Sylvie Tencé-Girault

Vincent Woehling

Evdokia K Oikonomou

Szilvia Karpati

Sophie Norvez
email: sophie.norvez@espci.fr.

About the Art and Science of Visualizing Polymer Morphology using Transmission Electron Microscopy

Transmission electron microscopy is a unique tool to visualize polymer morphology, an intimate organization of the matter, encompassing crystalline features in semi-crystalline polymers and a kaleidoscopic collection of patterns produced by micro-separated phases in polymer blends. This manuscript aims at demonstrating the various opportunities this technique enables, through a miscellany of studies that have been performed in our laboratory. Materials as different as bulk and composite compounds, thin films, hollow fiber membranes, rubbers are presented, from the viewpoint of the interrelation of TEM with other techniques like scattering, mechanical and thermo-mechanical experiments.

Introduction

Exquisite and intriguing complex patterns provided by transmission electron microscopy (TEM) reveal secrets of polymer morphology. [START_REF] Michler | Electron Microscopy of Polymers[END_REF][START_REF] Saywer | Polymer microscopy[END_REF] Polymer morphology is an active area of research, aiming at understanding the properties of the end product or improving its processing. [START_REF] Guo | Polymer Morphology: Principles, Characterization, and Processing[END_REF] Indeed, properties of polymeric materials (mechanical, thermal, optical, …) are to a considerable extent governed by morphological detail. [START_REF] Ruzette | Block copolymers in tomorrow's plastics[END_REF][START_REF] Corté | Crystalline organization and toughening: example of polyamide-12[END_REF][START_REF] Pernot | Design and properties of co-continuous nanostructured polymers by reactive blending[END_REF][START_REF] Orilall | Block copolymer based composition and morphology control in nanostructured hybrid materials for energy conversion and storage: solar cells, batteries, and fuel cells[END_REF] Morphology of polymers has its roots in either crystallization features, or macro/microphase separation, or even in a combination of both. Semi-crystalline polymers develop, either by cooling from a quiescent melt or after solvent evaporation, a hierarchical organization consisting of a crystal structure (0.1-1 nm, observable by WAXS (Wide Angle X-ray Scattering)), organized in lamellae (10-100 nm, accessible by SAXS (Small Angle X-ray Scattering), AFM (Atomic Force Microscopy) and TEM). The lamellae develop into microscopic superstructures, in particular spherulites (> 1000 nm, visible by optical microscopy or scanning electron microscopy (SEM)) consisting of crystalline layers radiating from the spherulite center. [START_REF] Schultz | Polymer Crystallization -The development of Crystalline Order in thermoplastic Polymers[END_REF][START_REF] Schultz | Self-generated fields and polymer crystallization[END_REF] Lamellar morphology is a periodic structure of crystalline and amorphous layers. Constituent chains participate to crystalline lamellae and amorphous phase, and when connecting at least two different crystalline lamellae, they contribute to the plastic and elastic behavior of semi-crystalline polymers. [START_REF] Jabbari-Farouji | Role of the Intercrystalline Tie Chains Network in the Mechanical Response of Semicrystalline Polymers[END_REF] Such a partial crystallization is due to the length of the flexible polymeric molecules that cannot disentangle from each other in the highly viscous melt. Since only a fraction of the polymer chains is transformed into crystals under such conditions of restraint, the crystallinity (volume or weight fraction of crystalline phase), rarely attains more that 50%. [START_REF] Schultz | Polymer Crystallization -The development of Crystalline Order in thermoplastic Polymers[END_REF] Unlike most monomeric substances, polymer crystallization occurs under conditions far from equilibrium. Whereas the most stable state would be that of the fully extended chain, the crystals grow faster by chain folding. [START_REF] Schultz | Polymer Crystallization -The development of Crystalline Order in thermoplastic Polymers[END_REF] On the other hand, morphological features (juxtaposition of phases different in nature) appear in blends of immiscible components. In this case, a macro-or microphase separation appears, governed by the chemistry and the composition of the mixture (vide infra). As most of polymers are immiscible, a kaleidoscopic variety of morphologies may be obtained, furthermore extended in cases where amorphous and semi-crystalline polymers or copolymers are combined. This fine organization unique to polymers became accessible to the research community some 60 years ago with the advent of commercial electron microscopes. A number of groups since then reported TEM observations of semi-crystalline polymers, [START_REF] Sano | Lamellar morphologies of melt-crystallized polyethylene, isotactic polypropylene and ethylene-propylene copolymers by the Ru04 staining technique[END_REF][START_REF] Castillo | Crystallization and morphology of biodegradable or biostable single and double crystalline block copolymers[END_REF][START_REF] Nojima | Morphology of melt-quenched poly(3-caprolactone)-blockpolyethylene Copolymers[END_REF] block copolymers, [START_REF] Sakurai | Morphology Transition from Cylindrical to Lamellar Microdomains of Block Copolymers[END_REF][START_REF] Stadler | Morphology and Thermodynamics of Symmetric Poly(A-block-B-block-C) Triblock Copolymers[END_REF][START_REF] Corté | Annealing and Defect Trapping in Lamellar Phases of Triblock Terpolymers[END_REF] or polymer blends. [START_REF] Abetz | Phase Behaviour and Morphologies of Block Copolymers[END_REF][START_REF] Inoue | Polymer Blend Handbook, Chap. 8: Morphology of Polymer Blends[END_REF][START_REF] Radjabian | Structure Formation of Binary Blends of Amphiphilic Block Copolymers in Solution and in Bulk[END_REF] TEM is however restricted to solid samples stable in the vacuum environment of the electron microscope. In parallel, cryo-electron microscopy was developed, allowing for the observation of frozen liquid samples. Winners of the 2017 Chemistry Nobel, Dubochet, Frank and Henderson shared the prize for developing techniques of biomolecules imaging. 20 More recently a liquid cell electron microscopy has emerged, when modern microfabrication techniques could build thin windows of silicon nitride with a controlled submicrometer separation, between which a liquid could be confined. [START_REF] Ross | Opportunities and challenges in liquid cell electron microscopy[END_REF] This new technique is well positioned to explore phenomena in evolution, e. g. nanomaterial growth, fluid physics or electrochemical processes. Deformation mechanisms may also be followed by in-situ TEM nano-mechanical testing. Hitherto restricted to hard materials, the technique has very recently been extended to polymeric samples. [START_REF] Velez | Development of Quantitative In Situ TEM Nanomechanical Testing for Polymers[END_REF] Owing to significant instrumentation progresses over the last two decades, substantial advances have also been made in new stain-free imaging methods based either on phase contrast or on spectroscopic contrast. [START_REF] Libera | Advances in the Transmission Electron Microscopy of Polymers[END_REF] As microphase-separated structures have become increasingly complicated with the development of controlled polymerization, three-dimensional imaging has also been of growing importance. Transmission electron microtomography (TEMT) is particularly useful when microphase separation of block copolymers produces interpenetrated three-dimensional morphologies. [START_REF] Jinnai | Transmission electron microtomography in polymer research[END_REF][START_REF] Jinnai | Three-Dimensional Visualization and Characterization of Polymeric Self-Assemblies by Transmission Electron Microtomography[END_REF] Besides, atomic force microscopy, which belongs to the family of scanning proximity probe microscopies developed since the late 1990s, has become a widely used technique that complements electron microscopy in studies of polymers. 26 AFM may provide direct real-space access on morphologies on all length scales of hierarchical ordering of polymers, and can be applied in a broad range of experimental conditions, including in liquid media, which renders the technique applicable for in-situ studies. In terms of ultimate resolution and tomographic capabilities, AFM cannot rival electron microscopy. 27 However, the technique is accurate enough to, for example, distinguish polymer backbone and side chains, or afford quantitative information about branching topology. [START_REF] Yu-Su | Molecular Imaging and Analysis of Branching Topology in Polyacrylates by Atomic Force Microscopy[END_REF] Morphological studies based on indirect methods such as scattering, spectroscopic, calorimetric measurements interpret bulk behavior to deduce local polymer structure. In scattering experiments, a sample volume around 10 9 µm 3 is probed, in good adequacy with the macroscopic properties exhibited by the materials. However, because of the disorder and polydispersity inherent to polymeric materials, scattering signals are generally broad and multiple orders of diffraction are absent, rending somewhat difficult a precise interpretation of the spectra. Alternatively, TEM investigates a much smaller volume at the µm 3 scale, allowing for the examination of morphological details hidden in tiny domains. Even though TEM imaging can provide detailed information at levels down to atomic dimensions, such high resolution is hardly attainable in case of polymers. Indeed, on one hand polymers are sensitive to electron irradiation, and on the other hand, a poor contrast is expected from low atomic weight constituents of organic compounds. Nevertheless, since repetition scales in polymer morphologies are of the same order as the dimensions of the molecular coils (1-10 nm), TEM imaging provides, within this range, information which is relevant for these materials, that can rarely be obtained by other means.

