J Archez

Nathalie Texier-Mandoki

Xavier Bourbon

Jean-François F Caron

S Rossignol
email: sylvie.rossignol@unilim.fr

Adaptation of the geopolymer composite formulation binder to the shaping process

Keywords: Geopolymer, Composite, Shaping process, Casting, Additive manufacturing, Feasibility

teaching and research institutions in France or abroad, or from public or private research centers.

I. INTRODUCTION

Cigéo is the radioactive waste disposal facility project led by the French National Radioactive Waste Management Agency (Andra). This deep geological disposal designed for long term management of the high and intermediate-level radioactive waste will be built in the east of the Parisian basin (France). The high-level radioactive waste cell concept is based on a steal liner inserted in a tunnel dug in geological medium, and whose primary function is mechanical to ensure safety, security, and retrievability during the operating phase. The use of geopolymers reinforced with inorganic elements could be an innovative solution for the liner to reduce metallic use in the project and meet the mechanical specifications.

Geopolymers are inorganic materials synthesized by dissolving an aluminosilicate source in a silicate alkaline solution [START_REF] Glukhovsky | Soil silicates[END_REF][START_REF] Davidovits | Geopolymers and geopolymeric materials[END_REF]. The reactive mixture obtained is under a viscous liquid form until a fast setting phase. The setting time is depending on the formulation of the geopolymer (as a function of the alkaline solution [START_REF] Panda | Extrusion and rheology characterization of geopolymer nanocomposites used in 3D printing[END_REF][START_REF] Arnoult | How to control the geopolymer setting time with the alkaline silicate solution[END_REF], the aluminosilicate source [START_REF] Romagnoli | Rheological characterization of fly-ash-based suspensions[END_REF][START_REF] Arnoult | Geopolymer synthetized using reactive or unreactive aluminosilicate. Understanding of reactive mixture[END_REF] or the use of additives [START_REF] Dupuy | Metakaolin-based geopolymer: formation of new phases influencing the setting with the use of additives[END_REF][START_REF] Bong | Efficiency of different superplasticizers and retarders on properties of 'one part' fly ash-slag blended geopolymers with different activators[END_REF][START_REF] Sri Umniati | Workability enhancement of geopolymer concrete through the use of retarder[END_REF]). The setting is achieved at room temperature by polycondensation and geopolymerization reactions. Geopolymer materials present a wide range of mechanical properties: compressive strength between 10 to 110 MPa and bending strength from 3 to 17 MPa depending on the formulation or reinforcements [START_REF] Sé Ribeiro | A review of particle and fiber reinforced metakaolin based geopolymer composites[END_REF]. Geopolymers also exhibit high temperature resistance and chemical durability (acids) [START_REF] Provis | Geopolymers. Structure, Processing[END_REF]. By-products can also be used as an aluminosilicate source [START_REF] Xu | The geopolymerization of alumino-silicate minerals[END_REF][START_REF] Bakharev | Thermal behaviour of geopolymers prepared using class-F fly ash and elevated temperature curing[END_REF][START_REF] Capasso | Reuse of mining waste as aggregates in fly ash-based geopolymers[END_REF]. As an example, argillite from the Callovo-Oxfordian layer (taken from the French underground level laboratory at Bure site) was used to make a grout [START_REF] Dupuy | Thermal resistance of argillitebased alkali-activated materials. Part I: effect of calcination processes and alkali cation[END_REF][START_REF] Dupuy | Formulation of an alkali-activated grout based on Callovo-Oxfordian argillite for an application in geological radioactive waste disposal[END_REF]. In the literature, inorganic reinforcements such as basalt fibers [START_REF] Welter | Evolution of the fibre-matrix interactions in basalt-fibrereinforced geopolymer matrix composites after heating[END_REF][START_REF] Rill | Properties of basalt fiber reinforced geopolymer composites[END_REF], glass fibers [START_REF] Steinerova | The Brittleness and chemical stability of optimized geopolymer composites[END_REF][START_REF] Sathanandam | Low carbon building : experimental insight on the use of fly ash and glass fiber for making geopolymer concrete[END_REF], or wollastonite needles [START_REF] Silva | Fibre reinforcement and fracture response in geopolymeric mortars[END_REF][START_REF] Bong | Properties of one-part geopolymer incorporating wollastonite as partial replacement of geopolymer precursor and sand[END_REF] have been used with geopolymers or alkali-activated materials to reinforce the material and improve its ductility through controlled microcracking.

