Karine Martel

Christelle Dodane

Marion Blondel

Fanny Catteau

Multimodal focalization processes during French family dinners: a comparison between speaking and signing families

published or not. The documents may come

Multimodal focalization processes during French family dinners: a comparison between speaking and signing families

Marion Blondel, Christelle Dodane, Karine Martel, Fanny Catteau

To cite this version:

Introduction Family dinners

A privileged interactive situation as participants need to coordinate two kind of activities using one's mouth and hands : ✓ acting (eating, serving…) ✓ languaging (transmitting information to the other family members).

Our research questions ✓ How both adult and child dinner participants mark information salience in multiparty conversations, in which discourse topics are intermingled? ✓ How focus is shaped across modalities (audio-vocal and visuo-gestural), and which prosodic markers are used by '(gesturers-)speakers' and signers? Our hypotheses ✓ Focus markers are articulated in contrastive multimodal patterns ✓ A parallel can be drawn between 'spoken' French and LSF, in terms of the prosodic parameters and patterns used.

Background

Discourse combines shared information and new information (Lambrecht, 1994). New information is foregrounded, i.e. focused with a variety of processes including speech prosody (Rossi 1999, Di Cristo 1999, a.o.), sign prosody (Wilbur 1994 ;

Crasborn & van der Kooij 2013 a.o.) and (hearing-deaf) shared gestures (Ferré, 2003, a.o.).

In interaction, focus is implemented via multimodal phenomena: focalization is relatively well described in spoken dialogue, it remains understudied in signed interactions, and in both signed and spoken multiparty conversations.

Multimodal focalization processes during

HAL

  is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come

••

  Amplified parameters value / Hyperarticulation / Contrastive patterns (including scansion)/ Markedness with (de)synchronisation and coarticulation Intermodal parameters for embodied languages Data: Family dinners Selected diners • 1 French speaking family (3 children = boys, 2, 3 and 9 y.o) • 1 LSF family (2 children = girls, 6 and 2,6 y.o) Selected sample • 30 minutes of each dinner • 60 utterances containing a focus DinLang (ANR-20-CE27-0010) • Families who primarily use French or LSF • Two wide-angle cameras (pilot study) + one 360°camera, one 360°sound recorder (DinLang setting) Relatively strong amplitude of the arm movement • Slight hold • Hyper articulated labialization LSF: SIGN-NAME(Ea) FORGET QUESTION SUNDAY!, KNOW GO SIGN-NAME(asso)!? Translation: 'Oh, Charlotte, I forgot, I have a question for you: on (next) Sunday, do you know who is coming to (the association) DLS?" LSF: PLEASE JUICE 'PEACH/APPLE', handshake IDIOT, PLEASE JUICE 'ORANGE/APPLE', knock-gesture PLEASE! JUICE! APPLE! gesture Translation: 'Please, some ape..., uh no, I'm stupid, please some apor... Ah! I'm really stupid, please some apple juice!!!' • Extended head nod • Extension of the bust • Manual hyper-articulation • Labial hyperarticulation (with vocalization [pɔm]) Prosodic focalization on "o": ▪ Syllable lengthening ▪ Pitch and intensity peaks ▪ Presence of a pause ▪ Glottal stop ▪ Hyperarticulation • Body markers: ▪ Head movements ▪ Right hand (iconic gesture) ▪ Eyebrows & mimic ▪ Speech synchronization • Prosodic focalization on each syllable: ▪ Syllable lengthening ▪ Pitch and intensity peaks ▪ Hyperarticulation ▪ Rhythmic scansion pattern • Body markers: ▪ Left arm movement ▪ Speech synchronization SPOKEN FRENCH : 'Non, c'est pas beaucoup, c'est pas beaucoup !' Translation: 'No it's not a lot ! It's not a lot !' SPOKEN FRENCH : 'Mais les ronds, c'était des "o" en fait !' Translation: 'But the circles were actually o's.'