TEM is thus an ultimate tool that comes to support hypotheses or models deduced from scattering techniques that give structural information. This microscope is like an eye in the heart of the matter, giving a direct view of polymer morphology, as soon as tricks inherent to the technique have been avoided. This manuscript aims at highlighting the wide power of this technique in the elucidation of polymer morphology, through a collection of studies that have been recently performed in our laboratory, though using a simple and conventional transmission electron microscope. 29 Materials as different as bulk compounds, thin films, hollow fiber membranes, rubbers are presented. It will be set forth, in particular, co-continuous structures in which two semi-crystalline polymers crystallize in domains as small as 10 nm, giving rise to improved optical and thermo-mechanical properties; nanocomposite structures in which carbon nanotubes act as nucleating agents for epitaxial crystallization of polyamide due to a fit of the cell parameters between both crystalline structures; how a triblock copolymer may act as a dispersing agent for carbon nanotubes, with the help of a selective solvent; how antifouling additives may be localized around the pores of hollow fiber membranes; how a block copolymer remains nanostructured in the constrained space of lamellar gallery of a semi-crystalline polymer, owing to the size of the nano-objects that fits the interlamellar distance.

Transmission electron microscopy and small-angle X-ray diffraction yield complementary results. TEM is also assisted by thermal or thermo-mechanical techniques to explain mechanical properties of polymer materials. Our studies are here reported from the viewpoint of interrelation among these techniques.

Discussion.

TEM is not such an easy-access technique, information about polymer morphology are obtained with various degrees of difficulty. Sample preparation and staining are crucial and highly skilled steps to obtain artifact-free imaging. When thin polymer films are interrogated, they may be simply cast from solution onto microscopy grids covered with a carbon film. For solid samples however, ultrathin sections (40-60 nm) are required to be transparent to electrons. The sections must be carefully manufactured using ultra-microtomes, at a temperature below all glass transitions of the material to maintain the polymeric matter rigid enough during sectioning, most of the time around  100 °C (ultra-cryo-microtomy). The cutting experimental conditions vary according to the materials chemistry, structure, morphology and geometry. Optimized protocols consisting in the delicate combination of the cutting temperature, speed and film thickness have to be developed for each system. In the case of fragile materials as porous fibers, inventive solutions must be found to preserve the integrity of samples. Here porous fibers were embedded in an Agar epoxy resin. [START_REF]Fibers were placed for 1h in a mold containing the Agar resin (4.8 g of LV Resin, 1.6 g of VH1 Hardener, 3.6 g of VH2 Hardener and 0.25 g of accelerator), at room temperature under dynamic vacuum[END_REF] Specific problems as poor adhesion properties between the polymer and the resin had to be overcome at the microtomy step. Ultrathin sections are then transferred on a specific grid, using a glycerol drop. The nature of grids, copper or gold, depends on the staining agent that may oxidize copper. Selective staining is then applied to the material deposited on grids through contact with solutions (phosphotungstic acid (PTA) 31 ) or vapors (OsO4 or RuO4) 32 of heavy metal salts or oxides. OsO4 reacts with isolated double bonds (C=O, C=C), but not with conjugated double bonds. [START_REF] Inoue | Polymer Blend Handbook, Chap. 8: Morphology of Polymer Blends[END_REF] RuO4 does not react directly with chemical species, but rather forms clusters, staining most polymers but to a different degree dependent on the diffusion rate. RuO4 diffuses preferably into the regions of lower density such as the amorphous regions of semi-crystalline polymers, staining them whereas the crystalline phase appears clearer. [START_REF] Inoue | Polymer Blend Handbook, Chap. 8: Morphology of Polymer Blends[END_REF] The choice of the staining agent may result in a very different appearance of the same morphology. For instance Figure 1 shows the same morphology of a mixture of polyamide-6 (PA) with a PS-b-PBA-b-PS (polystyrene-polybutylacrylate-polystyrene) triblock copolymer. [START_REF] Dronet | Matériaux nanostructurés obtenus par combinaison de polymérisation radicalaire contrôlée et mélangeage réactif[END_REF] In the left image, PA stained by PTA appears as black globules with sharp interfaces, while in the right image, RuO4 stains preferentially the styrene block of the copolymer. Additional morphological details cover the PA globules that appear now in white. This is one of the major tricks that should be considered with great care, in particular when measuring the sizes of the nano-objects by TEM. Such a dual staining may however be of particular interest to differentiate polymers of similar chemical composition, e. g. different acrylic blocks. [START_REF] Ruzette | Molecular Disorder and Mesoscopic Order in Polydisperse Acrylic Block Copolymers Prepared by Controlled Radical Polymerization[END_REF] [START_REF] Dronet | Matériaux nanostructurés obtenus par combinaison de polymérisation radicalaire contrôlée et mélangeage réactif[END_REF] After this introduction on conditions to obtain valuable TEM images, we will discuss different polymer morphologies, first in relation with the juxtaposition of phases in blends of immiscible polymers, then with crystallization features in semi-crystalline polymers.

Polymer blending has long been considered as an efficient way to provide materials with improved properties. 35 In addition, blending represents an economical strategy that may bring significant cost reduction without substantial loss in properties, or improvement of the processability of some interesting polymers difficult to shape as neat. However, mixtures of polymers generally phase separate macroscopically, because the free energy of mixing is generally positive when mixing two long-chain polymers. [START_REF] Rubinstein | Polymer Physics[END_REF] The free energy of mixing decomposes into an entropic and an energetic (enthalpic) part. The latter, reflected in the Flory interaction parameter , may promote mixing when negative. But generally, interactions between components are of the van der Waals type, meaning that they are weak and repulsive, leading to a positive value of  and to an enthalpic contribution opposing mixing. On the other hand, entropy always promotes mixing, but the gain is very little in case of long-chain polymer mixtures. Thus miscible polymer blends are very unlikely, unless specific interactions may occur between components (e. g. PMMA/PVDF mixtures, as it will be discussed later). This polymer immiscibility has been exploited to create materials with combination of improved mechanical, barrier, optical properties. Nevertheless, a key lies in the scale at which the components may structure. Block copolymers, in which immiscible blocks are covalently attached, exhibit local segregation of the blocks, yielding molecular-size structured objects.

Such microphase-separated block copolymers combine at the nanometer scale the intrinsic properties of constituting homopolymers. [START_REF] Ruzette | Block copolymers in tomorrow's plastics[END_REF] Self-assembly and morphology of block copolymers depend on their composition and architecture. Lamellae, hexagonally packed cylinders, bicontinuous gyroid or body-centered cubic structures are thermodynamically stable phases that have been observed. [START_REF] Mai | Self-assembly of block copolymers[END_REF][START_REF] Khandpur | Polyisoprene-Polystyrene Diblock Copolymer Phase Diagram near the Order-Disorder Transition[END_REF] The micro-phase separation is dictated by the degree of segregation,N, where N is the total number of segments in the copolymer chain. [START_REF] Leibler | Theory of Microphase Separation in Block Copolymers[END_REF][START_REF] Matsen | Unifying Weak-and Strong-Segregation Block Copolymer Theories[END_REF] For diblock copolymers, lamellar phases are obtained when both blocks occupy equal volume fractions. With increasing asymmetric compositions, curved interfaces yield cylinders and then spheres. Architecture intervenes as an extra parameter for multiblock and graft copolymers.