The influence of wollastonite and glass fibers on geopolymerization reaction, viscosity, and mechanical properties of geopolymer composite have been studied previously to formulate geopolymer composites [START_REF] Archez | Influence of the wollastonite and glass fibers on geopolymer composites workability and mechanical properties[END_REF]. To shape these composites, a common process is to cast materials in molds [START_REF] Peyne | Feasibility of producing geopolymer binder based on a brick clay mixture[END_REF][START_REF] Chindaprasirt | Workability and strength of coarse high calcium fly ash geopolymer[END_REF]. Other processes can also be used such as mold pressing [START_REF] Chen | Feasibility of manufacturing geopolymer bricks using circulating fluidized bed combustion bottom ash[END_REF][START_REF] Huang | Properties of waste-based geopolymer building blocks[END_REF][START_REF] Wang | High strength inorganic-organic polymer composites (IOPC) manufactured by mold pressing of geopolymers[END_REF] or injection [START_REF] Koutnik | Low viscosity metakaolinite based geopolymer binders[END_REF][START_REF] Medri | Metakaolin-based geopolymer beads: Production methods and characterization[END_REF]. Low viscosity reactive mixture can also be sprayed as droplets using a spray gun [START_REF] Temuujin | Thermal properties of spray coated geopolymer type compositions[END_REF][START_REF] Matthews | Large-Diameter Sewer Rehabilitation Using a Spray-Applied Fiber-Reinforced Geopolymer Mortar[END_REF]. Using this "spray technique", hollow cylinders have been produced with a low viscosity geopolymer onto a rotating cylindrical mold [START_REF] Mairitsch | Composition and properties of a metakaolin-based geopolymer binder suitable for shaping using a slinger[END_REF]. The addition of reinforcement leads to an increase in viscosity and consequently reduces the flowability of the material and its workability. In the presence of short or micrometric fibers, the decrease in flowability has been observed by Alomayri [START_REF] Alomayri | The microstructural and mechanical properties of geopolymer composites containing glass microfibers[END_REF] and a maximum rate of 2 % of fiber by volume was emitted.

Moreover, Soliman et al. [START_REF] Soliman | Effect of Natural Wollastonite Microfibers on Early-Age Behavior of UHPC[END_REF] observed a decrease of the concrete flowability up to 12 % with the addition of 17 %w of wollastonite due to the interlocking of wollastonite needles. Vickers et al. [START_REF] Vickers | Strategies to control the high temperature shrinkage of fly ash based geopolymer[END_REF] also observed a 53 % decrease in flowability with the addition of 13 %w of wollastonite.

High viscosity reactive mixtures can be shaped using other techniques such as extrusion or additive manufacturing with a robocasting (or Direct Ink Writing) process [START_REF] Panda | Extrusion and rheology characterization of geopolymer nanocomposites used in 3D printing[END_REF]. In these cases, the rheological properties of the reactive mixture must be controlled to allow a pumpability, a printability, and a buildability of the material with an adapted setting time [START_REF] Lim | Developments in construction-scale additive manufacturing processes[END_REF][START_REF] Le | Mix design and fresh properties for high-performance printing concrete[END_REF]. The robocasting process has been used in the literature with alkali-activated composites [START_REF] Panda | Anisotropic mechanical performance of 3D printed fiber reinforced sustainable construction material[END_REF] or with the addition of organic adjuvant such as poly(ethylenglycole) PEG or poly(acylic acid) PAA in geopolymers [START_REF] Franchin | Direct ink writing of geopolymeric inks[END_REF]. The authors studied the rheology of the geopolymers and shown that geopolymers could behave like Bingham fluid with a yield stress and a fast viscosity recovery after shear stress significant of a high shape retention after extrusion. This behavior makes geopolymer suitable to be used in additive manufacturing. The rheology is then commonly used to verify the extrudability of the composition in presence of several additives (plasticizers, adjuvants …) [START_REF] Franchin | Direct ink writing of geopolymeric inks[END_REF][START_REF] Bong | Fresh and Hardened Properties of 3D Printable Geopolymer Cured in Ambient Temperature[END_REF][START_REF] Paul | Fresh and hardened properties of 3D printable cementitious materials for building and construction[END_REF]. The use of organic adjuvants to adapt the rheology is prohibited for our specific application. Another approach has here been chosen: without the rheology, but by studying the formulation (metakaolin, wollastonite, glass fibers) as a function of the way of shaping. Some authors have already compared the difference in the mechanical behavior of the same composition produced by casting or robocasting with concrete [START_REF] Nerella | Studying the Printability of Fresh Concrete for Formwork-Free Concrete Onsite 3D Printing Technology (CONPrint3D)[END_REF][START_REF] Bos | Ductility of 3D printed concrete reinforced with short straight steel fibers[END_REF] or alkali-activated [START_REF] Paul | Fresh and hardened properties of 3D printable cementitious materials for building and construction[END_REF][START_REF] Panda | Anisotropic mechanical performance of 3D printed fiber reinforced sustainable construction material[END_REF]. An increase in bending mechanical resistance in the order of 14 % was observed in robocasting compared to the casting process due to the orientation of the fibers perpendicular to the stress. These data must be linked to the manufacturing process. However, the presence of fibers during extrusion [START_REF] Steinerova | The Brittleness and chemical stability of optimized geopolymer composites[END_REF][START_REF] Nematollahi | Effect of type of fiber on inter-layer bond and flexural strengths of extrusion-based 3D printed geopolymer[END_REF], or the use of unsuitable parameters (extrusion speed and pressure, nozzle height) may cause the formation of voids [START_REF] Panda | Measurement of tensile bond strength of 3D printed geopolymer mortar[END_REF], reduces the adhesion of the layers [START_REF] Al-Qutaifi | Mechanical properties of layered geopolymer structures applicable in concrete 3D-printing[END_REF][START_REF] Sanjayan | Effect of surface moisture on inter-layer strength of 3D printed concrete[END_REF] and therefore decrease the mechanical properties. To our knowledge, there is no use of a same geopolymer formulation that can be shaped by casting and robocasting or no studies allowing to adapt a formulation to different shaping processes without the use of organic adjuvants.

