study deals with three hemp concretes used for building walls. These materials differ in their composition and manufacturing methods: one of them is precast, the second one is sprayed and the last one is moulded. The aim of this study is to compare and analyse the hygroscopic behaviour of the three materials and to identify whether composition and manufacturing have an impact on hygric properties. The investigations are based on the measurement of the sorption curve, the water vapour permeability and the moisture buffer value. Moisture diffusivity is then calculated versus water content from the sorption curve and the water vapour permeability.

Methods

Sorption isotherm

The sorption isotherm relates the amount of equilibrium moisture content to the ambient relative humidity for a given temperature.

Sorption isotherms can be measured according to continuous or discontinuous methods [START_REF]Reporting physisorption data for gas/solid systems with special reference to the determination of surface area and porosity[END_REF]. The continuous method consists of measuring the sorption curve under quasi-equilibrium conditions. The adsorptive is admitted (or removed) at a slow and constant rate. The variation of the amount adsorbed by the specimen, with increase (or decrease) in pressure is measured by the volumetric or gravimetric method. The discontinuous method consists of measuring the amount adsorbed by the specimen at successive stages of increasing (and then decreasing) pressure. It can be performed with desiccators and saturated salt-solutions, with climatic chambers or with DVS (dynamic vapour sorption) that has been developed to reduce the running time of measurement but can be used with small specimens only [START_REF] Xie | The dynamic water sorption behaviour of natural fibres and kinetic analysis using the parallel exponential kinetics model[END_REF].

In this study, the sorption isotherms are measured according to the discontinuous method: the moisture content is determined at successive stages of increasing (and then decreasing) relative humidity. The specimens are placed in a climatic chamber (Vötsch VC4060) which regulates temperature and relative humidity. They are weighed two to three times a week. The sorption isotherm is measured at 23 ± 0.1 • C. Relative humidities used for this study are [START_REF] Garnier | Life assessment of hemp concrete wall manufactured by spraying, in: 2nd International conference on building energy and environment[END_REF][START_REF] Tran Le | Transient hygrothermal behavior of a hemp concrete building envelope[END_REF][START_REF] Mclean | Moisture transmission testing of building materials and the presentation of vapor permeability values[END_REF][START_REF] Derome | Model for hysteretic moisture behavior of wood[END_REF]58,81,90, 95 and 97%RH. The water content w is calculated from the mass of the specimen [START_REF] Cerolini | Moisture buffering capacity of highly absorbing materials[END_REF]. In order to reduce the time of exposure (to avoid moulds growing), the kinetic of water content is modelled according to [START_REF] Simonson | Heat and mass transfer between indoor air and a permeable and hygroscopic building envelope: part 1 -field measurements[END_REF]. The test runs until the rate between the experimental variation and the variation when steadystate is reached , defined in Eq. ( 3), is higher than 2/3. Moreover, the calculated water content at equilibrium should also show a discrepancy lower than 0.1% between the last three fits with the kinetic model.

w = m -m 0 m 0 = m w m 0 (1)
w: water content (%), m: mass of wet specimen (g), m 0 : mass of dry specimen (g), m w : mass of water (g).

w(t) = w i + w(t); with w(t) = a[1 -b exp(-ct)] (2)
w(t): water content at time t (%), w i : initial water content of the stage (%), w(t): variation of water content within initial time and time t of the stage (%), a, b and c: fitting parameters (-).

= w exp,t -w i w ∞,t -w i (3)
w exp,t : experimental water content at time t (%), w i : initial water content of the stage (%), w ∞,t : water content at equilibrium, calculated with experimental values at time t (%).

Several models have been developed to describe the sorption curve [START_REF] Brunauer | Adsorption of gases in multimolecular layers[END_REF][START_REF] Barett | The determination of pore volume and area distributions in porous substances -I. Computations from nitrogen isotherms[END_REF]. Guggenheim [START_REF] Guggenheim | Application of Statistical Mechanics[END_REF], Anderson [START_REF] Anderson | Modifications of the Brunauer, Emmett and Teller[END_REF][START_REF] Anderson | Modifications of the Brunauer, Emmett and Teller, equation II[END_REF] and De Boer [START_REF] De Boer | The Dynamical Character of Adsorption[END_REF] have developed the GAB model (4). This model relates the water content to the specific surface area of the material for multilayer sorption. Despite it being physically valid when there is no capillary condensation; the GAB model covers a wide range of relative humidity (0.05 to 0.8-0.9) and is convenient to fit experimental adsorption data all over the RH range.

w w m = C G • k • ϕ (1 -k • ϕ)(1 -k • ϕ + C G • k • ϕ) (4)
with w m : the monomolecular water content (kg/kg), C G , k: fitting parameters of the GAB model, ϕ: relative humidity (-).

Water vapour permeability

The water vapour permeability characterises the ability of a material to transfer moisture under a vapour pressure gradient once the steady state is reached. The commonly called "vapour permeability" includes (i) vapour transfer by diffusion (transport by collision of water molecules with each other), (ii) vapour transfer by effusion (transport by collision of water molecules with walls of pores) and (iii) liquid transfer (connected with capillary condensation).

Water vapour permeability is measured according to the cup method (EN 12572, 2001) under isothermal conditions (23 • C) for several sets of relative humidity: (0/50), (0/23), (43/58) and (58/81). These measurements were taken in adsorption. Firstly, the specimens were dried and tests were carried out from lowest RH to highest RH. Prior to each test, the specimens were stabilised to the lowest RH of the test.

The specimen is embedded at the top of the cup (Fig. 1). The relative humidity in the cup, ϕ int , is controlled by saturated salt solutions or silica gel while the relative humidity around the cup, ϕ ext , is controlled by air conditioning. The difference of water vapour pressures leads to a flux. The device is weighed periodically and when the gain in mass is constant, the mass rate G is calculated by linear regression of the kinetic of mass and the water vapour permeability is then deduced:

G = m t (5) = G • e A • ( p v ) (6)
where G: mass rate (kg/s), m: mass variation (kg), t: time (s), : water vapour permeability (kg/(m s Pa)), e: thickness of the specimen (m), A: exposed surface area (m 2 ), p v : vapour pressure difference (Pa). The vapour pressure is calculated from temperature and relative humidity measured during test period with the usual relationship:

p v = ϕ • 100 exp 18.986 - 4052 235.89 + T (7)
where T: temperature (K).

The experimental data on water vapour permeability versus relative humidity are fitted with a power law relationship according to [START_REF] Galbraith | Moisture permeability data presented as a mathematical function applicable to heat and moisture transport models[END_REF]:

= A + B • ϕ C (8)

Moisture diffusivity

Under the vapour pressure gradient, moisture transfer occurs through interconnected pores.

In an isothermal case, Fick's law states the relationship between the water vapour diffusion rate in air and the gradient of water vapour pressure:

g v = -ı • ∇p v (9)
where ı is water vapour diffusion permeability in air and p v (Pa) is the water vapour partial pressure.