04366270 A set of intermodal prosodic markers Vocal markers

		Gestural markers
		Manual and non-manual cues
	• Increasing of pitch and
	intensity	• Elongations of the movement
	• Syllabic lengthening	▪ hold
	• Hyperarticulation	▪ amplitude
	• Pauses	▪ repetition
	• Glottal stops	• Hyperarticulation
		▪ acceleration
		▪ extended fingers
		▪ mouthing

Marion Blondel, Christelle Dodane, Karine Martel, Fanny Catteau. Multimodal focalization processes during French family dinners: a comparison between speaking and signing families. MMSYM 2023 : 1st International Multimodal Communication Symposium, Apr 2023, Barcelona, Spain. hal-


Nicolas J S Testard

Christine Chevallereau

Philippe Wenger

Static analysis of an under-actuated bio-inspired robot

Introduction

The human neck is comprised of seven vertebrae, offering a relatively limited range of motion. In contrast, bird necks possess a higher number of vertebrae, typically ranging between 11 and 25. This increased vertebral count provides birds with the ability to execute more intricate and dexterous movements, facilitated by a sophisticated network of tendons and muscles. Such neck dexterity enables birds to employ their necks analogously to how humans use their arms, allowing them to grasp and manipulate objects. Furthermore, birds' necks exhibit remarkable speed in motion, as exemplified by the rapid pecking movements of woodpeckers.

The exploration of bird neck performances has inspired the development of new robots. In a study by Furet et al. [START_REF] Furet | Estimating motion between avian vertebrae by contact modeling of joint surfaces[END_REF], the motion between bird neck vertebrae was investigated. It was observed that the motion between two vertebrae could involve either a pure rotation or a rolling motion of an ellipse on another. Pure rotation can be replicated using a revolute joint, while the rolling of ellipses can be modeled with an anti-parallelogram joint, also known as X-joints [START_REF] Snelson | Continuous tension, discontinuous compression structures[END_REF]. These joints, discussed in [START_REF] Stachel | Flexible Cross-Polytopes in the Euclidean 4-Space[END_REF], can be actuated using two antagonistic cables to simulate the effects of muscles and tendons. Notably, research by Muralidharan et al. [START_REF] Muralidharan | Variable Stiffness and Antagonist Actuation for Cable-Driven Manipulators Inspired by the Bird Neck[END_REF] highlights that revolute joints lack co-actuation properties compared to X-joints, making the latter more attractive for the development of bio-inspired robots.

In a study conducted by Fasquelle et al. [START_REF] Fasquelle | Identification and Control of a 3-X Cable-Driven Manipulator Inspired From the Bird's Neck[END_REF], a fully-actuated robot comprising three X-joints and four cables was successfully built and controlled, demonstrating the feasibility of the mechanism. In the context of mechanisms inspired by the bird neck, where the aim is to limit the number of actuators, the use of a restricted number of cables becomes an interesting consideration. In such cases, the system under investigation becomes underactuated. The objective of this report is to examine the impact of cables in statics on underactuated robots constructed with X-joints actuated by antagonistic cables.

Section 2 provides an overview of the underactuated robots under study. In Section 3, the influence of cable tensions on the robot is explored, revealing that an increase in cable tensions leads the robot to converge to a predictable configuration, regardless of the mass and elastic parameters. The report concludes with Section 4.

Presentation of the robots

This report focuses on the analysis of two robots depicted in Fig. 1. The first robot consists of 2 X-joints actuated by 2 cables, each pulling on the left and right sides of the joints. The second robot comprises 6 X-joints and is actuated by 4 cables. One cable pulls all joints on one side, while the remaining three cables pull two joints each on the other side. This cable routing is inspired by nature, resembling the structure found in certain bird species where a long ventral muscle pulls several vertebrae. Both robots are underactuated since two joints linked by the same cables cannot move independently from one another. Additionally, springs are incorporated in parallel with the cables to maintain a stable configuration at rest.

We will consider b = 0.05 m, L = 0.1 m, a mass of 0.16 kg for the top bar, and 0.026 kg for the diagonal bars.

Each joint i has one degree of freedom, which is defined as the orientation of the top bar compared to the base bar α i . The static model has been computed in [START_REF] Van Riesen | Dynamic analysis and control of an antagonistically actuated tensegrity mechanism[END_REF] [START_REF] Fasquelle | Dynamic modeling and control of a tensegrity manipulator mimicking a bird neck[END_REF] and is given by:

g(α) = Z(α)f (1)
where:

• α is the vector of the joint angles.

• g(α) represents the effects of gravity and the springs. • Z(α) = -dl dα ⊤ , with l as the vector of cable lengths.

• f is the vector of cable tensions.