This work aims to determine a range of formulation adaptable to different shaping. For this, the feasibility of shaping of different geopolymer composite formulation was studied by varying the amount of metakaolin, wollastonite, and glass fibers. The geopolymer composites were then shaped by casting and robocasting and the properties of the formulations were compared to their feasibility of shaping.

II. EXPERIMENTAL 1. Raw materials and samples preparation

To elaborate on the geopolymer composites, the reactive mixture is obtained by dissolving a commercial metakaolin provided by Imerys called M1 (Si/Al = 1.17 The nomenclature used is MxWyGz, where M, W, and G stand for the Metakaolin, the Wollastonite and the Glass fibers respectively, whereas x refers to the quantity of metakaolin in grams added in 15,6 g of alkaline solution S3 and y, z represent the weight percentage of wollastonite and glass fibers respectively, relative to the mass of the binder (S3 + M1). As an example, for 15,6 g of solution S3, 16 g of metakaolin M1, 3.16 g of wollastonite W, and 0.63 g of glass fibers G, the composite will be referenced as M16W10G2. The wollastonite and the glass fibers were added in two geopolymer binders (M16 and M19) that had, respectively, a ratio nSi/nAl equal to 1,55 and 1,49 and a ratio nK/nH2O equal to 0,141.

Process of fabrication

The reactive mixture is cast in a closed mold or used by additive manufacturing (Figure 1).

The casting is realized by pouring the reactive mixture in cylindrical mold (Φ = 15 mm, H = 30 mm, e= 10 mm) (Figure 1-a). The mold is then placed on a vibrating table (50 Hz) for five minutes. The cylinder was unmolded when the reactive mixture started to present a mechanical resistance (around 12 h). The central part is first removed then the piece is extracted using a piston.

The additive manufactured samples are elaborated by robocasting with a 3D Potterbot printer and the printing path (gcode) is coded with Rhinoceros/Grasshopper software (Figure 1-b). To print on a large scale, the reactive mixture is extruded through a large nozzle of 10 mm. The flow is set up manually during the printing to maintain a layer width of 10 mm with a nozzle speed of 3 mm/s. A layer height of 6,5 mm is used to press and deform the new layer on the underneath layer and to ensure a better contact area and interface between the layers [START_REF] Al-Qutaifi | Mechanical properties of layered geopolymer structures applicable in concrete 3D-printing[END_REF][START_REF] Bos | Additive manufacturing of concrete in construction: potentials and challenges of 3D concrete printing[END_REF].

The temperature could have been adapted for the process, however, a temperature had to be optimized for each formulation [START_REF] Autef | Role of the silica source on the geopolymerization rate: A thermal analysis study[END_REF]. In order to compare the formulations, the process was then carried out at room temperature. The consolidated material cast or printed is finally stored in a climatic chamber at 20 °C and 85 % RH with a saline solution of KCl.

Sample characterization

The viscosity measurements of the reactive mixture are carried out on a Brookfield DV-II viscometer (with an estimated error of 1 %) on 60 cm 3 of the reactive mixture in a cylindrical container twenty minutes after mixing the raw materials. To override the thixotropic effect and compare the measurements, the average viscosity value is determined over a one-minute measurement with a spindle LV4 -64. The spindle's speed is set up according to the viscosity, with values ranging from 0.1 to 100 rpm. The maximum viscosity value measurable is 6000 Pa•s. Differential Thermal Analysis (DTA) and Thermogravimetric Analysis (TGA) are carried out on an SDT Q600 apparatus from TA Instruments, using Pt/Pt -10 % Rh thermocouples under a flowing dry-air atmosphere (100 cm 3 /min). The powder samples were stored at 20°C and 85 % relative humidity, and then heated up in platinum crucibles to 500 °C with a 5 °C.min -1 heating slope.

The compressive tests were realized on six cylindrical samples (Φ = 15 mm, H = 30 mm) for each composition after seven days of consolidation. The cylindrical samples were rectified and tested using an Instron 5969, at a constant speed of 0.5 mm.min -1 with a load cell of 50 kN.

Three-point bending tests were carried out on six prismatic samples (20 x 20 x 100 mm) with an Instron 6022 apparatus, a span of 60 mm, a constant speed of 5 µm•min -1, and a load cell of 10 kN. The strains have been measured with strain gauges (Model KFGS-5-120-C1-11, Kyowa Electronic Instruments) centered under the sample, where the strain is maximum. The Young's modulus is determined by measuring the slope at the origin of the stress/strain curve.

III. RESULTS

Determination of the feasibility of shaping

The shaping feasibility of reactive mixtures was first studied according to different metakaolin, wollastonite, and glass fibers content. Different compositions have been observed visually from the reactive mixture extruded with a syringe (Φnozzle = 20 mm / manual pressure).