For building porous material, in large pores, vapour diffusion can be compared with the diffusion of water vapour in air. In small pores, the collision between molecules and pore walls are more numerous than collision between molecules: this mechanism is called effusion or Knudsen transport. Nevertheless, the effects of the porous structure can be described by water vapour diffusion resistance factor . At a macroscopic scale, moisture transfer under a vapour pressure gradient can be expressed as [START_REF] Boutin | Etude des caractéristiques environnementales du chanvre par l'analyse de son cycle de vie[END_REF] where = ı/ is commonly called "the vapour permeability". It was argued that may be considered independent of temperature [START_REF] Mclean | Moisture transmission testing of building materials and the presentation of vapor permeability values[END_REF][START_REF] Tveit | Measurements of moisture sorption and moisture permeability of porous materials[END_REF].

g h = -• ∇p v
Besides, under isothermal conditions and for one-dimensional transfer, the flux of moisture can also be calculated with:

g v = -0 • D u • ∂w ∂x (11)
where D u is the moisture diffusivity. Thus, the moisture diffusivity D w of a material characterises the rate of change of its moisture content under transient moisture evolutions.

Taking the sorption isotherm into account, this equation can be rewritten as:

g v = -0 • D u • ∂w ∂ϕ • ∂ϕ ∂x (12)
Considering that the vapour pressure gradient is linear in the specimen, the relative humidity gradient is linear too and so:

g v = -0 • D u • ∂w ∂ϕ • ϕ 2 -ϕ 1 e = 0 • D u • ∂w ∂ϕ • 1 p vs • p v2 -p v1 e (13)
So, moisture diffusivity is calculated from sorption and water vapour permeability versus ambient relative humidity with:

D u = • P vs 0 • 1 ∂w/∂ϕ (14)
De Vries has shown that the variation of moisture diffusivity D u versus water content w evolves according to three phenomena [START_REF] De | Simultaneous transfer of heat and moisture in porous media[END_REF] (Fig. 2): -for low water content, moisture transfer is essentially due to vapour transport (diffusion and effusion). The condensed phase exists in the form of an adsorbed film or in small islands of water. -when water content increases, small islands of water increase in number and in size, the area for vapour flux decreases and moisture transfer occurs by mechanisms of condensation and evaporation at vapour-liquid interfaces. -then, for high water content, liquid transfer is predominant.

Moisture buffer value

The moisture buffer value MBV quantifies the moisture buffering ability of a material.

It is measured according to the method defined in the NORDTEST project. This project defines the practical moisture buffer value of materials, measured under dynamic conditions [START_REF] Rode | Moisture Buffering of Building Materials[END_REF][START_REF] Rode | Moisture buffer value of materials in buildings[END_REF][START_REF] Peuhkuri | Using dynamic moisture loading tests for the determination of moisture buffer value[END_REF]. This value relates the amount of moisture uptake (and release), per open surface area, under daily cyclic variation of relative humidity according to Eq. ( 15). This value is mainly but not only a property of the material as the mass transfer coefficient at the boundary plays a role. Though, for many materials, the internal resistance to moisture transport is significantly larger than the convective surface resistance.

MBV = m A • (RH high -RH low ) (15)
with MBV: moisture buffer value (kg/(m 2 %RH)), m: moisture uptake/release during the period (kg), A: open surface area (m 2 ), RH high/low : high/low relative humidity level (%). The test method requires prismatic specimens to be sealed on five out of six sides. After stabilisation at (23 • C; 50%RH), specimens are exposed to daily cyclic variations: 8 h at high relative humidity (75%) followed by 16 h at low relative humidity (33%).

Within the NORDTEST project, a round robin test was held on nine representative building materials. It gave initial results and leads to a classification of moisture buffer values (Fig. 3).

The device used for MBV test consists of a climatic chamber (Vötsch VC4060) that can be controlled in the range +10 to +95 • C and 10 to 98%RH. The study is held at 23 • C. The relative humidity in the chamber is switched manually (75%RH; 33%RH). Temperature and relative humidity are measured continuously with Sensirion SHT75 sensors and with the sensor of the climatic chamber. The air velocity is measured in the surroundings of the specimens: the vertical velocity is in the range 0.07-0.14 m/s and the horizontal one is 0.1-0.4 m/s. The specimens are weighed out of the climatic chamber five times during the absorption period and eight times during the desorption period. The weighing instrument reading is 0.01 g, and its linearity is 0.01 g. The accuracy of the moisture buffer value is thus about 5%. According to the NORDTEST project, stability is reached when the change in mass is the same between the last three cycles with a discrepancy of less than 5%.

Materials

Composition and manufacturing

This study deals with three kinds of hemp concrete used for building walls: a precast compacted hemp concrete, a sprayed hemp concrete and a moulded hemp concrete with fibred hemp shiv. Hemp concrete proportioning is the same as usually used by our industrial partners. For this project, hemp concrete is manufactured in moulds of 30 cm × 30 cm × 16 cm. This size is representative of a wall thickness or of industrial precast blocks.

Table 1 gives the proportion of the mix and the manufacturing method of the three kinds of hemp concrete.

The precast hemp concrete (PHC) is manufactured by our industrial partner, the SME EASY Chanvre. The composition of the hemp concrete results from the optimisation of the manufacturing process used by the industrial partner. Firstly, CaO is mixed with water to obtain slaked lime. Then hydraulic lime and hemp shiv are added. The mixture is then poured in moulds and blocks are formed by compaction in the moulds under vibrations (Fig. 4).

The sprayed hemp concrete (SHC) is manufactured by our industrial partner SI2C. This SME applies hemp concrete by spraying in a vertical formwork. Hemp shiv and lime based binder (Tradical 70 -BCB) are mixed together and constitute a dry mix that is blown along a pipe by a flow of compressed air. Water is added to the mix at the end of the pipe, the quantity of which may be controlled by the operator via one valve (Fig. 5). The commercial binder is chosen according to the setting time and hardening properties of hemp concrete. For this study, hemp concrete is sprayed in stacked moulds. For moulded hemp concrete (MHC), fibred hemp shiv is mixed with commercial lime-based binder (Tradical 70 -BCB) in a mixer. Water content is adjusted to obtain fresh hemp concrete with a satisfactory rheology. Moulds are filled with the mixture and the hemp concrete is slightly compacted.

Once manufactured, blocks are stabilised at 23 • C, 50%RH.

Density and porosity

Table 2 gives the apparent density at (23 • C, 50%RH), the total porosity and the open porosity of studied materials.

The apparent density of the three hemp concretes ranges between 430 and 460 kg m -3 . It is in the range of values commonly used for walls in France [START_REF]Bio-aggregate-based Building Materials: Applications to Hemp Concretes[END_REF][START_REF]Règles Professionnelles d'Exécution d'Ouvrage en Bétons de Chanvre[END_REF], while lower values can be met elsewhere [START_REF] Shea | Hygrothermal performance of an experimental hemp-lime building[END_REF]. Sprayed hemp concrete and moulded hemp concrete show similar matrix density due to the fact that these mixtures are made with the same binder and with the same binder/hemp mass ratio. Their total porosity is about 79% while the total porosity of precast hemp concrete is slightly lower: 72%. Lastly, the open porosity of precast and of sprayed hemp concretes is slightly lower than 70% while it is 77% for moulded hemp concrete.