Figure 2 shows SAXS and TEM observations recorded on a film made of a SBM triblock copolymer (polystyrene-b-polybutadiene-b-polymethylmethacrylate, S16B20M64, Mn PS 11 k.mol 1 ) containing 22 wt% of the parent SB diblock copolymer. The film was obtained by slow casting from CHCl3, a good solvent for the three blocks of the copolymer. [START_REF] Périé | Nanostructured films and composites from carbon nanotubes dispersed by ABC block terpolymers in selective solvent[END_REF] The SAXS profile in Figure 2a exhibits three main peaks localized at q*, 2q* and 3q*, leading to a period d of 65 nm (d = 2/q*). As peaks are broad, we cannot exclude the existence of 2q* or 3q*, and 7q*signals characteristic of a cylinder organization. Whereas SAXS cannot allow to differentiate lamellar or cylinder organization, TEM picture (Figure 2b) showing an end-on view of the cylinders brings an intimate image of the exact polymer morphology. In this picture, the characteristic distance between two cylinders is evaluated around 55 nm, in accordance with the SAXS profile. TEM observations provide another crucial information: the SB diblock is well incorporated in the SBM triblock microstructure, as no macrophase separation was observed. On the contrary such a phase separation between SBM and SB was previously observed in a SBM lamellar phase during annealing. [START_REF] Corté | Annealing and Defect Trapping in Lamellar Phases of Triblock Terpolymers[END_REF] Figure 2. a) SAXS profiles of SBM films cast from CHCl3 with three possible indexations: lamellae, cylinders in hexagonal or square array. b) Cylinder stacking of SBM observed by TEM. The B block is stained in black, the S block in light grey by OsO4 vapor. [START_REF] Périé | Nanostructured films and composites from carbon nanotubes dispersed by ABC block terpolymers in selective solvent[END_REF] The same SBM triblock copolymer was used, in combination with a solvent selective to one of the blocks, to homogeneously disperse carbon nanotubes (CNT). [START_REF] Périé | Nanostructured films and composites from carbon nanotubes dispersed by ABC block terpolymers in selective solvent[END_REF] Indeed, whereas chloroform is a good solvent for the three S, B and M blocks (interaction parameter  around 0.0-0.3 for each), the situation is different with acetone, a poor solvent of S and B,  = 0.4 and 1.0, respectively, but a good one for the M block. This unbalanced solubility induces curvature at the interface of the blocks, thereby allowing a better swelling of soluble chains, as schematically depicted in Figure 3. When CNT are mixed with a chloroform or acetone solution of SBM (0.1 wt% CNT; ratio SBM/CNT: 3/1), they respectively aggregate or disperse homogeneously (Figure 3a,b). The blocks in poor solvent strongly adsorb onto the carbon nanotube surface to minimize their interaction with acetone, whereas the M block alone ensures the solubilization of the SBM. The polymer adsorbed onto the carbon surface entropically stabilizes the mixture, allowing for a homogeneous dispersion of the CNT. This situation which was only a hypothesis by observing the mixture in solution (Figure 3a,b) was proved by TEM (Figure 3c). One drop of the solution in acetone was deposited and evaporated onto a TEM carbon-coated copper grid, and stained by OsO4 vapors. S and B blocks, marked in black, clearly appear located onto the surface of the nanotubes, owing to the solvophobic effect that is the driving force for the dispersion in acetone. Seen also in the TEM image are free "micelles" of SBM, namely SB cores surrounded by an M shell. Such stable suspensions were used to form master batches containing up to 25 wt% of CNT, easily dispersible into polymer matrices miscible with PMMA (e. g. PVDF 42 ). [START_REF] Périé | Nanostructured films and composites from carbon nanotubes dispersed by ABC block terpolymers in selective solvent[END_REF] Apart from covalent attachment in multiblock copolymers, other strategies to prevent macrophase separation of immiscible polymers consist either in using interfacial agents also called compatibilizers, or in reactive blending. [START_REF] Koning | Strategies for Compatibilization of Polymer Blends[END_REF] Research on compatibilizers aiming at understanding and controlling the parameters relevant for blending has been widely developed in academic laboratories, whereas reactive blending is more attractive for industry. Generation of a copolymer in a one-shot process in continuous machines like extruders offers a simple and industrially scalable way to prepare stable polymer blends. Using a co-rotating twin-screw compounder at high temperatures, where all components are liquid and finely dispersed by the shearing, two functionalized and reactive homopolymers may react and organize at the molecular scale. The MAH (maleic anhydride)/NH2 couple is commonly used for its high reactivity. MAH-functionalized polyethylene (FPE) and NH2-terminated polyamide-6 (PA) blends containing 20% PA were reacted at high temperature in a twin-screw microcompounder, giving rise to co-continuous structures. [START_REF] Pernot | Design and properties of co-continuous nanostructured polymers by reactive blending[END_REF][START_REF] Gani | Co-continuous Nanostructured Blend by Reactive Blending: Incorporation of High Molecular Weight Polymers[END_REF] These thermodynamically stable cocontinuous nanostructured blends exhibit outstanding properties: transparency, excellent mechanical properties at low and high temperatures and solvent resistance. To understand the structure and properties of these blends, TEM (Figure 4a) proved to be a crucial experiment.