Pictures of the feasibility tests for four compositions MxWy (with x = 10, 14, 16, 19 g) are presented in the Table 1. Whatever the formulation, the same behaviour is observed: the viscosity of the reactive mixture increases with the addition of wollastonite. The formulation M10Wy is not very viscous for "y" less than 53 %w (ƞi < 3900 Pa•s) and flows after being extruded. For an "y" value ranging from 53 to 65 %w (3900 ≤ ƞi ), the geopolymer retains its shape after extrusion. For a high mass percentage of wollastonite (y > 65 %w), the material is too viscous to be extruded with manual pressure. When using a higher amount of metakaolin (M14Wy, M16Wy et M19Wy), the value of "y" required to reach the extrusion domain decreases (33 %w, 19 %w, and 8 %w respectively).

Thanks to these tests, the shaping domains have been reported in ternary diagrams in moles of aluminum (coming from the metakaolin), wollastonite, and glass fibers with M16WyGz and M19WyGz compositions are presented in Figure 2. The moles of aluminum have been chosen because, as shown in previous studies [START_REF] Archez | Influence of the wollastonite and glass fibers on geopolymer composites workability and mechanical properties[END_REF], the aluminum concentration controls the viscosity and mechanical properties of the geopolymer composite. In order to study the formulations according to their domain of shaping, eight compositions were selected in the ternary diagrams.

The geopolymer binders (a0: M16 and a0': M19) belonging to the casting domain are the compositions of reference. The addition of wollastonite and glass fibers provides castable compositions (a: M16W2G2 et a': M19W0.5G2). Two compositions were selected at the boundary between the casted and extruded domain (mixed domain) (b: M16W10G2 et b': M19W2G2) and two formulations belong to the extruded domain (c: M16W21G2 et c': M19W10G2). The addition of reinforcements allows determining domains of shaping feasibility (casting, extruded, and non-extruded) reported in the ternary diagrams based on molar percentages of aluminum, wollastonite, and glass fibers. The shaping domains evolve with the metakaolin content. In particular, the castable domain decreases with an increase of the metakaolin content (x = 19g).

The compositions M16WyGz (Figure 2-a) have a large castable domain meaning that a large amount of wollastonite and glass fibers can be added while maintaining the castability of the composition. On the other hand, the extrusion domain exists only for a large amount of wollastonite and / or glass fibers. Such amounts also affect the aspect and homogeneity of the extruded material (texture, cluster of fibers). When the metakaolin amount increases (x = 19 g Figure 2-b), the binder viscosity increases and the castable domain decreases at the expense of the extrusion domain. As can be seen, it is possible to determine the castable and extrusion domains of the geopolymer composites depending on the metakaolin, wollastonite, and glass fibers amount. The results obtained with the formulations a0', a', b', c' will be used in the discussion part.

Shaping

In order to verify their shaping feasibility, the compositions a0, a, b, c have been cast in molds and shaped by additive manufacturing to form a hollow cylinder. The photos of the shaping as well as the viscosity of the compositions are displayed in the Table 2. Some compositions could be elaborated with a casting process but not with a robocasting process and vice versa. The geopolymer binder M16, with lower viscosity (η = 23 Pa•s) could be shaped by casting and has a smooth surface appearance without cracks. However, the low viscosity of this composition does not allow a shaping by robocasting since the layers collapse entirely under the weight of the upper layers. A slight increase in viscosity by the addition of wollastonite and glass fibers (M16W2G2, η = 148 Pa•s) allows obtaining the same shaping results. For an even higher viscosity and wollastonite content (composition M16W10G2, η = 800 Pa•s), the reactive mixture could be shaped by casting but present defects (air bubbles) related to the high viscosity of the reactive mixture. This composition can be shaped by robocasting but shows a slight settlement of the lower layers (sagging ratio (hcodehlayers)/hcode equals to 33 %). With more wollastonite, the viscosity is even higher (M16W21G2, η > 6000 Pa•s.) and this composition can only be shaped by robocasting and present a lower settlement (sagging ratio equals to 21 %).

The addition of reinforcement consequently increases the viscosity of the reactive mixture and modifies the feasibility of shaping. A low viscosity composition is preferable to be used in casting while a high viscosity composition can be used in additive manufacturing. Some compositions with intermediate viscosity (M16W10G2) can be elaborated by casting and robocasting but are not optimal and show defects. These data confirm the feasibility of shaping domains observed with a syringe and underline that the choice of shaping must be adapted to the viscosity of the composition and vice versa. It is important to note that the extrudable compositions are hardly castable to elaborate complex molds (hard to cast and presence of bubbles) but could be cast to elaborate compressive and flexural specimens without defects thanks to the use of a vibrating table.

Impact of the formulations on the mechanical properties

First, the results of the thermal analysis and the evaluation of the mechanical properties will be compared. Data relating to the formulations of the ternary (a: M16W2G2, b: M16W10G2 et c: M16W21G2) are presented in Figures 3 and4 The formulations belonging to the extrudable domain have a higher mechanical resistance than the formulations of the castable domain due to a higher amount of reinforcements. The shaping by robocasting consequently allows using compositions that are more heavily loaded and which have greater mechanical properties. As shown in the Figure 1 of supplementary files, it can be noted that the process can induce slightly the mechanical properties between the specimens elaborated by casting or robocasting. The differences are caused by the orientation of fibers during the process (as shown in the Figure 2 of supplementary files) and by the presence of defects caused by the robocasting process. However, it won't be discussed in this paper as all the specimens were cast in mold thanks to the use of a vibrating table.