This open porosity includes a wide range of pores that are interconnected:

-at a macro scale, the porosity due to the arrangement between the hemp shiv and the hemp-binder adhesion can reach a millimetric width (Fig. 6), -in the binder matrix, the porosity due to trapped air shows a width up to 50 m and the porosity due to hydrates arrangement is lower than 0.01 m (Fig. 7), -in hemp shiv, the width of the porosity goes from 5 to 50 m (Fig. 8).

Specimens

The representative volume of hemp concrete was studied from the variation of apparent density against volume [START_REF] Collet | Porous structure and water vapour sorption of hemp-based materials[END_REF]. It was shown that cubic specimens with edges of 5 cm are representative of the material. Evrard [START_REF] Evrard | Transient hygrothermal behavior of Lime-Hemp materials[END_REF] also studied the representative volume element from visual analysis. He showed that specimens larger than 100 cm 3 (side >4.7 cm) can take into account the specific pore and particle distribution of the material. Specimens are cut from the blocks. Their sizes are chosen to embed the representative volume of the material. So, the specimens used for sorption curves are cylinders 5 cm in diameter and 7 cm high for sprayed and moulded hemp concrete and are cubes with edges of 5 cm for precast hemp concrete. The specimens used for water vapour permeability are cylinders 5 cm thick with an exchange surface area of 10 cm in diameter. Lastly, the specimens used for the moisture buffer value are a right square prism 7 to 8 cm thick (higher than the penetration depth) and with 15 cm sides. The exposed surfaces correspond to external surfaces of blocks for the MBV test and permeability test.

For each material, the numbers of specimens used are: (i) six for the sorption curve, (ii) three for the (0/50%RH) point and one for the other points of the water vapour permeability, and (iii) six for the moisture buffer value. is reduced to 20-40 days for each stage. The total time to measure the whole adsorption-desorption curve is about one year and nine months.

Results and discussion

Sorption isotherms

Hemp concretes are highly hygroscopic materials. Fig. 10 gives the sorption isotherms of the three studied hemp concretes. These curves are sigmoid and are classified as type II or III according to the IUPAC's classification [START_REF]Reporting physisorption data for gas/solid systems with special reference to the determination of surface area and porosity[END_REF]. This is consistent with the fact that these classes are given for macroscopic media. Moreover, these sorption curves show hysteresis which extends to the lowest pressures.

The sorption curves of sprayed and moulded hemp concretes are close to each other. Their water contents are similar for adsorption and for desorption branches, leading to similar hysteresis. For low and middle relative humidity, the gravimetric water content increases slightly versus relative humidity to reach about 3% at 58%RH for the adsorption branch. For higher relative humidity, the water content strongly increases and reaches about 20% at 97%RH. The sorption curve of precast hemp concrete differs from these curves. For relative humidity lower than 81%, the water content shows slightly lower values for precast hemp concrete than for sprayed and moulded hemp concretes. The slope of the sorption curve is also lower for PHC than for SHC and for MHC. For relative humidity higher than 81%, the increase in water content is greater for precast hemp concrete leading to much higher water content: at 97%RH, the gravimetric water content is about 44% for PHC. In this range of relative humidity, capillary condensation appears intense for PHC, while it starts gradually and occurs on a wide range of relative humidity for SHC and MHC. According to the BJH Method [START_REF] Barett | The determination of pore volume and area distributions in porous substances -I. Computations from nitrogen isotherms[END_REF][START_REF] Collet | Porous structure and water vapour sorption of hemp-based materials[END_REF], in the range of relative humidity 81-97%RH, the capillary condensation occurs in pores of width from 0.005 to 0.040 m. This size of pore is met in the skin of the cell wall of hemp shiv and in the inter-particle pores of the binder. Sprayed and moulded hemp concretes are made of the same binder and the same hemp/binder ratio so they logically show similar behaviour. Precast hemp concrete having a higher hemp/binder ratio leads to higher water content at high relative humidity. Table 3 gives the fitting parameters of the GAB model for the three hemp concretes. This fitting is held on experimental data up to 95%RH. The correlation coefficient between experimental data and fitting curves is higher than 0.998. Adding the 97%RH experimental data with the same fitting curve, the correlation coefficient remains higher than 0.98. In line with the previous comments, the parameters are similar for SHC and MHC and slightly differ for PHC.

Adsorption and desorption branches are nearly parallel over a wide range of relative humidity for the three hemp concretes (Fig. 10). The hysteresis observed for precast hemp concrete is less important than the one observed with sprayed and moulded hemp concretes, as shown in Fig. 11. For the three materials, the highest hysteresis is observed around 80%RH. At middle relative humidity, the hysteresis is about 4% for the sprayed and the moulded hemp concretes and slightly lower than 3% for the precast hemp concrete. This hysteresis is commonly explained by the capillary condensation hysteresis, the contact angle hysteresis and the inkbottle effect [START_REF] Derluyn | Hysteretic moisture behavior of concrete: modelling and analysis[END_REF]. After desorption, an outgas at higher temperature leads to lower residual moisture content values. So, the low pressure hysteresis can be attributed on the one hand to the presence of micropores and on the other hand to irreversible uptake of molecules in pores (or through pore entrances) of the same width as that of the adsorbate, or to irreversible chemical interaction of the adsorbate with the adsorbent [START_REF]Reporting physisorption data for gas/solid systems with special reference to the determination of surface area and porosity[END_REF]. Lastly, a part of the residual mass may also be due to the start of lime carbonation that probably occurred during the tests at high relative humidity.

Xie et al. [START_REF] Xie | The dynamic water sorption behaviour of natural fibres and kinetic analysis using the parallel exponential kinetics model[END_REF] provide an example of adsorption-desorption curve of pure hemp shiv and Zaknoune [START_REF] Zaknoune | Etude du comportement thermohydrique de matériaux « chanvre-chaux » lors de la phase de séchage -estimation par technique inverse des propriétés hydriques[END_REF] gives desorption curves of used hemp shiv. These curves are similar to each other. They are sigmoid and reach 25% of moisture content at highest relative humidity. At low and middle relative humidity, their water content ranges from about 3.5% at 20%RH and 16% at 80%RH. Moreover, the hysteresis remains lower than 2% over the RH range. So, hemp concretes show lower sorption curves than hemp shiv but induce larger hysteresis. The porosity of the binder largely influences the hygroscopic behaviour of the mix.

Water vapour permeability

Fig. 12 gives an example of the kinetic of mass during a water vapour permeability test. For all the tests, the steady state is reached after ten to twenty days. The test goes on up to the saturation of silica gel or of saturated salt solutions. The water vapour permeability is then calculated from the slope of the kinetic of mass along 20-40 days during steady-state.

Fig. 13 gives the variation of moisture permeability versus ambient relative humidity for the three hemp concretes. Experimental data are fitted with a power law relationship (8). The fitting parameters are given in Table 4.