While the crystallization of both components (FPE and PA) was demonstrated by thermal, [START_REF] Pernot | Design and properties of co-continuous nanostructured polymers by reactive blending[END_REF]45 mechanical and diffraction analyses (WAXS, Figure 4b), the co-continuity was substantiated using TEM and solvent extraction experiments. Indeed, the co-continuous nanostructured organization presents a short-range order, no specific signal appears in SAXS experiment (Figure 4b). A well-defined peak appears only after alignment of the morphology after squeezing. [START_REF] Rotella | Shear-induced Orientation of Cocontinuous Nanostructured Polymer Blends[END_REF] TEM image of Figure 4 was obtained from microtomed annealed extrudates cut perpendicularly to the flow direction, stained for 5 min at room temperature with an aqueous solution containing 2 wt% of phosphotungstic acid and 2 wt% of benzyl alcohol. In this TEM picture, the minority phase PA forms continuous domains appearing in black. The major phase, light grey, corresponds to FPE. The characteristic size of the morphology, addition of the distance between PA domains  60 nm and PA thickness  15 nm is in agreement with the shoulder at 70 nm observed in the SAXS spectrum. In such a short-range order nanostructuration, TEM pictures were determinant to interpret SAXS data. Nanostructured blends of PMMA and PA were also prepared by reactive blending. [START_REF] Freluche | Self-organized materials and graft copolymers of polymethylmethacrylate and polyamide-6 obtained by reactive blending[END_REF][START_REF] Freluche | Graft Copolymers of Poly(methyl methacrylate) and Polyamide-6: Synthesis by Reactive Blending and Characterization[END_REF] The grafting reaction occurred between the amino end-group of PA and glutaric anhydride units randomly distributed along the backbone of PMMA. It was shown that short PA grafts facilitated reaction at the polymer interface during blending, whereas use of long PA chains led to macrophase separation and thereby poor mechanical properties. Nonetheless, by using triblock PMMA-PBA-PMMA copolymers instead of PMMA homopolymer, it was possible to efficiently graft long PA chains. [START_REF] Iliopoulos | Glassy-Crystalline Nanostructured Polymers Via Reactive Blending[END_REF] The higher efficiency of reactive blending in the case of triblock copolymer, compare to homopolymer, has been attributed to the ability of the ungrafted triblock to mix with the grafted derivative formed during the blending process. [START_REF] Iliopoulos | Glassy-Crystalline Nanostructured Polymers Via Reactive Blending[END_REF] To understand the relationship between the position of reactive groups and the grafting efficiency (which thereby influences the mechanical properties), different acrylic architectures were synthesized by ATRP with a controlled distribution of the reactive groups. [START_REF] Dronet | Matériaux nanostructurés obtenus par combinaison de polymérisation radicalaire contrôlée et mélangeage réactif[END_REF] For example, diblock copolymers composed of a first unreactive PBMA block (polybutylmethacrylate) and a second reactive PBMA block containing methacrylic acid monomers are schematized in Figure 5a (main PBMA chain in blue, the red spots indicating reactive acrylic acids define the second block of the copolymer. This second block is drawn in red in the insets of Fig. 5c and5d). This strategy permitted tuning the grafting density by varying the length and the distribution of reactive functions in diblock and triblock copolymers. [START_REF] Dronet | Matériaux nanostructurés obtenus par combinaison de polymérisation radicalaire contrôlée et mélangeage réactif[END_REF] By reactive blending in an extruder operated at 220 °C (speed 200 rpm, for 15 min under nitrogen atmosphere), NH2-terminated PA chains (green chains in Figure 5) were grafted onto the COOH counterparts. For example, a symmetrical 50/50 unreacted diblock copolymer presents, right after extrusion, a spherical morphology, favored by the reacted block which imposes a curvature (Figure 5c). PA stained by phosphotungstic acid appears in black as 40-60 nm spheres. Annealing reveals that the morphology was not at equilibrium at the end of the blending process: after 24h at 235 °C (above the melting temperature of PA), the morphology has evolved toward the formation of vesicles. (Figure 5d). The sphere structure presents neither continuity nor bridges between PA domains: as seen in the DMA profile (Figure 5b), the mechanical properties of the blend are poor, and the material flows above 120 °C. After extrusion, the blend presents a higher storage modulus, and flows above 210 °C, the melting temperature of PA. The mechanical behavior of the blends is thus driven by crystallization of PA: before annealing, PA chains are distributed in small domains, which impedes crystallization. After annealing, the organization in multilamellar vesicles affords larger domains where PA can crystallize. Numerous PA chains can incorporate these crystals, thereby connecting the PBMA backbones. The evolution of the mechanical behavior is hence explained by the morphology observed by TEM. Reactive blending was also developed in the case of rubber mixtures, not with the use of extruders, but by competitive crosslinking after blending in an internal mixer. Our group reported that epoxidized natural rubber (ENR) could be efficiently cross linked by dicarboxylic acids (Figure 6). [51][START_REF] Pire | Imidazole-promoted acceleration of crosslinking in epoxidized natural rubber/dicarboxylic acid blends[END_REF][START_REF] Pire | Imidazoleaccelerated crosslinking of epoxidized natural rubber by dicarboxylic acids: a mechanistic investigation using NMR spectroscopy[END_REF] For instance, the curing of ENR25 (containing 25 wt% epoxy groups) with dodecanedioic acid is complete in 20 min at 180 °C. The crosslinking reaction occurs in bulk, through opening of the epoxy functions creating ester links along the chains. The resulting chemical network exhibits mechanical properties as good as the ones obtained when ENR is classically cross linked using sulfur or peroxides, in essence because such cross linked rubber preserves its capacity to crystallize under strain. [START_REF] Imbernon | Strain-induced crystallization in sustainably crosslinked epoxidized natural rubber[END_REF] The reaction goes faster when the level of epoxidation increases. ENR50 is fully cross linked in 12 min, much quicker than ENR10. This difference in reactivity was exploited to quench the macrophase separation of the two immiscible ENR by competitive crosslinking. [START_REF] Imbernon | Semi-interpenetrating Networks in Blends of Epoxidized Natural Rubbers[END_REF] By increasing the fraction of ENR50 in a mixture ENR10/ENR50, the resulting material switches from a soft rubber to a strong elastomer (Figure 7a). TEM explains this behavior: For 15% ENR50, nodules of ENR50 are dispersed in a soft matrix of non crosslinked ENR10 (Figure 7b), but above 37.5% ENR50, a co-continuous structure is obtained, in which ENR50 is cross linked while ENR10 is not (Figure 7c).

Enlargement detailing a nodule of ENR50 (Figure 7d) shows crystalline features associated with the migration of the dicarboxylic acid crosslinker into the more reactive and polar ENR50. [START_REF] Imbernon | Réticulation non-permanente, physique ou chimique, du caoutchouc naturel époxydé. Propriétés dynamiques et recyclage[END_REF] Whereas depletion of the crosslinker in one phase was a drawback for reactive compatibilization, it turned out that the swelling of the more reactive phase by the curative was beneficial for the formation of a network. This opens the way to double networks of elastomers, since ENR10 is still available for crosslinking. TEM imaging also allows for the direct observation of low amounts of additives in a mixture. Antifouling additives have been widely used to improve the hydrophilic properties of porous membranes used for water purification. However, the exact localization of the active moieties in the porous matrices was never demonstrated before our group recently reported on the visualization of a polar biofouling agent in hollow fibers made of PVDF. 57 So far, only methods giving macroscopic information, as for example contact angle measurements, static protein adsorption or Raman spectroscopy [START_REF] Dufour | Quantitative PVP mapping in PVDF hollow fiber membranes by using Raman spectroscopy coupled with spectral chemiometrics analysis[END_REF] were available to attest hydrophilicity or fouling mitigation. Observation of the pore structure by transmission electron microscopy was made possible by embedding the fibers into a resin that filled in the voids and by specific staining of the antifouling additives. Figure 8 emphasizes the characterization of the porous system at different scales. The cryo-fractured hollow fiber shows a porous structure using a scanning electron microscope (Figure 8a,b). A large dispersion of pore size (0.1-10m) is observed by SEM inside the fiber, the pore size is finely controlled only in the outer skin of the fiber (10-30 nm). 57 After embedding the delicate fiber in a resin, which permitted thin-sectioning, details of the pores were highlighted by TEM. Pores filled by the resin appear uniformly clear. The polar additive, polyvinylpyrrolidone, PVP, specifically stained in black by RuO4 vapors (Figure 8c,d) appear darker all around the pores. This protocol for observing the localization of active additives in porous membranes is an efficient tool for the development of antifouling materials. Finally, we want to demonstrate through the two following examples that TEM is also a unique tool to observe how crystallization of a semi-crystalline polymer may be subtly affected by the presence of additives. First consider the system where polyamide-6 (PA) was blended with increasing amounts of CNT (0-10%). [START_REF] Brosse | Effect of multi-walled carbon nanotubes on the lamellae morphology of polyamide-6[END_REF] Non-isothermal crystallization from the melt observed by DSC is presented in Figure 9a. For neat PA, the crystallization peak presents a sharp maximum at 190 °C. With increasing amounts of well dispersed CNT, this peak broadens, shifts to higher temperatures and splits into two components. The temperature shift is more pronounced for peak 2, whose relative proportion increases with increasing CNT amount. At the crystallographic scale explored by SAXS and WAXS, there were no differences that could explain the presence of this second crystallization peak. [START_REF] Brosse | Effect of multi-walled carbon nanotubes on the lamellae morphology of polyamide-6[END_REF] The overall crystallinity was only slightly increased and no changes in cell parameters or lamellae period were observed. TEM only gave the answer, using staining with phosphotungstic acid and benzyl alcohol. Benzyl alcohol helps the diffusion of WO3 in amorphous polyamide layers, thereby revealing a contrast between the stained amorphous domains and the crystalline lamellae of PA appearing whiter (Figure 9b). The splitting of the exothermic peak was thus assigned to morphological modifications: two types of lamellae stacks were formed, one for each peak of crystallization: lamellae independent of CNT in the matrix (visible in some parts of Figure 9c) and trans-crystalline lamellae growing perpendicularly to the CNT surfaces, with the polyamide chains parallel to the axis of the nanotubes (Figure 9d). This trans-crystalline lamellae formation is permitted by the crystallographic lattice of PA-6, which matches that of the graphitic hexagonal lattice of the carbon nanotube surface. This morphology is expected to have important consequences on the electrical properties of the composites, as the trans-crystalline polymer layer should behave as an insulating layer around the CNT. In the second example, we explain by TEM why mechanical properties of semicrystalline PVDF may be enhanced through intimate mixing with a nanostructured diblock copolymer. [START_REF] Oikonomou | Swelling of semi-crystalline PVDF by a PMMA-based nanostructured diblock copolymer: Morphology and mechanical properties[END_REF] The diblock copolymer (DB) is composed of a glassy PMMA block fully miscible with the amorphous part of PVDF and a soft acrylate block (PBA) which has no affinity for the PVDF. TEM image in Figure 10a shows that DB copolymer exhibits a nano-phase separation between blocks: domains of PBA (diameter  6 nm), marked in black by RuO4, appear dispersed in the PMMA matrix. The average inter-domain distance is estimated at  20 nm, in accordance with the SAXS profile of copolymer cast films, showing a unique characteristic distance at q ∼ 0.27 nm -1 corresponding to a 23.5 nm distance (Figure 10a). SAXS experiments on PVDF/copolymer blends indicate a swelling of the crystalline/amorphous lamellar morphology.