IV. DISCUSSION

The different results showed that there exist different domains of shaping (casting/robocasting) depending on the formulation of the geopolymer composite and inducing different mechanical properties. This part deals with discussing the formulation parameters influencing the shaping and the induced mechanical properties.

In order to determine the formulation parameters influencing the shaping, the mass loss values (42-500 °C) have been plotted as a function of the aluminum concentration for the formulations a0, a0', a, a', b, b' and c, c' (Figure 5). Water loss is directly linked to polycondensation reactions inducing the mechanical properties of the geopolymer [START_REF] Dupuy | Metakaolin-based geopolymer: formation of new phases influencing the setting with the use of additives[END_REF][START_REF] Arnoult | How to control the geopolymer setting time with the alkaline silicate solution[END_REF].

Aluminum concentration was chosen because it takes into account the metakaolin and the amount of the reinforcement. The concentration of aluminum increases with the addition of metakaolin and decreases with the addition of reinforcements. The same trend is observed depending on the metakaolin amount: an increase of the aluminum concentration leads to an increasing in the water loss observed with thermal analysis and a decrease of the mechanical properties of the consolidated material. Formulations with more metakaolin (a0', a', b', c') can be shaped by casting and additive manufacturing on a greater variation of aluminum concentration. Thus, a formulation heavily loaded with metakaolin and with fewer reinforcement elements (c': M19W10G2) allows obtaining similar mechanical strength (100 MPa) than a formulation weakly charged in metakaolin with more reinforcement elements (c: M16W21G2). In addition, formulations with similar aluminum concentration (a: The relationship between the fresh state properties (viscosity), that condition the shaping, and the requirement of the consolidated state (mechanical properties) have also be checked.

The viscosity values of the composition a0, a, b and c have been plotted as a function of the resistance values in compression and bending. (Figure 6). The two shaping areas and their limits are also reported. The maximum viscosity of 6000 Pa•s corresponds to the measurement limits of the viscometer. The compression and bending mechanical properties evolve similarly according to these domains of shaping: they are weaker for lower viscosities (castable domain) and stronger for higher viscosities (extrusion domain). Reactive mixtures with no or little reinforcements (M16, M16W2G2) can be used in casting due to their low viscosity and has compressive mechanical strengths of 71 and 89 MPa. These values are in the range of mechanical properties of geopolymers (from 10 to 110 MPa [START_REF] Sé Ribeiro | A review of particle and fiber reinforced metakaolin based geopolymer composites[END_REF]). A higher amount of wollastonite increases the viscosity of the reactive mixture and allows it to obtain a composition (M16W10G2) castable and extrudable with satisfactory mechanical properties (89 MPa). In comparison, Panda et al. [START_REF] Panda | Anisotropic mechanical performance of 3D printed fiber reinforced sustainable construction material[END_REF] and Paul et al. [START_REF] Paul | Fresh and hardened properties of 3D printable cementitious materials for building and construction[END_REF] obtain respectively maximum compressive strengths of 35 MPa at 28 days and 58 MPa at 21 days using alkali-activated materials which are both castable and extrudable. An additional amount of wollastonite (M16W10G2) induces an increase of the mechanical properties (99 MPa) and allows to use the robocasting process. These values are high compared to the materials usually used in robocasting. For example, Bong et al. [START_REF] Bong | Fresh and Hardened Properties of 3D Printable Geopolymer Cured in Ambient Temperature[END_REF] and Kashani et al. [START_REF] Kashani | Optimisation of Mixture Properties for 3D Printing of Geopolymer Concrete[END_REF] used alkali-activated materials adapted to the robocasting process which present maximum compressive stresses in compression of 17 and 58 MPa respectively.

To our knowledge, no value is listed for extrudable geopolymers. The amount of wollastonite consequently permits to choose the shaping process (casting or robocasting) while controlling the mechanical properties of the consolidated material. Moreover, the robocasting process permits to use of compositions that are more heavily loaded and have higher mechanical properties than the casting process.