Moulded hemp concrete shows a slight increase of water vapour permeability from 1.7 × 10 -11 to 6.2 × 10 -11 kg m -1 s -1 Pa -1 . Sprayed and precast hemp concretes show similar results with a nearly constant value of water vapour permeability for low and middle relative humidity (about 3.2 × 10 -11 , Fig. 12. Kinetic of mass of one specimen of precast hemp concrete during the cup test. resp. 2.5 × 10 -11 kg m -1 s -1 Pa -1 ). For high relative humidity, an abrupt increase appears: moisture permeability reaches 1.7 × 10 -10 kg m -1 s -1 Pa -1 (resp. 1.3 × 10 -10 ). The increase of the water vapour permeability with relative humidity is due to the enhancement of macroscopic moisture transport induced by microscopic liquid transfer in water filled pores (due to capillary condensation). For hysteretic materials, the water vapour permeability thus depends on the moisture content [START_REF] Derome | Model for hysteretic moisture behavior of wood[END_REF]. Fig. 14 shows the variation of moisture permeability versus water content considering the main adsorption curve for the determination of water content. For lowest values of water content (up to 4%), the moisture permeability is similar for the three hemp concretes and follows a power law relationship. For highest values of water content, the moisture permeability of moulded hemp concrete evolves following the same fitting curve while sprayed and precast hemp concrete show an exponential increase. This underlines the efficiency of microscopic liquid flow due to capillary condensation in open porosity.

Moisture diffusivity

Fig. 15 gives the variation of moisture diffusivity versus gravimetric water content. The hydric diffusivity is in the range 1.3 × 10 -9 to 1.5 × 10 -8 m 2 /s. The shape of these curves is in agreement with De Vries theory: the first wave corresponding to hydric diffusivity under vapour transfer is observed. For precast hemp concrete, only the decrease of diffusivity is perceived. At lowest water content, the moisture diffusivity of precast hemp concrete is highest. It soon becomes the lowest: when water content reaches 0.8%. Moulded and sprayed hemp concretes show similar variation of hydric diffusivity. In a first part, the moisture diffusivity increases up to 7.8 × 10 -9 m 2 /s (resp. 6.7 × 10 -9 m 2 /s) for water content equal to 0.9% (resp. 1.1%). Moisture transfer occurs through a "diffusion and effusion of vapour" phase. Then moisture diffusivity decreases in a similar way for the two materials. Due to capillary condensation, moisture transfer occurs by mechanisms of condensation and evaporation at vapour-liquid interfaces. When moisture content is equal to 3%, the moisture diffusivity reaches down to 3.7 × 10 -9 m 2 /s. Lastly, the moisture diffusivity of sprayed hemp concrete is nearly constant while it goes on decreasing for moulded hemp concrete. For sprayed and moulded hemp concrete, the sorption curves being very close to each other, the difference in moisture diffusivity is mainly due to the difference in moisture permeability for high water content (i.e. RH).

Moisture buffer value

Fig. 16 gives an example of the kinetic of mass during the test. The kinetic is similar for all the specimens of the three hemp concretes. The steady state is reached from the fourth cycle: the change in mass m and the moisture buffer value vary less than 5% within each cycle.

Table 5 gives the average value of the moisture buffer value calculated from cycles 4 to 7 in adsorption, desorption and the average for the three materials. The value is very slightly higher in desorption than in adsorption. Sprayed and moulded hemp concretes show similar values of MBV (respectively 2.15 and 2.14 g/(m 2 %RH) in average) while precast hemp concrete shows a lower value (1.94 g/(m 2 %RH)). This is consistent with the results obtained previously. Actually, the moisture buffer value is proportional to the moisture effusivity of the material [START_REF] Rode | Moisture Buffering of Building Materials[END_REF]. The moisture effusivity is linked to the moisture permeability and to the derivative of the sorption isotherm [START_REF] Rode | Moisture buffer value of materials in buildings[END_REF]. As the precast hemp concrete shows a lower derivative of sorption curve and a smaller hysteresis than sprayed and moulded hemp concrete, it has a lower moisture buffering capacity. Thus, its moisture buffer value is logically lower than the one for SHC and MHC.

Lastly, according to the classification of the NORDTEST Project, these materials appear as excellent (MBV >2 g/(m 2 %RH)) or nearly excellent (good: 1 < MBV < 2 g/(m 2 %RH)) hygric regulators.

Conclusions

The three studied materials are highly porous, with open and interconnected porosity. The results underline their high moisture transfer and storage capacities; they are classified as excellent (or nearly excellent) hygric regulators.

The results obtained for sorption curves are very close for two of the three hemp concretes (SHC and MHC): these materials are made of the same binder and the same hemp shiv/binder ratio. The sorption curve of the third hemp concrete (PHC) leads to lower moisture content for low and middle relative humidity. For high relative humidity, the moisture variation is more abrupt, in connection with capillary condensation phenomena in open porosity (cell wall of hemp shiv and inter-particles porosity of binder). The three hemp concretes show a high hysteresis loop between adsorption and desorption curves. The hysteresis is slightly lower for the precast hemp concrete. The water vapour permeability of the three hemp concretes is high (1.7 × 10 -11 to 1.7 × 10 -10 kg m -1 s -1 Pa -1 ). For two of the three materials (PHC and SHC), it increases widely at high relative humidity, in connection with microscopic liquid flow in open porosity. The moisture diffusivity ranges between 1.3 × 10 -9 and 1.5 × 10 -8 m 2 /s and is essentially linked to vapour transfer, while liquid transfer appears negligible for relative humidity lower than 80%. Lastly, in the same way as for sorption curves, the moisture buffer values of two materials (SHC and MHC) are close while it is slightly lower for the third one (PHC). For the three hemp concretes, the moisture buffer values are excellent, showing the ability of the material to regulate ambient relative humidity. Finally, it seems that the composition and the manufacturing method have a low, but non negligible, impact on hygric properties of hemp concretes.

All these data appear necessary to simulate the hygrothermal behaviour of the building envelope. The use of sorption curve and water vapour permeability alone cannot lead to a good prediction of hysteretic behaviour. Actually, it was shown that uncertainty on this kind of data hampers reliable simulation of hygroscopic buffering [START_REF] Roels | Reliability of material data measurements for hygroscopic buffering[END_REF]. Moreover, measurement of the sorption curve and water vapour permeability is long and tedious. So, dynamic testing of the moisture buffer value is a good additional dynamic test to evaluate the moisture buffer capacity of materials. Additionally, the data from this test can be used for benchmarking buffering models but does not lead directly to sorption and permeability values. A reverse method should be built to identify characteristic parameters from an MBV test.

Lastly, it should be emphasised that the moisture buffering capacity of these materials would allow energy savings while maintaining adequate air quality and hygrothermal comfort [START_REF] Evrard | Hygrothermal performance of lime-hemp wall assemblies[END_REF][START_REF] Tran Le | Transient hygrothermal behavior of a hemp concrete building envelope[END_REF]. However, in most cases, hemp concrete is plastered. The slight difference between the three hemp concretes would thus probably be reduced once they have been plastered, while the moisture buffering capacity of the wall would be lower.

Fig. 1 .

 1 Fig. 1. Test cup.

Fig. 2 .

 2 Fig. 2. Variation of hydric diffusivity versus water content according to De Vries theory [13].

Fig. 3 .

 3 Fig. 3. Ranges for practical moisture buffer value classes [10].

Fig. 5 .