Effect of the cable tensions

The objective of this section is to investigate the impact of minimal cable tensions on the overall equilibrium of the underactuated robots. The matrix Z has a rank of N c , where N c is the number of cables. However, during control, only N c -1 degrees of freedom are controllable, as one is designated to maintain the cable tensions positive. For instance, in the case of the robot with 6 joints and 4 cables, only 3 degrees of freedom are controllable. These degrees of freedom can be represented by the end-effector position and orientation, denoted as X = [x, y, γ] ⊤ = f X (α). Given a desired end effector position and orientation X des , the static equilibrium position of the robot can be calculated as follows:

(α, f ) = min α,f ||f || s.t. g(α) = Z(α)f f X (α) = X des min(f ) ≥ f min (2)
The springs are assumed to be symmetric on the right and left sides, with stiffness values from bottom to top of [1000, 850, 800, 650, 400, 250] N/m. They have a free length of 0.046 m, an initial orientation of π/4, and are subject to gravity. Additionally, the pulley radius is considered to be null (R p = 0).

Figure 2 illustrates the variation of α for a given X des , accompanied by the corresponding cable tensions depicted in Figure 3, as the minimal cable tension f min is modified. These figures indicate that as tensions increase, the robot converges to a configuration where joints actuated by the same cables have identical angles. Specifically, it converges to a position where the Z matrix loses one rank, as shown in Figure 4. Two different robot configurations for distinct minimal tensions are presented in Figure 5, demonstrating that X remains constant while joints angles α differ.

In the presence of a non-null pulley radius (R p ̸ = 0), Figure 6 demonstrates that the robot converges to a configuration where the angles linked by actuation have different values. However, in this configuration, the rank of the matrix Z decreases by 1, as illustrated in Figure 7.

The decrease in rank of Z can be explained. We express f = cf L , where c is a vector of constants expressing the ratio between the cable tensions (compared to the left cable tension). The static equation can therefore be written as:

Z(α)c = 1 f L g(α) (3)
Thus, it can be observed that as the cable tensions approach infinity (f L → +∞), c becomes a null space vector of the Z matrix, and consequently, the rank of Z decreases.

For example, for the robot with 2 joints and 2 cables, we have f = [f L , f R ], where f L and f R are the tensions in the left and right cables, respectively. Moreover, by defining c = [1, c] with c = f R /f L and solving the Z(α)c for different values of c, it is possible to predict the position of the robot when the cable tensions increase, as presented in Fig. 8 and9.

We set spring stiffnesses to 100 N/m and 600 N/m on the left of the first joint and 500 N/m and 200 N/m on the right of the first joint. In the presence of gravity and a null pulley radius, Fig. 10 and 11 show the evolution of the joint angles in simulation [START_REF] Testard | Comparison of Explicit and Implicit Numerical Integrations for a Tendon-Driven Robot[END_REF], when the cable tensions are increasing with a constant ratio. In Fig. 10, the ratio is c = 1, and the joint angles converge to 0 • as expected by Fig. 8. Similarly, in Fig. 11, c = 0.61676, and the joint angles converge to 50 • as expected by Fig. 8. Thus, these figures confirm the evolution of the joint angles to a configuration where the rank of Z decreases when the cable tensions go to infinity.

Conclusion

This report has presented under-actuated robots inspired by the bird neck. These robots are built with X-joints that are actuated through 2 antagonistic cables.

It has been shown that as cable tensions are increased, robots converge to a configuration where the rank of the actuation matrix Z decreases by one. This indicates that only N c -1 degrees of freedom can be freely controlled, while the remaining one, used for maintaining the positivity of the cable tensions, has less impact.

Figure 1 :

 1 Figure 1: Representation of and under-actuated robots with 2 joints and 2 cables and another one with 6 joints and 4 cables

Figure 2 :Figure 3 :Figure 4 :Figure 5 :

 2345 Figure 2: Evolution of the robot joint angle for a set X des depending on the minimal tension (null pulley radius)

Figure 6 :Figure 7 :Figure 8 :Figure 9 :

 6789 Figure 6: Evolution of the robot joint angle for a set X des depending on the minimal tension (pulley radius of 0.01 m)

Figure 10 :Figure 11 :

 1011 Figure 10: Simulation of the joint angle evolution when the tensions are increase with a ratio c = 1 with R p = 0


T Honorio

F Masara

F Benboudjema
email: farid.benboudjema@ens-paris-saclay.fr

(ICCC2023) "Further Reduction of CO2 -Emissions and Circularity in the Cement and Concrete Industry" September 18-22, 2023, Bangkok, Thailand Behavior of water in C-S-H