In order to compare these data and those of the literature, the reinforcement amounts (%w) of glass fibers and wollastonite from previous work on cement [START_REF] Soliman | Effect of Natural Wollastonite Microfibers on Early-Age Behavior of UHPC[END_REF][START_REF] Low | Mechanical properties of high performance cement binders reinforced with wollastonite micro-fibres[END_REF][START_REF] Ransinchung | Investigations on Pastes and Mortars of Ordinary Portland Cement Admixed with Wollastonite and Microsilica[END_REF][START_REF] Kizilkanat | Mechanical properties and fracture behavior of basalt and glass fiber reinforced concrete: An experimental study[END_REF] alkali-activated materials [START_REF] Steinerova | The Brittleness and chemical stability of optimized geopolymer composites[END_REF][START_REF] Vickers | Strategies to control the high temperature shrinkage of fly ash based geopolymer[END_REF][START_REF] Novais | Effective mechanical reinforcement of inorganic polymers using glass fibre waste[END_REF][START_REF] Nurjaya | Thermal effect on flexural strength of geopolymer matrix composite with alumina and wollastonite as fillers[END_REF][START_REF] Nematollahi | Properties of fresh and hardened glass fiber reinforced fly ash based geopolymer concrete[END_REF] and geopolymers [START_REF] Ren | Durability performances of wollastonite, tremolite and basalt fiber-reinforced metakaolin geopolymer composites under sulfate and chloride attack[END_REF][START_REF] Li | Short fiber reinforced geopolymer composites manufactured by extrusion[END_REF] were compared with the domains of shaping of the composite M16WyGz (Figure 7). The compositions of the literature are mainly located in the castable or mixed domains. Glass fibers have been used up to a maximum of 5 %w [START_REF] Steinerova | The Brittleness and chemical stability of optimized geopolymer composites[END_REF] corresponding to the extrusion domain. Wollastonite has been used up to 19 %w [START_REF] Low | Mechanical properties of high performance cement binders reinforced with wollastonite micro-fibres[END_REF] (excepted for Ransinchung et al. [START_REF] Ransinchung | Investigations on Pastes and Mortars of Ordinary Portland Cement Admixed with Wollastonite and Microsilica[END_REF] that used up to 43 %w of wollastonite with a particle size of 4 µm, smaller than the cement particles, increasing the workability [START_REF] Soliman | Effect of Natural Wollastonite Microfibers on Early-Age Behavior of UHPC[END_REF]). The compositions used in this study (a0, a, b, c) have a glass fiber content of the same order of magnitude as the data observed in the literature while staying below a critical threshold to limit the formation of voids and balls of fibers [START_REF] Martinie | Rheology of fiber reinforced cementitious materials: classification and prediction[END_REF][START_REF] Swamy | Influence of fibre-aggregate interaction on some properties of steel fibre reinforced concrete[END_REF]. Moreover, compositions used in the extrudable domain (c, c') are more heavily loaded with wollastonite than the data in the literature. However, the extrusion domain depends on the nozzle diameter: the percentage of glass fibers must remain below the critical threshold to keep the material extrudable. This threshold was here equal to 7 % w with the M16 composition and a 20 mm nozzle). As a result, the robocasting process makes it possible to use compositions having higher mechanical properties linked to a greater quantity of reinforcements inserted.

V. CONCLUSION

This study focuses on the determination of a range of formulation for geopolymer composites to use with different shaping processes. The shaping feasibility for different composite formulations was first studied by varying the amount of metakaolin and wollastonite and/or glass fibers as reinforcements. The geopolymer composites were then shaped by casting and by robocasting. The mechanical properties of the formulations were compared.

It has been possible to:

-control the viscosity of the reactive blend by adding wollastonite, -shape hollow cylinders by casting and robocasting with accurate formulations, -map mechanical properties according to the shaping process with an optimum for extruded formulations linked to a higher amount of reinforcement elements, -obtain a castable and extrudable formulation with compression = 89 MPa and bending = 15 MPa.

In future work, the different formulations could be shaped, at the full scale by casting or robocasting, in the function of their shaping feasibility, to elaborate high-level nuclear waste cell liner.

  ) in a commercial potassium silicate solution supplied by Woellner called S3 ([K] = 7 mol/L). After homogenization (3 minutes), inorganic reinforcement elements such as wollastonite and short glass fibers were added and the total mixing time was ten minutes. The wollastonite is acicular particles (L. = 5-170 µm, D. = 3-15 µm) provided by Imerys, and glass fibers are alkali resistant (L. = 6 mm, D. = 13-15 µm) supplied by Owens Corning.

. 4 .

 4 The curves of thermal analysis (DTA-TGA) of compositions a, b and c (Figure 3) display the same trend with different weight loss values. The weight loss between 25 and 200 °C, associated with the endothermic profile, is characteristic of the water loss of geopolymers [52] respectively assigned to physisorbed water (25 -42 ° C), to poral water (42 and 200 ° C) and structural water (200 -500 ° C). The castable composition M16W2G2 (Figure 3 -a) shows a weight loss value (42 -500 °C) of 21 % which gradually decreases to 20 and 17 % for the compositions M16W10G2 et M16W21G2 (Figure 3 -bc). This is due to the modification of the polycondensation reactions induced by the addition of wollastonite and glass fibers [6, 23]. The lower mass loss is due to the kinetics of the promoted polycondensation reactions in the presence of a high wollastonite content. These data underline that the transition from a casting composition to an extrusion composition induces modifications of networks formed on a local scale. The compression and bending stress/strain curves of these same formulations are presented in Figure The different compositions were poured into cylindrical polystyrene tubes and prismatic silicone molds using a vibrating table in order to respectively produce compression and bending specimens. The compositions exhibit brittle fractures in compression and ductile or brittle fracture in bending but also different maximum stress values. The composition M16W2G2 has maximum compressive stress of 83 ± 2 MPa. As seen previously, the wollastonite content increases the maximum stress values which are equal to 89 and 99 MPa respectively for the composition M16W10G2 et M16W21G2. The data relating to the bending stresses present the same variations. The flexural strength of the formulation M16W2G2 is equal to 13 ± 1 MPa and exhibits a ductile fracture. The addition of wollastonite induces an increase of 15 to 18 MPa respectively for the formulations M16W10G2, M16W21G2. The fragile behaviour can be explained by an increase in the stiffness of the material. The castable composition (M16W2G2) presents indeed a Young modulus of 11 ± 1 GPa. This value increases slightly with the wollastonite content to reach 15 GPa for the composition M16W21G2.