 5 Fig. 5. Device for spraying hemp concrete (SHC) -dry mixer, shutter.

Fig. 6 .

 6 Fig. 6. Porosity of hemp concrete at macroscale.

Fig. 9

 9 Fig.9gives an example of the adsorption kinetics obtained for one specimen of sprayed hemp concrete. It is representative of the results obtained for all specimens. This figure shows the high degree of correspondence between the experimental data and the fit with the kinetic model. Thanks to this model, the time of the experiment

Fig. 8 .

 8 Fig. 8. MEB view of hemp shiv (left: length view, right: cross section).

Fig. 9 .

 9 Fig. 9. Kinetics of adsorption of one specimen of sprayed hemp concrete (points: experimental data -lines: model of kinetic).

Fig. 10 .

 10 Fig. 10. Sorption isotherm of studied hemp concretes -top: linear plot; bottom: semilogarithmic plot.

Fig. 11 .

 11 Fig. 11. Hysteresis loop between adsorption and desorption branches versus relative humidity.

Fig. 13 .

 13 Fig. 13. Variation of moisture permeability versus ambient relative humidity.

Fig. 14 .

 14 Fig. 14. Variation of moisture permeability versus gravimetric water content.

Fig. 15 .

 15 Fig. 15. Variation of moisture diffusivity versus gravimetric water content.

Fig. 16 .

 16 Fig. 16. Moisture uptake and release for the specimen SHC 4.5 and monitored relative humidity.

Table 1

 1 Mixes proportioning and manufacturing method of studied hemp concretes.

	Material	PHC: precast hemp	SHC: sprayed hemp concrete	MHC: moulded hemp concrete
		concrete
	Manufacturing	Precasting	Spraying	Moulding
	Binder	CaO: 72%	Lime based binder (Tradical 70)	Lime based binder (Tradical 70)
		hydraulic lime: 28%
	Hemp shiv	Usual Hemp shiv	Usual Hemp shiv	Fibered hemp shiv
	Hemp/binder mass ratio	0.65	0.5	0.5
	Water/binder mass ratio	1.2	0.8	1.6

Fig. 4. Device for precasting hemp concrete (PHC) -mixer; forming process.

Table 2

 2 Density and porosity of studied hemp concretes.

		460	430	430
	Matrix density [kg m -3 ]	1655	1997	2002
	Total porosity [%]	72	78	79
	Open porosity [%]	68	66	77

Material

PHC SHC MHC Apparent density at (23 • C; 50%RH) [kg m -3 ]

Table 3

 3 Fitting parameters of the GAB model for the three hemp concretes.

	Material	PHC	SHC	MHC
	wm	0.0104	0.0130	0.0124
	CG	0.8586	6.5615	2.1928
	k	1.0021	0.9463	0.9499

Table 4

 4 Variation of water vapour permeability versus relative humidity: fitting parameters of the power-law relationship.

	Material	PHC	SHC	MHC
	A	2.52E-11	3.19E-11	3.24E-12
	B	2.24E-10	5.18E-10	6.70E-11
	C	4.94	8.38	0.65

Table 5

 5 Moisture buffer value in adsorption, desorption and average for the three kind of hemp concrete.

	Material	PHC	SHC	MHC
	MBV -adsorption [g/(m 2 %RH)]	1.91	2.14	2.12
	MBV -desorption [g/(m 2 %RH)]	1.97	2.15	2.17
	MBV -average [g/(m 2 %RH)]	1.94	2.15	2.14

Acknowledgments

This article presents results following the French national project ANR-06-MAPR-0002 "Béton de chanvre" -Programme MAPR 2006 and the Breton regional project "PRIR Ecomatx". These projects were conducted with the financial support of the French National Research Agency (ANR) and the Brittany Regional Council.

The authors thank the SMEs Easy Chanvre and SI2C for their contribution to the manufacturing of hemp concrete.


Laurent Marmoret
email: laurent.marmoret@u-picardie.fr

Florence Collet

Hassen Beji

Moisture adsorption in glass wool products

Keywords: Insulating material, mineral wool, glass fiber, adsorption isotherm, BET model, GAB model, TSS model

Two glass wool insulating materials are studied. After describing the microscopic and macroscopic structure of the wool, the investigations are concentrated on water vapour sorption isotherm. The aim of this study is to calculate the values of parameters obtained by the regression of water sorption experimental data using Brunauer, Emmett and Teller (BET) and Guggenheim, Anderson and de Boer (GAB) and Three Sorption Stages (TSS) isotherms. We have chosen these isotherms because of their complementarity's range of relative pressures regression. BET isotherm can be applied for data until 0.4 even though GAB isotherm can be fitted until 0.84 and TSS one can be used on the whole range of relative pressures. Usually, new parameters are calculated independently for each (BET, GAB or TSS) model. There after, these values obtained from different models are compared. We have used this method in a first time. In a second time, another method is proposed: parameters are not independently calculated but values of the two parameters (monolayer and the energy constants) determined with the BET model are retained and used in the GAB model. So, we fit the experimental data with the BET values and a new additional constant, denoted k. Thereafter, GAB parameters are completed in TSS model by introducing a new constant, called h* to fit the whole range of relative pressures.

IntroductIon

Mineral wool based materials are frequently used in the form of thermal insulation boards. This porous insulation material may be submitted to heat conduction, heat convection due to air motion, radiative heat flux among internal surfaces, moisture diffusion due to water vapour concentration gradients, water vapour convection due to air motion and phase transformation. The main processes involved with the accumulation of moisture within the insulation are either adsorption or condensation. Moisture accumulation due to adsorption occurs at the molecular level; i.e. mono-layers of water vapor molecules collected on the surfaces of glass-fibers [1]. This sorption process is often accompanied by thermal energy exchange that can alter the local temperatures significantly inside the material [2,3]. Energy is also released during the adsorption process as the molecules of water vapor become bound to the glassfiber surfaces. Although the amount of moisture accumulation through adsorption is usually much smaller than that for condensation, the heat of adsorption can be up to four times as high as the heat of vaporization. Due to the complexity of the interaction among these physical effects, it is often difficult to analyze the data obtained from field measurements [4]. Adsorption phenomena can be described using the relationship between the equilibrium pressure of the gas and the amount adsorbed at constant temperature, known as adsorption isotherm. The Brunauer-Emmett-Teller (BET) model [5,6] and the extension known as Guggenheim-Anderson-de Boer (GAB) model [START_REF] Van Den Berg | Water activity and its estimation in food systems: theo-[] retical aspects[END_REF]8] are widely used. The GAB model becomes inadequate at relative pressures higher than 80 to 90%. Thereafter, a new stage becomes available for the sorbate molecules (which are true liquid-like properties): the Three Sorption Stage (TSS) [9].

In this paper, two mineral insulating materials manufactured by Isover are studied. In a first part, we describe the microscopic and macroscopic structure of the wool to assess materials properties. In a second part, water vapour sorption isotherm is studied to analyse the moisture adsorption phenomena. The sorption curves are fitted with BET, GAB and TSS models and values of the parameters are compared.