Keywords: Confined water, Surface water, Adsorption, Molecular simulations, Properties

The behavior of confined and surface water in hydrophilic systems is known to differ from bulk behavior. C-S-H is a hydrophilic micro/meso-porous phase with a large surface area. Understanding how water behaves in C-S-H is crucial to elucidate phenomena associated with water sorption and dynamics, which includes mass transport properties and durability, sorption-induced volume changes, thermal properties, and viscoelastic response. Molecular simulations are a powerful tool to quantify water behavior on the atomic level. In this work, these simulations are deployed to quantify the changes in the main physical properties -namely, density, self-diffusion, viscosity, bulk modulus, thermal expansion, heat capacity, and heat of adsorption -of liquid water confined in C-S-H as a function of the pore size under osmotic equilibrium. Then, we focus on surface water and how the properties of water change as a function of the distance from the C-S-H surface. For (slit) pores smaller than about 3-5 nm, the properties of water exhibit a transition from liquid-like to a more solid-like behavior. Surface water behavior differs from bulk behavior up to the fourth adsorbed layer. The results provided are critical inputs for multiscale modeling concerning the properties of confined and bound water. Also, they provide new physical insights to revisit sorption models and understand drying processes.

Introduction

The interactions of water with pore surfaces are a crucial factor in determining how water will behave. In hydrophilic phases such as C-S-H, the water adsorbed onto the surface is less mobile, is more compact, and exhibits different energetics from bulk water [START_REF] Abdolhosseini Qomi | Advances in atomistic modeling and understanding of drying shrinkage in cementitious materials[END_REF], [START_REF] Honorio | Surface water in C-S-H: effect of the temperature on (de)sorption[END_REF]). When the pore is small enough so that the effects of two opposing surface walls superpose, the behavior of the adsorbed fluid deviates even further from its bulk form [START_REF] Abdolhosseini Qomi | Advances in atomistic modeling and understanding of drying shrinkage in cementitious materials[END_REF]). In C-S-H, interlayer water is precisely in this strongly confined situation. Understanding how water behaves in C-S-H is crucial to elucidate the mechanisms associated with water sorption and dynamics, which includes mass transport properties and durability, sorption-induced volume changes, electromagnetic response (for non-destructive evaluation), thermal properties, and viscoelastic response. Here, molecular simulations are deployed to quantify the changes in the main physical propertiesnamely, density, self-diffusion, permeability, viscosity, bulk modulus, thermal expansion, heat capacity, and heat of adsorption -of liquid water confined in C-S-H as a function of the pore size under osmotic equilibrium. Molecular simulation is the well-suited technique for this task because it allows computing properties under well-controlled thermodynamic conditions in the relevant scale (often difficult to assess experimentally properly). Then, we focus on surface water and how the properties of water change as a function of the distance from the C-S-H surface.

Molecular Models and Methods

Molecular simulations are performed using the C-S-H atomic structure proposed by Kunhi [START_REF] Kunhi Mohamed | An atomistic building block description of C-S-H -Towards a realistic C-S-H model[END_REF] with structural formula 1.67CaO.SiO2. nH2O. ClayFF [START_REF] Cygan | Advances in Clayff Molecular Simulation of Layered and Nanoporous Materials and Their Aqueous Interfaces[END_REF]) is adopted as a force field. Extensive validation of the structural features of the atomistic model in comparison with experimental data is provided by [START_REF] Honorio | Heat capacity, isothermal compressibility, isosteric heat of adsorption and thermal expansion of water confined in C-S-H[END_REF]. Various pore sizes are constructed by increasing the interlayer distance for one of the pores present in this C-S-H model. Grand canonical Monte Carlo simulations are performed to get the equilibrium water content for each pore size under ambient conditions (temperature of 300 K and 100% RH [START_REF] Honorio | Heat capacity, isothermal compressibility, isosteric heat of adsorption and thermal expansion of water confined in C-S-H[END_REF]). Simulations for surface water are performed for a single pore size that is big enough so that superposing effects of the opposing pore surfaces are negligible and a significant portion of the pore behaves like bulk water (see details in [START_REF] Honorio | Surface water in C-S-H: effect of the temperature on (de)sorption[END_REF]). Properties are computed using the appropriate fluctuation formula as detailed in each study.