  [Al] = 7,5 mol/L and c': [Al] = 7,6 mol/L) but different métakaolin amount (16 and 19 g) exhibit different mechanical properties (83 et 100 MPa) and different way of shaping. The compositions that can be cast or extruded have similar mechanical properties linked to a quantity of metakaolin and different reinforcements.

Figure 1 :Figure 2 :Figure 3 :Figure 4 :

 1234 Figure 1: (a) characteristics of the mold used to make hollow cylindrical parts by casting and (b) 3D printer (3D Potterbot) used to make robocasting.

Figure 5 :

 5 Figure 5: values of weight loss as a function of the aluminum concentration and the compressive stress of the composition (,) a0, a0', (,) a, a', (,) b, b', and (,) c, c'.

Figure 6 :

 6 Figure 6: viscosity values as a function of () compressive and () bending stress for the compositions () a0, () a, () b et () c.

FlowabilityFigure 7 :

 7 Figure 7: representation of the feasibility of shaping domains as a function of the weight percentage of () wollastonite and () glass fibers for the () synthesized samples M16WyGz and the samples used in the literature with ( [34, 52, 53]  [54]) cements, ( [ 35 , 56 ],  [ 55 , 57]) alkali-activated materials, ( [ 58 ],  [19]) geopolymers and ( [38, 59]) samples used in extrusion.

Table 1 :Table 2 :

 12 photos of the feasibility tests made with a syringe (Φnozzle= 20 mm) to determine the shaping domains for the compositions M1xWy with x= 10, 14, 16, 19 g. photos of the compositions a0, a, b et c elaborated by casting and robocasting.

Funding

This work was supported by the French National Radioactive Waste Management Agency (Andra) in collaboration with IRCER and Navier laboratories.


K Dallah

A Bellel

O C Lezzar

S Sahli

P Raynaud

Modeling of interdigital electrodes geometrical parameters effects on chemical sensor response

The detection of volatile organic compounds (VOCs), humidity and toxic industrial chemicals is important for various environmental and industrial applications. The design of interdigital capacitor (IDCs) sensor is carried out in such a way that it would be suitable for microelectronic technology. The basic geometry of IDCs is defined by some parameters such as: number of electrodes N, electrode width W, electrode length L and the separation between electrodes G. The interactions between IDCs sensitive coating and analyte induced a change in the sensors capacitance due to the permittivity variation of the sensitive layer and to the change in polymer thickness (swelling). In this work, a fairly new approach of IDCs based sensor in terms of capacitance calculation has been presented. The results have been obtained from the modeling of the sensors geometry 2D and 3D using multi-physics simulation software COMSOL. The effect of some geometry parameters coupled with swelling measurements for polymeric films has been studied.

Introduction

Detection of volatile organic compounds (VOCs) becomes the world interest in the last few decades, owning to concerns about environmental protection, human health care, industrial processing and air quality control [START_REF] Tsai | Toxic Volatile Organic Compounds (VOCs) in the Atmospheric Environment: Regulatory Aspects and Monitoring in Japan and Korea[END_REF]. Alcohols such as methanol and ethanol are volatile organic solvents that are used in many workplaces and laboratories, medicine and food industry. High concentration exposure to some VOCs over a short or long term may cause diseases or serious irreversible effect [START_REF] Zhou | Health risk assessment of personal inhalation exposure to volatile organiccompounds in Tianjin, China[END_REF][START_REF] Sait | An assessment of indoor air concentrations and health risks of volatile organic compounds in three primary schools[END_REF]. VOCs do not only harm the human and survival health but also pollute the environment due to their contribution to stratospheric ozone depletion. The identification and monitoring of VOCs have become serious tasks in many countries of the world and are important for the early control of environmental pollution. The on-line monitoring and the in-situ analysis of gases represent one of the main objective of current research in the sensor field. In this context, one widely investigated device is the interdigital capacitors (IDCs). These structures have been used in many applications such as surface acoustic wave [START_REF] Wei | Distributed capacitance of planar electrodes in optic and acoustic surface wave devices[END_REF], humidity [START_REF] Wu | Voltage tunable capacitors using high temperature superconductors and ferroelectrics[END_REF] and chemical [START_REF] Alley | Interdigital capacitors and their application to lumped-element microwave integrated circuits[END_REF] sensors. Typical IDCs sensors are made with two comb electrodes deposited on the top of an inert substrate with sensitive coating applied over the electrodes.

The transduction mechanism relies on the permittivity changes and swelling of the sensitive layer, to inflict a change in the sensor capacitance. To achieve high sensitivity from IDCs transducers in chemical detection, an accurate estimation of the electrical parameters (capacitance, impedance, electric field) as a function of the electrode geometrical parameters is crucial. In this work, the simulation of the interdigital capacitor structure has been carried out by COMSOL multiphysics software. The variation of the capacitance for a particular sensor configuration is a function of the materials dielectric permittivity, the ratio between the electrodes gap (the metallization ration), finger widths and the variation of the sensitive layer thickness. Our goal is to explain the effect of these parameters on the sensor sensitivity.