MaterIals and saMples

We study two different glass wools, denoted L1 and L2, sold in the form of panels. They are both intended for the insulation of roofs. To product the wool, glass fibers are interconnected by a synthetic binder and by additives such as anti-mould admixtures. According to the manufacturer, they are both generally made for 90% of glass fiber and for 10% of formo-phenolic binders.

Microscopic structure and chemical analysis

Scanning Electron Microscopy (SEM) shows heterogeneity of the geometry of fibers and the random distribution of fibers (fig. 1). Wools are composed by fibres of 14 µm diameter which is a rather significant dimension with respect to the wools standards. Binders appear in the form of droplets and clusters. We have observed that the binder is distributed fairly regularly along the fibers. The average thickness of the binder is estimated at about 500 nm. Coupling the SEM with the EDX detector, the chemical composition of fibers and binder is analysed. The L1 and L2 fibers are made, in a large proportion, of recycled glass and its chemical composition is classified into the classic E-type [10]. According to the type of wool, the contents of silicon (Si), sodium (Na), calcium (Ca) and potassium (K) are greatly different [11]. Moreover, the binder of glass wool noted L1 is distinguished by the presence of magnesium (Mg), and sulfur (S) is found in the binder in L2.

The Thermo-Gravimetric Analysis (TGA) has been used to determine the temperature which caused the degradation of the glass wools binders. The global amount of mass change can be also calculated. But, this technical method does not distinguish between free water and bound water [12] of the water contents inside the amount of mass change. Both L1 and L2 thermograms (fig. 2) show two-step combustion in air of the coated glass fibers. The first step is due to evaporation of the adsorbed moisture (from 100 up to 210°C) and the second one can be assigned to the decomposition of binders (210-550°C). When samples are immersed in liquid water for 24 h at a temperature of 20 ± 1°C, L1 looses approximately 64% of water even though L2 looses almost 70% (fig. 2) during the first step. Moreover, we observe in fig. 2 that after 200°C, mass change of L2 (almost 1%) is less than mass change of L1 (almost 4%). This difference can be explained by a dilution of a part of the binder in liquid water. This part of the binder can be evaporated before the decomposition of binders (210-550°C) and explained the least mass change of L2 than L1 during this period in fig. 2. Zinck and al. [13] have also proposed this hypothesis to explain the ageing of the glass fiber. Their conclusion is the main cause of ageing is due to the binders and the alteration of glass constituting fibers comes much later. During the adsorption phenomena, the surface of contact with the moisture is the binder. But the binder can de diluted if liquid water appears in the porous structure of the wool.

Macroscopic analysis

The structure of wools was characterized by morphological parameters such as porosity, density and volumetric surface. Total porosity ε is calculated with the apparent bulk density of the sample in a dry state and with the density of its solid matrix constituted of E-type glass. Volumetric surface S V expresses the degree of division of the solid phase. Its value is obtained theoretically by carrying out the relationship between developed surface and the unit of volume of matter constituting the solid phase. For fibrous insulators, according to the work of Klarsfeld and Al. [14], volumetric surface can be calculated by: S V = 4 / φ where φ represents the average diameter of fibre. The wools L1 and L2 having densities higher than 20 kg.m -3 and porosities near 96% (table 1), they can be classified in the category of heavy insulators. The insulators used in building industry come from this category in general.

porous structure analysIs froM sorptIon IsotherMs

As, our wools are very porous (ε > 95%) and have an important volumetric surface, the surface of contact between the absorbate and the absorbent is significant. The behaviour of the adsorbate on the adsorbent can lead to a monolayer adsorption, where all the adsorbed molecules are in contact with the surface of the adsorbent, or to a multilayer adsorption in which the adsorption space accommodates more than one layer of the adsorbate.

sorption models theory

In the lower half of the range of relative pressures (0.05 < ϕ < 0.35 -0.40), molecules are strongly sorbed in a monomolecular layer (First stage, Fig. 2).

The amount of adsorbate needed to cover the surface with a complete monolayer of molecules is known as monolayer capacity and the surface area of the adsorbent may be calculated from the monolayer capacity. The Brunauer, Emmett and Teller (BET) sorption equation represents a fundamental model in the interpretation of this range of relative pressures. The success of the BET model is more qualitative than quantitative because it can be performed only over the lower half of the range of relative pressures (0.05 < ϕ < 0.4). This inability to fit the experimental data over the whole range of the relative pressures has induced that the principal application of the BET equation has been the estimation of the surface area. Only two constants characterize the BET isotherm equation, namely ω m , the monolayer sorption capacity and C, a parameter related to the energy difference of the sorbate molecules in the first layer and in the other 'liquid-like' layers (or in the pure liquid).

With increasing relative pressures, molecules are sorbed in multimolecular layers (Second stage). In almost every case, the amount sorbed by the sorbent is less than that predicted by the BET isotherm [5,6]. By postulating that the state of the sorbate molecules in the second and higher layers is the same but different from that in liquid-like state, Guggenheim, Anderson and de Boer (GAB) [START_REF] Van Den Berg | Water activity and its estimation in food systems: theo-[] retical aspects[END_REF]8] introduce a second well differentiated sorption stage for the sorbate molecules. GAB model can reproduce the experimental data up to ϕ ≤ 0.9. This isotherm necessarily contains a third constant k, which quantifies the difference between the standard chemical potentials of the molecules in the second sorption stage and in the pure liquid state. In most practical cases, k is less than the unity because, a lower sorption than allowed by the BET model is predicted for relative pressures greater than 40%. Lastly, capillary condensation appears at higher relative pressures (Third stage). A refinement of the GAB model is to introduce a third stage into the formulation and thereby derive a Three Sorption Stage (TSS) isotherm. As BET and GAB method, the TSS isotherm will be deduced by a statistical method describing the sorption curve. Theoretical foundations are described by Timmermann [9]. TSS isotherm retains the mathematical form of previous isotherms and integrates two correction relations H(ϕ) and H'(ϕ) which depend on a new constant h*. These relations become important only at high relative activities of the sorbate.

The different mathematical expressions chosen to fit the experimental sorption data are:

ω is the experimental moisture content adsorbed on the sample at relative pressure ϕ P / P o where P is the pressure of adsorbate and P o is the saturated vapour pressure of adsorbate. ω m is the moisture content when the adsorbent surface area is covered with a complete monomolecular layer. In the GAB model, k is the GAB constant related to the properties of multilayer water molecules with respect to the bulk liquid. The parameters C can be correlated with temperature, using the following Arrhenius-type equations:

C C E E R T o m = -            exp .
1 where C 0 is pre-exponential factors, E 1 , E m and E L (kJ mol -1 ) aremolar sorption enthalpies, respectively, of the mono-molecular layer, of the multilayers covering the mono-layer and of the bulk liquid water. R and T are the universal gas constant and the absolute temperature.