The long period Lp varies from 12 nm in pure PVDF to 20 nm in the presence of 25 wt% DB copolymer (Figure 10c). TEM reveals that the microphase-separated domains of the copolymer are confined into the amorphous lamellar gallery of PVDF. Figure 10b shows aligned micelles of DB, whose PBA core is specifically stained by RuO4. This alignment highlights the crystalline lamellar organization of PVDF, which swells in accordance with DB content. [START_REF] Oikonomou | Swelling of semi-crystalline PVDF by a PMMA-based nanostructured diblock copolymer: Morphology and mechanical properties[END_REF] The copolymer can incorporate the amorphous phase between crystalline lamellae, and remained nano-structured, owing to the specific interactions between PMMA and PVDF components, and to the size of the micelles which is commensurable to the long period Lp of PVDF. Such a system, where the spherulitic lamellae of a semi-crystalline matrix integrates a nanostructured copolymer was new from an academic point of view, but also it yielded synergistically enhanced mechanical properties. Tensile tests demonstrated a 3-fold improvement of the elongation at rupture in presence of the copolymer, without significant loss of strength (Figure 10d). This break elongation improvement is likely related to the presence of the PBA block forming soft inclusions incorporated in the amorphous phase of PVDF, owing to miscible PMMA that serves to anchor PBA in PVDF matrix (Figure 10e).

Conclusion

Polymer morphology encompasses the crystalline features in semi-crystalline polymers and the luxuriant collection of patterns produced by macro-or micro-separated phases in polymer blends. TEM is one of the most powerful tool to understand the exact nature of the delicate inner organization of the polymeric matter. This manuscript aimed at demonstrating the various opportunities that this technique enables. Our group also wishes to share his "know-how" of optimized protocols for cutting conditions and staining, acquired through preparation and observation of many samples presenting different morphologies linked to their chemical nature and structure. Our results were obtained using a simple transmission electron microscope.

Beyond this conventional electron microscopy, the emerging techniques permitting observations in liquid cell or in-situ nano-mechanical experiments are expected in a near future to provide further informations, in particular about dynamic behavior of polymeric materials.

The morphological features are, to a considerable extent, under our control: we can shape them to our design. The strong efforts that have been made in the polymer community to characterize polymer morphology should further serve the development of new desirable properties and improved processes of manufacturing and recycling, as the ultimate goal of polymer morphology research should be the end product.

Table of Contents

Polymer morphology, which encompasses a luxuriant collection of patterns produced by micro-separated phases in polymer blends, composites, or semi-crystalline polymers, has a crucial impact on the macroscopic properties of these materials. Transmission electron microscopy is a unique tool to investigate these intimate organizations, in interrelation with scattering and thermo-mechanical experiments.

Figure 1 .

 1 Figure 1. Co-extruded PA/PS-b-PBA-b-PS blend thin sections stained with a) Phosphotungstic acid; b) Ruthenium tetroxide.[START_REF] Dronet | Matériaux nanostructurés obtenus par combinaison de polymérisation radicalaire contrôlée et mélangeage réactif[END_REF]

Figure 3 .

 3 Figure 3. Vials containing SBM/CNT (3/1) in a) chloroform; b) acetone; Selective swelling of

Figure 4 .

 4 Figure 4. a) Co-continuous structure of FPE/PA blends with schematic FPE in purple and PA

Figure 5 .

 5 Figure 5. a) Schematic diblock PBMA-b-(PBMA-g-PA) copolymer. Length of the reactive

Figure 6 .

 6 Figure 6. ENR crosslinking by dicarboxylic acids. For example, m = 0.25 for ENR25.

Figure 7 .

 7 Figure 7. TEM pictures after curing of ENR50 blended with ENR10. Ultrathin sections

Figure 8 .

 8 Figure 8. From macro to nano: a-b) Porous structure of a hollow fiber observed at different

Figure 9 .

 9 Figure 9. a) DSC cooling curves of PA/CNT composites at different CNT loadings. 59 b) Regular

Figure 10 .

 10 Figure 10. a) TEM image of DB copolymer; in insert: SAXS profile of neat diblock copolymer cast from NMP. 57 b) TEM image of blend PVDF containing 50% DB; micelles of DB whose

Acknowledgements

We are indebted to all PhD students and postdoctoral fellows who were major actors in all these studies: Anne-Carine Brosse, Gaëlle Carré de Lusancay, Séverin Dronet, Mathilde Freluche, Léa Gani, Cécile Gibon, Lucie Imbernon, Thomas Périé, Myriam Pire, and Cinzia Rotella. Arkema Group is sincerely thanked for financial support (A-C.B, S.D, M.F, L.G, C.G.), and for providing the CEM902 Zeiss electron microscope. Dr. Anne-Valérie Ruzette and Patrick Coupard (Arkema) who initiated the first TEM observations in our laboratory are sincerely thanked for training and kind sharing of their expertise. Dr. Ilias Iliopoulos is warmly acknowledged for fruitful discussions and his continuous and true support.


Magdalini D Titirla
email: magdalini.titirla@lecnam.net

Antoine Chalot

Laurent Michel

Emmanuel Ferrier

3D FINITE ELEMENT MODELLING OF NOVEL STRENGTHENING SOLUTIONS FOR RC WALL/SLAB CONNECTIONS

Keywords: Composite, FRP, Finite element model, Joins RC structures

The aim of this study is to create a nonlinear FE model able to predict the mechanical behavior of RC wall/slab connections strengthened by using Carbon Fiber Reinforced Polymers. The experimental mechanical behavior of 4 full scale RC wall/slab connections with a reference join and 3 strengthened by FRP are investigated from members of our researcher team. The 3D finite-element micromodel of the RC wall/slab connections is conducted utilizing the FE software ABAQUS, reproducing the actual geometry of the experiments, as well as the same boundary conditions and loading as in the experimental program. The analytical investigation is carried out through an extended comparative parametric study and is focused on the quantitative influence of certain simplified modelling assumptions and several critical modelling parameters on the response of the system. The accuracy of the 3D model was assessed against the experimental results.

Introduction

The safety of constructions is one of the major priorities of engineering globally, as well as the upgrade of the existing structures because of their deterioration, ageing, environmental induced degradation, a lack of maintenance, or the need to meet current design requirements.