Numerical modelling of the sensor capacitance

In this section, a numerical simulation of the sensors capacitance as function of IDCs geometrical parameters by developing total capacitance equations has been investigated. The COMSOL Multiphysics software was used to simulate the model design of interdigital transducer in (2D) and (3D) dimensions. The software applications are based on partial differential equations (PDEs). The prediction of the IDCs capacitance is based on finite element analysis. The simulation results are very important to design an optimum sensor structure for better performance. The value for electrostatic energy density We can be obtained from the simulation. The energy required to charge a capacitor should equal to that of the electrostatic field, which is given by :

w e = Q 2 2C (1)
We is available in the Electrostatics application mode; the software calculates it by integrating across the domain.

w e = D. E dΩ Ω ( 2
)
where D is the electric displacement, E is the electric field intensity and dΩ is the domain boundary.

The capacitance C is related to the charge on the two conductive electrodes Q and the voltage difference across those electrodes ΔV is given by:

C = Q Δv (3)
The calculation of C is carried out from the stored electric energy We and the voltage across the two electrodes ΔV:

𝐶 = 𝑄 2 2𝑤 𝑒𝐶 = 𝐶 2 𝛥𝑣 2 2𝑤 𝑒 (4) 𝐶 = 2𝑤 𝑒 𝛥𝑣 2
(5)

Modeling of IDCS based sensor response

The sensor responses in terms of capacitance change after analyte sorption have been also simulated in this study. The sensor sensitivity is related to the change in the sensitive layer thickness (because of swelling) and to the change in the sensitive layer permittivity (changing the dielectric constant of the polymer). The swelling phenomenon is related to the amount of analyte molecules that diffuses into the polymer, changing its permittivity [START_REF] Rui Igreja | Dielectric response of interdigital chemocapacitors: The role of the sensitive layer thickness[END_REF].

The new permittivity values have been calculated using the Clausius-Mossoti mixing rule [10]

ℇ mix -1 ℇ mix +2 = ℇ a -1 ℇ p +2 1 -ϕ s + ℇ a -1 ℇa+2 ϕ s (6)
Where:

εp, εa and are the dielectric constants of polymer and analyte, respectively. εmix is the new permittivity value.Φs is the volume fraction of the analyte molecules in the polymeric film which is given by:

ϕ s = Δh h 0 +Δh ( 7
)
Where h0 is the dry polymer film thickness and Δh= h -h0 is equal to the fraction volume change.

In this work, the sensitive layers have been deposited on quartz crystal microbalance (QCM) substrates in order to measure fraction volume change in the polymer. The measured fraction volume change due to polymer swelling has been used in the sensor response simulation. In case of coated QCM, an increase of mass into the crystal electrode due to sorption of analyte molecules induces a shift in the resonance frequency (Δf) according to the well-known Sauerbrey equation [START_REF] Sauerbrey | Verwendung von SchwingquarzenzurWaigungdunnerSchichten und zurMikrowaigung[END_REF] Δf = -

2f 0 2 p Q μ Q . Δm A = - 2f 0 2 p Q v Q . Δm A (8) Δm = P p . A. h (9) h = v Q .Δf 2f 0 2 P p ( 10
)
Where f0 is the resonant frequency, A is the active electrode area, pQ is the density of the quartz crystal, µQ is the shear modulus and vQ is the shear wave velocity of the quartz crystal, Pp is the density of polymer, h is the polymer film thickness, Δf is the frequency change and Δm is the change in mass per unit area. From this equation we may calculate the change in polymer thickness and the volume fraction in the polymer according to equation [START_REF] Guermat | Plasma Polymerization of Hexamethyldisiloxane and Tetraethoxysilane Thin Films for Humidity Sensing Application[END_REF].

Results and discussion

Effect of the coating layer thickness on the sensor capacitance

The effect of coating layer thickness on the IDCs structure capacitance has been studied using COMSOL Multiphysics. The simulation results shown in fig. 1 indicated that the value of IDCs capacitance increases with increasing sensitive layer thickness then reaches a steady state.

For layer thickness lower than about 200 nm, the capacitance increases significantly than slowly.

Beyond the thickness of about 330 nm, electric field distribution in the sensitive layer decreases with increasing layer thickness and the sensor capacity did not change much further. From this observation, we may conclude that the IDCs-based sensor is not sensitive to layer thickness greater than half of its wavelength.

Figure 1.

Sensor capacity variations as a function of layer thickness.

Effect of the metallization ratio on the sensor capacity

In this section, the effect of the geometrical parameters on the IDCs based sensor capacitance has been studied. The geometrical parameters have been defined by (fig. 2):

η = W W +G = 2W λ
; is the metallization ratio.

Fig. 3

 3 Fig.3shows the variation of the IDCs structure capacity with the metallization ratio. As expected, the sensor capacity increases with decreasing the inter electrode distance. High values of IDCs capacitance are obtained for the metallization ratio greater than 250µm.

Figure 3 .

 3 Figure 3. capacitance as a function of the metallization ratio

Figure 5 .

 5 Figure 5. Sensors Responses as a function of : (a) Methanol , (b) Acetone, and (c)Ethanol concentration

Table 1 .

 1 Geometrical parameters of the studied sensors

	Sensors	W(um)	G( um)	η
	Sensor 1	46	276	0.14

Acknowledgments

This work is supported by the Algerian Thematic Agency of Research in Sciences and Technology (ATRST).