Model Mathematical expression

BET [5,6] w w

C C m = - -+ . ( )( ) ϕ ϕ ϕ ϕ 1 1 (1)
GAB [START_REF] Van Den Berg | Water activity and its estimation in food systems: theo-[] retical aspects[END_REF]8] w w

C k k k Ck m = - -+ . . ( )( ) ϕ ϕ ϕ ϕ 1 1 (2) TSS [9] w w C H H k k k Ck m = - -+ . ( ). '( ). . ( )( ) ϕ ϕ ϕ ϕ ϕ ϕ 1 1 (3)
The function H(ϕ) and H'(ϕ) are defined by:

H k k k h ( ) . ( . ) * ϕ ϕ ϕ = + - - 1 1 1 (4) H H H k h h '( ) ( ) ( ) . ( . ) * ( *). ϕ ϕ ϕ ϕ ϕ ϕ = + - - - + - [ ] 1 1 1 1 1 (5)
Two values of h* (h* = 1 and h* → ∞) are interesting:

• If h* → ∞, H(ϕ) and H'(ϕ) → 1, eq (3) transforms into the GAB model (eq. 2). • If h* = 1, H(ϕ) and H'(ϕ) → H '( ) . ϕ ϕ ϕ → - - 1 1 k , eq (
3) transforms into the BET model (eq. 1).

experimental results and discussion

The measurements [START_REF]solid systems with special reference to the determination of surface area and porosity[END_REF] of adsorption isotherms were performed in laboratory conditions at 23 ± 1°C. The samples were placed in desiccators with different solutions (table 4) to simulate different values of relative pressures.

The initial state was dry material (m o ) after maintained samples in an oven at 80°C. The mass of samples was measured until the steady state value of the mass was achieved (m w ). Then, the equilibrium moisture content by mass (ω) was calculated according by gravimetric method:

ω = - - m m m w O O [ . ] kg kg 1 (6)
The volumetric water content (θ) can be calculated with θ l = (ρ l / ρ o ), ω where ρ l and ρ o are densities of water and material respectively. The experimental results on the equilibrium volumetric moisture content against relative pressures are given in Fig. 5. According to IUPAC classification [START_REF]solid systems with special reference to the determination of surface area and porosity[END_REF], these sorption curves are classified as type II corresponding to non-porous or macroporous media. The curves obtained for the two wools are quite the same but we notice that L1 is a little more hygroscopic than L2. Three clearly defined regions can be distinguished. For 0 < ϕ < 0.8, in the adsorptionally bound moisture region (with mono on the part ➀ and multi-molecular layer on part ➁), the amount of water adsorbed is very small. Volumetric water content doesn't exceed 0.1. In the capillary bound moisture region (ϕ > 0.8), the increase of volumetric water content is very important. For example, at ϕ = 0.90, volumetric moisture content is 0.30 for L2 and 0.34 for L1. The water content difference cannot be only assigned to the experimental error which doesn't exceed 5%. Ya and al. [16] have investigated specimens of glass fibers products as well as mineral wool manufactured by Isover (Netherland, Finland) and Paroc (Finland, Poland, Lithuania). Mean diameter of the glass fiber was 5 µm. The investigated products represent a material consisting of fine glass fibers interconnected by a synthetic binder. They have compared water content sorbed in glass fiber and in mineral wool. The investigated glass fiber product obtain a higher hygroscopy than the mineral wool one. Water content can be 5 or 10 times higher for the glass fiber boards than for the mineral wool of the same density. However, they assign the variation of water content to the binder content by testing different binders on a same glass fiber. Another interesting work [17] studies the effect of adding additives, such as anti-mould admixtures in the binder of mineral wools. They compare the behaviour of mineral wools manufactured by Rockwool with hydrophobic, with hydropholic admixtures and without any admixture. In the adsorption curve, we draw out the volumetric water content of each mineral wool for a relative pressure equal to 75% (at the end of the adsorptionally bound moisture region). A distinct result is obtained (table 4) with hydrophobic and with hydrophilic agent for quite the same density of material. Their effect on adsorption phenomena is clear but we don't have this information for our wools.

Model results and discussion

The following recipe was adopted to determine the values of the parameters C, ω m , k, h*, H(ϕ) and H'(ϕ) with Eqs. ( 1), ( 2) and (3) of the BET, GAB and TSS models.

BET Isotherm

Usually, the analysis of adsorption data in the BET range uses the linearised form of eq. ( 7) to determine the two characteristics constants (C B and ω mB ):

F C C C BET B mB B B mB ≡ - = + - ϕ ϕ ω ω ω ϕ ( ). . . . 1 1 1 (7)
By plotting the experimental data in the form F BET versus ϕ a straight line is obtained. The straight line intercept 1 C B mB .ω and slope ( ) .

C C B B mB

-1 ω can be easily evaluated. From the two equations for slope and intercept, the value of C B and ω mB are obtained separately. But BET isotherm with the linearised form overestimates values of C [18]. This is caused by the rapid increase of adsorption at low relative pressures which results in a distinct 'knee' on the isotherm. For an unknown porous sample the presence of micropores (according to IUPAC definition pores with sizes smaller than 2 nm) can not be excluded. The adsorption isotherm will have the shape inbetween isotherm types I and IV, the presence of micropores has to be checked and taken into account. We have to take the micropores into account because sorption curves of L1 and L2 are classified as type II (cf § II.2). Saito and al. [START_REF] Al-Muhtaseb | Water sorption isotherms of starch [20] powders Part 1: mathematical description of experimental data[END_REF] recently developed relations for average potential energy profiles of adsorbate in cylindrical pores of oxide adsorbents and used them to obtain the dependence of pore radius and relative pressure on pore filling by adsorbate. So by using Saito relations, it's possible to describe the combined adsorption in both micropores and macropores with the modified BET adsorption equation:

ω ω ϕ ϕ ϕ ϕ = + - -+ V C C mi m 0 1 1 . . ( )( ) (8)
Where V 0 mi represents the net volume of adsorbate which fills the micropores.

An alternative method of the linearised form (eq. 7) the non linear Levenberg-Marquardt algorithm have been used to determine the three isotherm parameters V 0 mi , C B and ω mB ,. Table 5 show results from different method. Whatever the method, the monomolecular moisture content ω mB is always greater for L2 than for L1. C B value is negative with linearised form (eq. 7) and tends towards an infinite value with BET method (eq. 1). ω mB value for linearised form is smaller than with BET method for the two wools. By using Saito relations (eq. 8), regression coefficient (R²) is better and the net volume of adsorbate which fills the micropores (V 0 mi ) is known. For C B , we have written in table 5 a value equal to 60 but a greater value can be incorporated because no effect on the fit is observed.

Figure 6 and 7 show water contents against relative pressures for L1 and L2 wools respectively. We can't obtain a good fit for relative pressures under 0.1 with linearised form.