In order to achieve these goals and minimise the effects of an earthquake, several strengthening techniques and studies have been developed. The most common in a concrete structure is by adding concrete and steel jacketing of the concrete frame elements [START_REF] Tsonos | Seismic resistance of type 2 exterior beam column joints reinforced with inclined bars[END_REF][START_REF] Lu | Seismic behavior of interior RC beam-column joints with additional bars under cyclic loading[END_REF][START_REF] Colajanni | Dissipative connections of rc frames with prefabricated steel-trussed-concrete beams[END_REF]. Another more modern technique is by adding devices that can increase the strength of the structure and dissipate a large percentage of the seismic energy without belonging to the supporting structure of the constructions, or by adding base isolation with some aspects, like the cost and the practical implementation, need to take into control [START_REF] Soong | Supplemental energy dissipation: state-of-the-art and state-of-thepractice[END_REF][START_REF] Symans | Energy dissipation systems for seismic applications: current practice and recent developments[END_REF][START_REF] Latour | A proposal for the design of seismic resistant precast concrete industrial buildings through application of energy dissipaters in the cladding walls[END_REF]. Finally, the other direction is by strengthening the joints, with inclined steel reinforcement in shear-critical joins [Engindeniz et al., 2005, Karayannis and[START_REF] Karayannis | Strengthening and rehabilitation of RC beam column joints using carbon-FRP jacketing and epoxy resin injection[END_REF] or by using Fiber Reinforced Polymers (FRP) [START_REF] El-Amoury | Seismic rehabilitation of beam-column joint using GFRP sheets[END_REF][START_REF] Antonopoulos | Experimental Investigation of FRP-Strengthened RC Beam-Column Joints[END_REF][START_REF] Ferraioli | Seismic performance of a mixed rc-masonry building strengthened with fiber composites[END_REF][START_REF] Akguzel | Assessment and Design Procedure for the Seismic Retrofit of Reinforced Concrete Beam-Column Joints using FRP Composite Materials[END_REF][START_REF] Titirla | On the mechanical response of an innovative energy dissipation device[END_REF]2018a].

In the present work, attention is focusing on the bonded fiber reinforced polymers (FRP) composites for seismic retrofitting RC structures and specially in the connections between beam-columns or columns-slab. Lee et al [START_REF] Lee | Reinforced concrete beam-column joint strengthened with carbon fiber reinforced polymer[END_REF] proposed the strengthening of the interior beam-column joints with CFRP layers wrapped around the column and joins. The experimental results show that the beam-column joints strengthened with CFRP can increase their structural stiffness, strength, energy dissipation capacity and the ductility of the joint. In another study for interior beam-column joints, Ma et al. [START_REF] Ma | Seismic retrofitting of full-scale RC interior beam-column-slab subassemblies with CFRP wraps[END_REF] experimentally studied the strengthening of full-scale interior subassemblies with slab and transverse beams with different CFRP retrofitting schemes. Esmaeeli et al [START_REF] Esmaeeli | A combination of GFRP sheets and steel cage for seismic strengthening of shear-deficient corner RC beam-column joints[END_REF] focused their study to a seismic strengthening of shear deficient joints of 3D reinforced concrete (RC) corner beam-column connections. Their technique is composed of a combination of GFRP sheets and a steel cage. The test results of this technique revealed a noticeable improvement in the seismic response of the strengthened specimen.

In order to demonstrate the effectiveness of these strengthening solutions, there are either the experimental or the numerical researches. Considering the numerical research, two different approaches have been followed: (i) the macromodels, based on the physical understanding of each solution [START_REF] Montuori | Modelling of floor joists contribution to the lateral stiffness of RC buildings designed for gravity loads[END_REF], Montuori et al. 2019a], and (ii) the micromodels, based on a finite element (FE) representation. FE models play a key role in the ordinary design process of new structures and in the assessment of existing ones [START_REF] Brownjohn | Civil structure condition assessment by FE model updating: methodology and case studies[END_REF][START_REF] Titirla | Finite element modelling of an innovative passive energy dissipation device for seismic hazard mitigation[END_REF][START_REF] Montuori | Problems of modeling for the analysis of the seismic vulnerability of existing buildings[END_REF], Montuori et al 2019c].

The Finite Element Method (FEM) has become the most popular method in both research and industrial numerical simulations, as it takes into consideration material laws, contact interface conditions and others parameters, which lead to the exact response of the strengthening solutions. Several algorithms, with different computation-al costs, are implemented in the finite elements codes, such as ABAQUS [START_REF] Simulia | Analysis user's manual volume IV. Simulia, analysis user's manual[END_REF], which is commonly used software for finite element analysis.

In the present work attention is focused on the mechanical behavior of 4 full scale specimens with a reference join and 3 strengthened by FRP, proposed and investigated by Chalot et al [START_REF] Chalot | Mechanical characterization of a RC wall-slab joist reinforced by FRP under alternating cyclic loading[END_REF]. The aim of this study is to create a FE model able to predict the mechanical behavior of RC wall/slab connections by using Carbon Fiber Reinforced Polymers. The numerical analyses is conducted utilizing the FE software ABAQUS [START_REF] Simulia | Analysis user's manual volume IV. Simulia, analysis user's manual[END_REF]. The 3D FEM model geometry reproduced the actual geometry of the experiments, as well as the simulation used the same boundary conditions and loading as in the experimental program. The study is focussed on a set of systematic procedures for finite element model calibration and parametric evaluation that enable robust simulation of the RC wall/slab connections under monotonic and cyclic loading with high fidelity using explicit timestepping time-history analysis methods. The accuracy of the 3D model was assessed against the experimental results and the validated model was subsequently used to generalize the experimental findings and to study the effects of various parameters. In this way, results come out that are harder to obtain experimentally. The obtained results reveal the overall mechanical behavior of the RC wall/slab connections reinforced by using Carbon Fiber Reinforced Polymers.

Short description of the investigated connections

In the present section, a short description of the 4 large scale specimens with a reference joint and 3 strengthened joints by FRP is given. The reference joint, referred to herein as RC, is a common wall/slab T connection, which in a real structure, is the junction between vertical side RC wall and RC floor. It was composed of a wall element with a thickness of 16 cm, a length of 100 cm and a width of 50 cm. The slab element was equal to 9 cm thick for a length of 100 cm (Figure 1a). The longitudinal reinforcement of the wall was consisted of 2x3 φ10 steel bars, and 2x8 ϕ10 steel bars in the transverse direction, while in the slab there were 2x9 ϕ6 steel bars in longitudinal direction and 2x7 ϕ6 steel bars in the transverse direction. The first strengthening solution, mention as RC1-CFRP, composed of 3 FRP strips of 60 mm wide and 600 mm long in each side of the wall, glued on the slab with spacing between strips of 40 mm (Figure 1b). The next one, mention as RC1-CFRP-Ali38-At, (Figure 1c) have been consisted of the same composite strips of the RC1-CFRP specimen, as well as (i) anchor wisps to the wall-slab connection and (ii) anti-buckling anchor wisps with an angle of 20° in the join have been added. The last one, referred as RC1-CFRP-ALc38-At, (Figure 1d) was similar to RC1-CFRP-Ali38-At with the exception that the anchor wisps are continuous to the right of the node.

The concrete was a C30/37 with the average experimental compressive strength equal to f cm = 36.7 MPa with a standard deviation of ± 1.1 MPa. The experimental splitting tensile strength of concrete was equal to f ct = 5.0 MPa with a standard deviation of ± 0.5 MPa.

The steel rebar had the grade of S500B. The 10 mm diameter steel rebar (D10) was tested in tensile. Their elastic strength was f y = 545 MPa with a standard deviation of ± 22 MPa, their ultimate strength was f u = 599 MPa with a standard deviation of ± 21 MPa. Their tensile modulus was Es = 202 GPa and their ultimate strain is ε su = 2.9 %. The FRP strips were an externally bounded Carbon Fiber Reinforced Polymer (CFRP), called as Foreva® FRP and marketed by FREYSSINET. In addition, it consisted of a bi-directional Carbon / Carbon textile with a 70/30 ratio, the matrix was two-component epoxy glue.