Results and Discussion

Figure 1 shows the evolution of various properties as a function of the interlayer distance in C-S-H under ambient conditions. The isochoric heat capacity cv, molar incremental enthalpy of adsorption ha, and bulk modulus K of water increase with the confinement. Regarding transport properties, self-diffusion increases with confinement with a change in the dynamical regime for interlayer pores below 3 nm thick [START_REF] Honorio | Water self-diffusion in C-S-H: Effect of confinement and temperature studied by molecular dynamics[END_REF]). The shear viscosity of water strongly increases with confinement, which is in agreement with experimental observations on various nanoporous systems [START_REF] Honorio | Permeability of C-S-H[END_REF]). For pores above 5-7 nm thick, water retrieves its bulk behavior overall. This means that larger portions of water have a bulk-like behavior, so that the contribution of surface water to the total behavior is less Sim.

Bulk water (Exp.)

Bulk water (SPC/E)

Effective pore thickness [Å]

pronounced. Properties like self-diffusion and dielectric permittivity are markedly anisotropic: the response perpendicular to the pore plan is strongly reduced in the case of self-diffusion [START_REF] Honorio | Water self-diffusion in C-S-H: Effect of confinement and temperature studied by molecular dynamics[END_REF]) and vanishes in the case of dielectric permittivity (Ait Hamadouche et al. ( 2023)). Figure 2 shows how the isochoric heat capacity cv, molar incremental enthalpy of adsorption ha, and bulk modulus K of surface water vary as a function of the layer position. Two poromechanical conditions are considered: liquid water-saturated (RH = 100%) and constant partial fluid pressure (Pr = 1 atm). The first layer is closer to the C-S-H surface. Each layer is 2.4 Å thick based on the analysis of water oxygen profiles, as detailed in Honorio et al. (2023a). Layers 1-3 are within the interphase defined by the C-S-H rough surface and microportlandite clusters adsorbed. The heat capacity peaks are close to the phase boundary between surface water and bulk water. The analysis of enthalpy of adsorption confirms the high hydrophilicity of the surface, with the position closer to the surface being energetically more favorable than the bulk portion of the pore (layer 5 and above). The bulk modulus of the first layers is significantly larger, corroborating the picture in which surface water exhibits a more rigid, solid-like behavior. The results above enable revisiting the classes of pore water required to fully explain the pore water behavior in cement-based materials. Only three classes of pore water are needed: 1. Interlayer water: it is the water confined in pores smaller than 3-4 nm. Due to the cohesion forces, the most prevalent interlayer distance is associated with the basal distance (the most stable one). Pores smaller than the ones associated with the basal distance are energetically unfavorable due to steric repulsion. The analysis of disjoining pressure profiles shows that mechanical instabilities may arise for some pore size immediately above (in the range of interlayer distance of 1.5 to 1.6 nm) the basal distance, which means that the distribution of interlayer pore size should be very narrow. Interlayer water can be seen as pore water since it diffuses, and (ii) the interlayer water molecules can exchange with neighboring pores reversibly under hydro-thermal variations (i.e. water can be dried out or readsorbed in the interlayer under the right RH and temperature conditions). The collapse of the interlayer space only occurs at extremely low RH (< 1%), which is not relevant for most of the applications. Property change under confinement is accompanied by changes in water molecules arrangements and H-bond network structure [START_REF] Honorio | Heat capacity, isothermal compressibility, isosteric heat of adsorption and thermal expansion of water confined in C-S-H[END_REF]). 2. Surface (or interfacial) water: it is the water adsorbed onto the C-S-H surface in pores with interlayer distance above about 5-7 nm, so that the effects of opposing C-S-H do not superpose. Most of surface water is located within the interphase containing C-S-H surface roughness, calcium counterions and hydroxides adsorbed on the surface. The total thickness of this interphase is about 7.5 Å according to density profiles (of water, silica, and adsorbed ions) (Honorio et al. (2023a)) and also according to the slip length determined from the analysis of hydrodynamics in C-S-H channels [START_REF] Honorio | Permeability of C-S-H[END_REF]). The first 3 to 4 water layers (defined according to the density profiles of water oxygen) adsorbed on the C-S-H surface have a distinct behavior from bulk water and should be Water Layer T considered as surface water. Each water layer is 2.4 Å thick up to temperatures exceeding around 300°C (Honorio et al. (2023a)). 3. Bulk water: water in the central portion of pores larger than 5-7 nm shows already bulk-like behavior.