GAB Isotherm

We have only used the Saito relations with the non linear Levenberg-Marquardt algorithm (NLLMA) to calculate GAB constants (V 0 mi , C B , ω m and k) in the range of relative pressures below ϕ max = 0.90. We want to compare results from two methods. The first one denoted 'GAB model with BET parameters' in figure 8 new parameters' doesn't use BET values but determines new values for V 0 mi , C B , ω m and k. This second method is the ordinary one because it allows a comparison of the results obtained with BET and GAB isotherm. For low relative pressures, the first method provides a better fit. But for the great relative pressures, the opposite interpretation can be done. That's why we observe for the wool L1 a better regression coefficient (table 6) for the second method than for the first one. For L2, the only difference appears for the low relative pressures. So the interest of using new parameters is not as obvious as we can think before this comparison. 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 0,000 > but variations are very small. Another interesting point concerned constant k. Timmermann [START_REF] Timmermann | Multilayer sorption parameters: BET or GAB values?[END_REF] says that k is always less than the unity for food. Only one case has been found for k > 1 in the literature. It corresponds to the system NaDNA-H 2 O studied by Gascoyne and Pethig [START_REF] Veiseh | Mathematical models for thermal conduc-[23tivity density relationship in fibrous thermal insulations for practical applications[END_REF]. The constant k introduce the difference of the free enthalpy (standard energy potential) of the sorbate molecules in the two states: the pure liquid and the second sorption stage corresponding to the layer above the first layer. The constant k determines the profile at the higher activity range regulating the upswing after the plateau following the 'knee' at the medium range. A too high k-value determines an upward curvature in the GAB plots as in the BET plots. As we obtain k > 1 for the two wools, with the integration of k in eq. ( 2), the sorption will become infinite at a value of the relative pressure less than unity denoting instability of the system. So, we can proposes two explanations: firstly, the larger the number of experimental points and the better their accuracy so we need more experimental data to verify our result and secondly, values of k less than unity is observed for food but it can be different for mineral wool.

TSS Isotherm

TSS isotherm is used to fit experimental data in the whole range of the relative pressures. A new characteristic h* is introduced in the relations H(ϕ) and H'(ϕ). As we conclude before that using new parameters bring not an obvious interest, we use to fit the TSS isotherm the alues obtained for GAB regression (k) and BET regression (V 0 mi , C B and ω m ). A good accuracy of the fitting can be admitted with the regression coefficient (R²). consider a good fitting if difference between experimental and predicted values are lower than 10%. Constant h* ranges between 0 and ∞. With the increase of h*, the effect of the function H and H' becomes more and more restricted to the region of highest values of relative pressures ϕ. Value of h* for L1 (h* = 11.1) is conform to Timmermann results [9] for interaction gas/solids (between 8 to 15). For L2, h* is near the unity so, as we have mentioned in § II.1, TSS model can be transformed into the BET model.

Solid surface area

Once the monolayer moisture content (ω m ) is known, the solid surface area (S in m² g -1 ) of the samples can be determined:

S N M m m = σ ω . . ( 9
)
where σ m is the area of a water molecule (1.06 10 -19 m² molecule -1 ), N is the Avogadro's number (6.023 10 26 molecules kg.mol -1 ) and M is the molecular weight of water (18 g mol -1 ). So, the specific surface area calculated from the BET value of monomolecular water content is 5 m².g -1 . Veiseh and al. [23] determine specific surface area of different fibrous insulation by an indirect test of fineness index based upon Darcy's law. The equipment utilized in this test is named Micronaire and they measure a fineness index: 3.0 and 5.0 m².g -1 . We can consider that our results are quite similar with L1 and L2.

conclusIons

Water vapour sorption of two different glass wools is studied. These high porous materials are composed of E-type glass fibers which are interconnected by formo-phenolic binder. With thermo-gravimetric analysis (TGA) the importance of the binder in adsorption phenomena is showed. We have distinguished three regions of the sorption isotherm. Firstly, in the monomolecular layer (for the relative pressure range: humidity 0.05 < ϕ < 0.35 -0.40), we have determined, by using the BET model, two parameters, respectively for L1 and L2: the monomolecular water content (ω m ) is 9.7 and 12.3 10 -4 kg.kg -1 and the specific surface area (S m ) is 3 and 4 m².g -1 . An improvement has been observed by the modified BET adsorption isotherm with Saito and Foley's expressions. By using Saito relation, we determine the net volume of adsorbate which fills the micropores to 6. 10 -4 kg.kg -1 . Secondly, for the range of relative pressures below ϕ max = 0.90, we obtain a constant k in the GAB model greater than the unity which have been rarely observed for adsorption isotherm. For relative pressure (ϕ) less than 80% (mono and multi molecular layers), the amount of water adsorbed is very small for L1 and L2. In the capillary bound moisture (ϕ > 80%), the increase of water content is important. We have used the TSS model to fit the whole range of relative pressures.

A good accuracy is obtained by using the values calculated before with BET and GAB regressions. references

  FIGURE 1Scanning Electron Microscopy of L1.

  FIGURE 2 TGA thermograms of L1 and L2 samples immersed in liquid water during 24 h [11].

  FIGURE 3Physisorption.

FIGURE 4

 4 FIGURE 4Sorption isotherm for glass wool (L1 and L2).

  FIGURE 5BET model for L1.

  FIGURE 6BET model for L2.

  FIGURE 7 GAB model for L1 (regression only with NLLMA + Saito relations).

TABLE 2

 2 Model equations fitted to the experimental sorption data.

TABLE 4

 4 Effect of Admixture on volumetric water content for ϕ = 75%.

		rockwool mineral wools [17]	our mineral wools
		With hydrophobic admixtures	with hydrophilic admixtures	without admixtures	l1	l2
	Density (kg.m -3 )	110	120	90	119	79
	Volumetric water content	0.059%	0.103%	0.096%	0.084% 0.074%

  We observed in table 6 best fit is obtained for a constant k near but greater than the unity. It is not conform to the fact related in the literature. We discuss of this point in the § II.3.4.As Timmermann [9], we have observed that ω m values with BET isotherm (denoted ω m (BET) ) are smaller ( )

	Water contents (g.g-1)		L2 Experimental data GAB model with BET parameters
	0,014		GAB model with new parameters
	0,012
	0,010
	0,008
	0,006
	0,004
	0,002
			Relative pressures
	FIGURE 8
	GAB model for L2
	(regression only with NLLMA + Saito relations). ( ) ω m BET <	ω	( m GAB	)	than ω m values with GAB
	isotherm (denoted ω m (GAB) ). For the energy constant C B , we have also obtained
	0,2 0,3 0,4 0,5 0,6 0,7 the same inequalities than Timmermann: C L1 experimental data Water content (g.g -1 ) L2 experimental data C B BET B GAB ( ) (	)
	0,1
	0,0
	0,0	0 ,2	0,4		0 ,6		0,8	1 ,0
			Relative pressures
	FIGURE 9
	TSS model for L1 and L2.

non linear levenberg-Marquardt algorithm (nllMa) using saito relations

	TABLE 6
	GAB parameters for L1 and L2.
		With Bet parameters	With new parameters
		l1	l2	l1	l2
	V 0 mi (kg.kg -1 )	0.00061	0.00060	0.0006	0.0006
	C B	60	60	0.42	257
	ω mB (kg.kg -1 )	0.00097	0.00123	0.00473	0.00126
	k	1.135	1.073	1.15	1.070
	R²	0.939	0.995	0.997	0.995

TABLE 7 TSS

 7

	parameters for L1 and L2.
		tss model with saito parameters (eq. 8)
		l1	l2
	h*	11,10	0.48
	R²	0.92	0.97
	TABLE 8
	Surface specific area for L1 and L2.
		l1	l2
	ω m (g.g -1 )	0.00097	0.00123
	S (m².g -1 )	3.25	4.12