Experimental study

Full-scale RC wall/slab connections (the reference and the strengthened) were experimentally investigated under monotonic loading. The RC wall/slab connections tested at a 90° rotation in order to focus our attention only on the connections in quasi-static tests and all the details are illustrated in Figure 2. The experimental set ups were conducted at the Laboratory of Composite Materials for Constructions (LMC2) at the University Claude Bernard Lyon 1. A hydraulic actuator operating in displacement control mode with a speed of 30 mm/min (fixed to a strong wall) was attached to the top of the slab using a specially designed clamping device. The displacement at the top of the slab increased gradually until the stroke of the actuator reached or until clear connection failure was observed. The load cell incorporated in the actuator was used to record the applied load at the top of the slab. The wall was fixed in the strong floor with the help of fixing blocks in both the horizontal and vertical directions. Nine linear variable differential transformers (LVDT) were positioned on each specimen and measured the corresponding displacement at different positions in the specimen (see Figure 2). Six strain gauges (nos. 1 to 6) measure the deformation values of the steel rebars inside the join, while other three strain gauges (nos. 7 to 9) measure the deformations of the CFRP reinforcement (for the strengthening connections). The specimen details of the experiment are presented by Chalot et al [START_REF] Chalot | Mechanical characterization of a RC wall-slab joist reinforced by FRP under alternating cyclic loading[END_REF]. reliable tool for the simulation of their study (devices/connections) to reduce the cost of the experiments in a parametric study [START_REF] Doudoumis | Finite element modelling and investigation of the behaviour of elastic infilled frames under monotonic loading[END_REF][START_REF] Nip | Cyclic testing and numerical modelling of carbon steel and stainless steel tubular bracing members[END_REF][START_REF] Larbi | Finite element formulation of smart piezoelectric composite plates coupled with acoustic fluid[END_REF][START_REF] Manos | Numerical simulation of the shear behaviour of reinforced concrete rectangular beam specimens with or without FRP-strip shear reinforcement[END_REF][START_REF] Titirla | Finite element investigation of a new seismic energy absorption device through simultaneously yield and friction[END_REF][START_REF] Larbi | Reduced order finite element formulations for vibration reduction using piezoelectric shunt damping[END_REF], Titirla et al., 2019a]. The study is focused on a set of systematic procedures for finite element model calibration and parametric evaluation that enable robust simulation of the RC wall/slab connections under monotonic and cyclic loading with high fidelity using explicit time-stepping time-history analysis methods.

Three-dimensional finite element models

The finite elements analysis calibration study included analytical modelling of the RC wall/slab connections. The 3D FEM model geometry reproduced the actual geometry of the experiments, as well as the simulation used the same boundary conditions and loading as in the experimental program (see Fig. 3). Several simulations have been conducted to identify the best meshing. Wall and slab were meshed using 3D reduced integration solid element C3D8R (eight-node bricks), for the steel rebars 3D wire elements were used with "beam behavior", while the FRP sheets were idealized as planar finite element and their actual thickness were utilized as a section property. Normally, a higher mesh density provides for higher accuracy but also increases the computational time without improving substantially the accuracy of the results, therefore, a trade-off between time and accuracy becomes crucial [START_REF] Simulia | Analysis user's manual volume IV. Simulia, analysis user's manual[END_REF]. The final mesh has 10244 elements for the RC1-REF model, 13424 for the RC1-CFRP model, 15296 elements for the RC1-CFRP-Ali38-At and 14628 elements for the RC1-CFRP-ALc38-At and the numerical results were a solution that correlated with the experimental results. In Figure 4, the FEM model used for the RC wall/slab connections is presented with the details of the steel rebars and the FRP in each connection. A standard test had been carried out, in order to establish the basic material properties of all the materials (concrete, steel rebars and CFRP). These experimentally derived material properties were utilized in the subsequent numerical study. The response of the concrete is described in the elastic and plastic field with the use of the 'Concrete Damaged-Plasticity' (CDP) model, which accounts the plasticity of the concrete Push Pull

F, u Uy=0 Ux=0 Ux=0 Ux=0 Ux=0 Uy=0
without neglecting the damage storage, typical of brittle-materials. The uni-axial concrete behavior, both in tension and compression, has been built based on the 'Fracture Energy Theory' [START_REF] Lee | Plastic-Damage Model for Cyclic Loading of Concrete Structures[END_REF][START_REF] Krätzig | An elasto-plastic damage model for reinforced concrete with minimum number of material parameters[END_REF][START_REF] Alfarah | New methodology for calculating damage variables evolution in Plastic Damage Model for RC structures[END_REF][START_REF] Earij | Nonlinear three-dimensional finite-element modelling of reinforced-concrete beams: computational challenges and experimental validation[END_REF]. The damaged plasticity model for concrete available in the ABAQUS material library was adapted to model concrete response, since it has been shown to perform satisfactorily in similar applications [START_REF] Malm | Predicting shear type crack initiation and growth in concrete with non-linear finite element method[END_REF]. The values adopted for the relevant material parameters, namely the angle of dilation h, the eccentricity, the ratio of equibiaxial to uniaxial compressive stress fb0/fc0, the ratio of the second stress invariant on the tensile meridian to that on the compressive meridian at initial yield Kc and the viscosity parameter were 40, 0.1, 1.16, 0.666 and 0 respectively and were all within the range encountered in literature [START_REF] Obaidat | The effect of CFRP and CFRP/concrete interface models when modeling retrofitted RC beams with FEM[END_REF]. In accordance with similar studies [START_REF] Obaidat | The effect of CFRP and CFRP/concrete interface models when modeling retrofitted RC beams with FEM[END_REF][START_REF] Titirla | Finite element modelling of RC wall/slab connections reinforced by using carbon fiber reinforced polymers[END_REF], the stress strain response of concrete in compression was derived according to Saenz [START_REF] Saenz | Discussion of ''equation for the Stress-strain curve for concrete[END_REF], whilst the tension stiffening response was defined in terms of tensile stress and axial deformation according to Cornelissen et al. [START_REF] Cornelissen | Experimental determination of crack softening characteristics of normal weight and ligthweight concrete[END_REF], assuming a fracture energy equal to 0.06. The uniaxial stress-strain correlation of the steel rebars were modeled as elastic with Young's modulus (Es) and Poisson's ratio (v) at typical values of 200 GPa and 0.3, respectively. Plastic behavior was defined in a tabular form, including yield stress and corresponding plastic strain. The experimentally obtained stress (σ nom )-strain (ε nom ) curves for the rebars was converted into the true stress (or Cauchy) (σ true )-logarithic plastic strain ( ) format and was further utilized in order to define the material response.

The CFRP sheets were assumed orthotropic under plane stress conditions and the material properties reported in Figure 5d were adopted. Moreover, damage and failure of the FRPs was explicitly modelled by adopting the Hashin damage model [START_REF] Hashin | Analysis of composite materialsa survey[END_REF] incorporated in ABAQUS. Only tensile failure in the principal direction was considered, whilst other failure modes were considered irrelevant to the present study.

The surfaces in contact between the concrete wall/slab and the FRP were modelled as perfect tie connection due to (i) the existence of the anchors of Φ10 (10 wires), as well as (ii) in the experimental results there was no debonding of the CFRP strip. Due to severe convergence problems typically associated with strongly nonlinear response and with materials exhibiting non-monotonic stress-strain response [Simulia, 2012, Crisfield and[START_REF] Crisfield | Solution strategies and softening materials[END_REF], such as concrete and cohesive elements, the explicit dynamics solver ABAQUS/EXPLICIT was employed to perform the nonlinear analyses. Quasi-static response was achieved by specifying a slow displacement rate and checking that the kinetic energy was smaller than 2% of the internal energy for the greatest part of the analysis.