Properties strongly affected by anisotropic effects, such as diffusion, permeability and dielectric permittivity, also show bulk-like behavior in the direction parallel to the pore surface. For these properties, the behavior in the direction perpendicular to the pore surface is roughly suppressed [START_REF] Honorio | Water self-diffusion in C-S-H: Effect of confinement and temperature studied by molecular dynamics[END_REF][START_REF] Ait Hamadouche | Dielectric permittivity of C-S-H[END_REF]), Honorio et al. (2023a)). With this classification, gel and capillary pores are a mix of both surface and bulk water, with the latter dominating in the case of large gel and capillary pores.

Conclusions

The behavior of confined and surface water was quantified using molecular simulations, which is a wellsuited technique enabling to assess the nanoscale under controlled conditions. Both surface and interlayer water exhibit reduced dynamics with an intermediary behavior between liquid and solid. The physical phenomena at the origins of the changes in the behavior of interlayer and surface water are water molecules arrangements, H-bond network structure, and changes in the system's local energetics. Only three distinct classes of water are needed to explain pore water in C-S-H: (i) interlayer water (pores smaller than 3-4 nm), (ii) surface water (water adsorbed onto C-S-H surface up to 1 nm distance from the surface in pores with interlayer distance above about 5-7 nm), and (iii) bulk water (water in the central portion of pores larger than 5-7 nm). These results are helpful inputs for multiscale modeling concerning confined and surface water properties. Also, they provide new physical insights to revisit sorption models and understand drying processes.

Figure 1 :

 1 Figure 1: Properties of water confined in C-S-H as a function of the effective pore size (as defined in Honorio (2022)): isochoric heat capacity cv, molar incremental enthalpy of adsorption ha, bulk modulus K, selfdiffusion Dyx (parallel to the pore plane), shear viscosity 𝜂, and dielectric constant 𝜀.

Figure 2 :

 2 Figure 2: Properties of surface water per layer (layer 1 being closer to the surface; layers 5 and above being in the bulk zone of the pore): isochoric heat capacity cv, enthalpy of adsorption ha, and bulk modulus K.

Acknowledgements

The financial support of the French National Research Agency (ANR) through the project THEDESCO (ANR-19-CE22-0004-01) is gratefully acknowledged.


F Masara

T Honorio
email: tulio.honorio@ens-paris-saclay.fr

F Benboudjema
email: farid.benboudjema@ens-paris-saclay.fr

(ICCC2023) "Further Reduction of CO2 -Emissions and Circularity in the Cement and Concrete Industry" September 18-22, 2023, Bangkok, Thailand C-S-H sorption under temperature and relative humidity changes

Keywords: C-S-H, Desorption, Temperature, Cavitation, Molecular simulations

Water vapor sorption measurements have positively contributed to the understanding of various phenomena affecting the durability and performance of cement-based materials. The temperature can have a great influence on these measurements. An in-depth research on the effect of temperature on sorption processes in cement-based materials informed by the molecular scale may offer new physical insights into understanding the phenomena. In this work, we aim to study water sorption in C-S-H. Specifically, we focus on the effect of temperature on water desorption in C-S-H at the molecular scale. Effective interactions and desorption isotherms are interpreted. Other features like water cavitation and stability under sorption are also analyzed. All these properties and features are investigated for temperatures between 27 and 150 °C through molecular simulation techniques. The influence of the pore size on the behavior of C-S-H under desorption is investigated. The effect of the temperature on the cohesion in C-S-H is also discussed. Cavitation shows a strong correlation with the temperature and the C-S-H pore size. The cohesion between the C-S-H layers increases with the temperature. These data can serve as valuable inputs for multi-scale models.

Introduction

Moisture is a key factor in the durability of cement-based materials, as many processes affecting the durability of cement-based materials are moisture dependent (e.g., cracking, drying and autogeneous shrinkage, creep, and fire spalling). Water vapor sorption isotherms describe the variation of the moisture content with the relative humidity (RH). The temperature can have a significant impact on the water sorption behavior of cement-based materials, which can consequently affect the shape of the sorption isotherm [START_REF] Poyet | Experimental investigation of the effect of temperature on the first desorption isotherm of concrete[END_REF]). C-S-H (calcium silicate hydrate), is the primary porous element of Portland cement concrete contributing to sorption in the material. The effect of temperature on sorption in C-S-H at the molecular scale is not yet fully addressed, especially in what concerns the interplay between temperature and RH changes. In this study, we investigate water sorption in C-S-H at different temperatures (27, 100, and 150 °C) and relative humidities (from 100 to 0 %) using molecular simulations. We consider C-S-H pores of sizes between 10 and 26 Å (i.e., in the domain of interlayer pores and small gel pores). We analyse the effective interactions, water desorption isotherms, cavitation, and stability under sorption. We also study cohesion in C-S-H and the effects of temperature and relative humidity on this property. The observables of this study can be used to develop a model of the behavior of cement-based materials at different scales. 2018)), which features an orthogonal structure with two micropores of 13.7 Å interlayer distance each. In this work, one of the micropores has a constant size (13.7 Å interlayer distance), while the other one varies in size between 10 and 26 Å. Ca1.67SiO3.7. nH2O is the molecular formula of C-S-H. The interactions between atoms are elucidated using the ClayFF force field [START_REF] Cygan | Molecular Models of Hydroxide, Oxyhydroxide, and Clay Phases and the Development of a General Force Field[END_REF]) and the SPC/E water model [START_REF] Berendsen | The Missing Term in Effective Pair Potentialst[END_REF]). Further details regarding the model can be found in [START_REF] Honorio | Heat capacity, isothermal compressibility, isosteric heat of adsorption and thermal expansion of water confined in C-S[END_REF], (2022); Masara et al ( 2023)). Figure 1 shows an atomic representation of one of the C-S-H pore sizes.

Models and Methods

C-S-H atomic details and force field

Simulation steps

In this study, LAMMPS [START_REF] Plimpton | Fast Parallel Algorithms for Short-Range Molecular Dynamics[END_REF]) is used to conduct hybrid Grand Canonical Monte Carlo (GCMC)-Molecular Dynamics (MD) simulations in two different ensembles: 𝜇VT ensemble for water and NVT ensemble for all the remaining particles. The first ensemble implies that the number of water molecules can flucuate (depending on the setted temperature and relative humidity). The second ensemble implies that the number of solid particles, calcium counterions and hydroxides is constant. Interlayer water molecules exchange with an infinite bulk water reservoir of a constant chemical potential 𝜇 and temperature T. The chemical potential of the water reservoir, which depends on the temperature and relative humidity, is given as 𝜇 ≈ 𝜇 0 (𝑇) + 𝑘 𝐵 𝑇ln(RH), where 𝜇 0 is the chemical potential when the system is saturated, 𝑘 𝐵 is the Boltzmann constant and RH is the relative humidity. The relationship between the temperature and vapor pressure (or the temperature and relative humidity) is expressed using the Clausius-Clapeyron equation [START_REF] Fugel | A corresponding-states analysis of the liquid-vapor equilibrium properties of common water models[END_REF]). Periodic boundary conditions are used and the solid layers are immobilized to minimize the simulations time.

Effective interactions

The thermodynamic potential or the potential of mean force (PMF), describing the effective interactions in C-S-H, is calculated as a function of the interlayer distance using:

Λ(𝑑) = Λ 0 (𝑑 0 , 𝜇, 𝑇) -𝑆 𝑠 ∫ 𝑃𝑑(𝑑) 𝑑 𝑑 0 (1)
where 𝑆 𝑠 is the surface area (constant), 𝑃 is the confining pressure, and 𝑑 is the imposed interlayer distance.

Results and discussion

Effective interactions

Figure 1 shows the evolution of the PMF with the interlayer distance from 100 to 0% relative humidity at 27, 100 and 150 °C. As shown in the figure, the shape of the PMF curve and the depth of the PMF well change with the relative humidity and the temperature. The minimum in the well refers to the most stable interlayer distance or the basal distance. At a given temperature, the basal distance decreases with the decreasing relative humidity. This implies the shrinkage of the pores upon desorption. The deepness of the PMF well increases when the relative humidity decreases with a jump occuring between 0.1 and 0 % relative humidity. The effect of the temperature on the depth of the PMF well is similar to that of relative humidity. At a constant relative humdity (range of relative humidities between 100 and 0.1%), the depth of the PMF well increases with the increasing temperature. For 0% relative humidity, the PMF well is independent of the temperature since water is totally desorbed at all the temperatures and the solid layers remain stable even when heated (the alteration of the solid layers upon heating is not simulated). The mobility of calcium counterions and hydroxides does not affect the PMF at this RH, which is an indication of the stability of microportlandinte clusters with temperature increase. The observed increase in the PMF well depth with the increasing temperature or decreasing relative humidity indicates a greater level of cohesion in C-S-H.