Validation and verification

A flowchart for carrying out the FEM analysis procedure is presented in Fig. 6. As it is previously mentioned, experimental stress-train curves of the material's behavior were converted into the true stress-strain curves and were inserted in ABAQUS [START_REF] Simulia | Analysis user's manual volume IV. Simulia, analysis user's manual[END_REF]. At the beginning, the 3D -FEM of the RC connection was modeled (meshing, boundary conditions, and loading procedure) and compared against the monotonic experimental data, which was presented in Section 2. Implicit analyses were carried out using Newton-Raphson equilibrium iterations that are augmented with automatic sub-incrementation. Next step was to rerun the previous monotonic experimental data with explicit dynamic analyses in order to calibrate explicit solution (e.g., explicit parameters, loading amplitude). These parameters are adjusted to control the simulation and to achieve convergence and/or acceptable results. At the end of this procedure, all the metrics for evaluating the kinetic energy and energy balance, and for verifying the quasi-static responses have been investigated. This model (RC1-REF) has been used to the validate the response of the first strengthening connection (RC1-CFRP).

Finally, the calibrated model was used in the validation/verification of the two others strengthening connections (RC1-CFRP-Ali38-At, RC1-CFRP-ALc38-At) using Explicit Dynamic Analysis. These results are compared against the previous experimental results. As a results, the validation of the numerical simulation is based on the measured behavior of two (2) half-scale reinforced concrete wall slab connection, without and with the FRP strips, while the accuracy of this model was verified with two (2) full-scale reinforced concrete wall slab connection that employed more complicated strengthening solutions with FRP strips. The moment rotation curves for the four investigated connection types, both numerical and experimental, is presented in Figure7. The FEM predicted values for the moment and rotation are in very good agreement with the corresponding experimental ones. The comparisons between the FEM analyses and the experiments show that the proposed FEM model is capable of reproducing the inelastic response of the RC wall/slab connection. Therefore, it is a reliable tool for the simulation of the hysteretic behavior of the RC wall/slab connection and the strengthening solutions with FRP and can be used in further studies in order to investigate the effect of various parameters.

Failure mode

In Figure 8 the experimental and numerical deformation and crack pattern for the wall/slab connection after the failure are presented. The results of numerical analysis were compared with the quasi-static performance of the tested wall-slab connection RC1-REF and its crack pattern. In summary, the modes of real failure and FE model are similar and the quality of the results is satisfactory.

Strain

In this section, the evolution of strain in steel rebars and FRP sheets in comparison with the load curves, for both experimental and numerical results, is illustrated. The position of each gauge was presented in the Section 3 (see Figure 2). Figure 9a shows the deformation of the longitudinal rebars in the slab of the specimen RC1-REF, while Figure 9b the deformation of the longitudinal rebars in the wall of the specimen RC1-REF.

(a) (b) Figure 9-Experimental and numerical strain for specimen RC1-REF Figure 10a shows the deformation of the longitudinal rebars in the slab of the specimen RC1-CFRP-ALc38-At, Figure 10c the deformation of the longitudinal rebars in the wall of the same specimen, while Figure 10e the deformation of the FRP sheets. In addition, Figure 10b shows the deformation of the longitudinal rebars in the slab of the specimen RC1-CFRP-Ali38-At, Figure 10d the deformation of the longitudinal rebars in the wall of the same specimen, while Figure 10f the deformation of the FRP sheets. We can notice that the FEM The success of the deployed numerical simulation is fully demonstrated by comparing the shape of the moment-rotation curves, the failure mode and the stain of the steel rebars with the experimental ones. From the above, it must be seen that the accurate numerical prediction of the behaviour is the result of all these features that were built into the numerical model together with the accurate representation of all the individual material features which were established by careful testing prior to the numerical simulation. The successful FE models, accurately capturing the basic structural response in terms of ultimate load and moment, failure modes and overall load-displacement response, have been developed and discussed.

Conclusions

The mechanical behavior of RC wall/slab connections by using Carbon Fiber Reinforced Polymers, was experimentally investigated and developed in the Laboratory of Composite Materials for the constructions at the University Claude Bernard Lyon 1 [START_REF] Chalot | Mechanical characterization of a RC wall-slab joist reinforced by FRP under alternating cyclic loading[END_REF][START_REF] Titirla | Finite element modelling of RC wall/slab connections reinforced by using carbon fiber reinforced polymers[END_REF]. The aim of the current study was to create a reliable numerical model to access the mechanical response of the investigated joints. Based on the findings of the present investigation, we are able to draw the following conclusions:

1. The successful numerical simulation of the strengthening RC wall slab connections with FRP sheets, which enhances the efficiency of these FRP sheets applied in the joint (RC1-CFRP-ALc38-At and RC1-CFRP-Ali38-At), was demonstrated by this study. 2. The success of the deployed numerical simulation is fully demonstrated by comparing the shape of the moment-rotation curves, the failure mode and the stain of the steel rebars with the experimental ones. 3. From the above, it must be seen that the accurate numerical prediction of the behaviour is the result of all these features that were built into the numerical model together with the accurate representation of all the individual material features which were established by careful testing prior to the numerical simulation. The successful FE models, accurately capturing the basic structural response in terms of ultimate load and moment, failure modes and overall load-displacement response, have been developed and discussed. 4. Based on the validated FE numerical models presented here, further research is underway to identify the key features affecting overall structural response and thus to optimize the structural arrangement of the investigated novel anchoring method (RC1-CFRP-ALc38-At and RC1-CFRP-Ali38-At) in terms of strength and ductility.

A further goal is to use the proposed FE model in further studies in order to investigate the effect of various parameters to a larger scale such a RC-frame. In order to complete this study, a more in-depth study of the mechanical behavior of the longitudinal anchors may be carried out, by quantifying precisely the effect of the number of threads and the angle of the anchor. Finally, it could be possible to investigate the dynamic response of these wall/slab connections.

  It had a thickness of t f = 0.48 mm, a tensile strength of f f = 1700 MPa and its tensile modulus is E f = 105 GPa. The epoxy resin had a tensile strength of f r = 27 MPa and a tensile modulus of E r = 2.3 GPa. The 20 mm anchors consisted of an assembly of 38 carbone wires, each of this wire has an ultimate load of P f = 2.6 kN. All the mechanical properties have been controlled during the manufacturing process. Details of the four RC wall/slab connections.

Figure 2 -

 2 Figure 2 -Details of the experimental setup

Figure 3 -

 3 Figure 3 -Load position and boundary conditions of (i) the experimental set up, (ii) the FE model of the RC wall/slab connections

Figure 4 -

 4 Figure 4 -The FEM model used for the RC wall/slab connections and details of steel rebars and FRP in each connection

  Stress-strain law of (a) concrete (compressive), (b) concrete (tensile), (c) steel rebars, (d) FRP

Figure 6 -

 6 Figure 6 -Proposed Cyclic Explicit Dynamic (CED) analysis procedure for validate the response of the RC wall/slab connections

  Numerical vs experimental load displacement curves, (a) RC1-REF, (b) RC1-CFRP, (c) RC1-CFRP-Ali38-At, (d) RC1-CFRP-ALc38-At

Figure 8 -

 8 Figure 8 -Experimental and numerical deformation and crack pattern for specimen RC1-REF

  Comparison of experimental and numerical strain (Steel and FPP) for the RC1-CFRP-ALc38-At and RC1-CFRP-Ali38-At wall/slab connections

Acknowledgements

The authors would like to acknowledge the French National Research agency ANR project 'ILISBAR' for funding the present study. The authors also thank the staff members of the Laboratory of Composite Materials for Construction LMC2 (E. Janin and N. Cottet) for their technical support.