Desorption isotherms

Figure 1 shows the desorption isotherms of C-S-H interlayer distances between 25.3 and 13.7 Å at 27, 100 and 150 °C. In all the examined pore sizes, the desorption isotherms demonstrate a noticeable dependency on the temperature. At 27 °C, the desorption isotherms for the interlayer distances ≥ 20.3 Å exhibit a discontinuous pattern, where the sudden decay in the water content reflects cavitation. With an increase in the temperature to 100 °C, the cavitation relative humidity increases. As the temperature increases more (case of 150°C), the desorption isotherms display decreased discontinuity. For interlayer distances < 20.3 Å, the desorption isotherms show a continuous behavior at the three temperature values. The effect of temperature on the desorption behavior in these pore sizes can be seen as an increased water desorption (or decreased water content) at higher temperatures. The sensitivity of desorption isotherm to the temperature was also found in the work of Maruyama et al. [START_REF] Maruyama | Cavitation of water in hardened cement paste under short-term desorption measurements[END_REF]). The authors of this work observed an increase in the cavitation relative humidity with the temperature for all the materials they tested (including concrete).

The desorption isotherms in this work show as well a sensitivity to the pore size. This appears as a decrease in the cavitation relative humidity with the decrease in the pore size. The study of Rasmussen et al. [START_REF] Rasmussen | Cavitation in Metastable Liquid Nitrogen Confined to Nanoscale Pores[END_REF]) on another microporous material reported a similar relationship.

Conclusion

This study aims to understand the combined effect of the temperature and relative humidity on sorption in C-S-H interlayer micropores with the help of molecular simulations. The effective interactions show an elevated cohesion upon water desorption, either due to the increased temperature or decreased relative humidity. This implies an increase in the strength of concrete due to the higher cohesion in C-S-H upon heating. The desorption isotherms show a large dependence on the temperature and the pore size. Cavitation appears in small mesopores (≥ 20.3 Å) and disappears in smaller pore sizes. For pores ≥ 20.3 Å, the cavitation RH increases with the temperature. The observations of this study can give important physical insights into predicting the drying shrinkage and creep of cement-based materials through the understanding of the molecular processes at the level of C-S-H leading to these phenomena.

  This study uses the atomistic C-S-H model of Kunhi Mohamed et al.(Kunhi Mohamed et al (

Figure 1 :

 1 Figure 1: Atomic structure of the 25.3 Å interlayer distance pore at a T =27°C and RH =100 %.

Figure 3 :

 3 Figure 3: The water content evolution during desorption in C-S-H interlayer distances between 13.7 and 25.3 Å at 27, 100 and 150 °C.

PMF versus the interlayer distance for various RH upon desorption at 27, 100 and 150 °C.

	2 ] PMF [kT/nm	0 175 -175	10	14	18 27	22 °C RH=100% 26 RH=70% RH=50%	10	14	18 100	22 °C RH=100% 26 RH=70% RH=50%	10	Water 14	18 150	OH -22 °C RH=100% 26 RH=70% RH=50%
									RH=30% RH=10%						RH=30% RH=10%	SiO4	RH=30% RH=10%
		-350			d [Å]	RH=1% RH=0.1% RH=0%			d [Å]	RH=1% RH=0.1% RH=0%	Calcium counterions d [Å] RH=1% RH=0.1% RH=0%
	Figure 2:
	[-] N/N T	0,6 0,8 1 1,2 0,4 0,2 0			27	°C bulk water 25.3 Å 24.3 Å 23.3 Å 22.3 Å 21.3 Å 20.3 Å 19.3 Å 18.3 Å 17.3 Å 16.3 Å 13.7 Å			100	°C 25.3 Å 24.3 Å 23.3 Å 22.3 Å 21.3 Å 20.3 Å 19.3 Å 18.3 Å 17.3 Å 16.3 Å 13.7 Å	150	°C 25.3 Å 24.3 Å 23.3 Å 22.3 Å 21.3 Å 20.3 Å 19.3 Å 18.3 Å 17.3 Å 16.3 Å 13.7 Å
				0	20	40		60	80 100	0	20	40	60	80 100	0	20	40	60	80 100
						RH [%]				RH [%]		RH [%]

Acknowledgment

The funding of the French National Research Agency (ANR) via the project THEDESCO (ANR-19-CE22-0004-01) is highly appreciated.