Gaelle Rondepierre

Franz De Soete

Nicolas Passade-Boupat

Francois Lequeux

Laurence Talini

Laurent Limat

Emilie Verneuil

Dramatic Slowing Down of Oil/Water/Silica Contact Line Dynamics Driven by Cationic Surfactant Adsorption on the Solid

We report on the contact line dynamics of a triplephase system silica/oil/water. When oil advances onto silica within a water film squeezed between oil and silica, a rim forms in water and recedes at constant velocity. We evidence a sharp (three orders of magnitude) decrease of the contact line velocity upon the addition of cationic surfactants above a threshold concentration, which is slightly smaller than the critical micellar concentration. We show that, with or without surfactant, and within the range of small capillary numbers investigated, the contact line dynamics can be described by a friction term that does not reduce to pure hydrodynamical effects. In addition, we derive a model that successfully accounts for the selected contact line velocity of the rim. We further demonstrate the strong increase of the friction coefficient with surfactant bulk concentration results from the strongly nonlinear adsorption isotherm of surfactants on silica. From the variations of the friction coefficient and spreading parameter with surface concentration, we suggest a picture in which the part of the adsorbed surfactants that are strongly bound to the silica interface is trapped under the oil droplet and is responsible for the large increase in line friction.

■ INTRODUCTION

The impact of surfactants on the wettability of solid substrates is of interest to many industries, ranging from industrial coating processes to controlled spraying of active agents, in agriculture for example. As such, it has been studied extensively. [START_REF] Fell | Influence of Surfactant Concentration and Background Salt on Forced Dynamic Wetting and Dewetting[END_REF][START_REF] Fell | Influence of Surfactant Transport Suppression on Dynamic Contact Angle Hysteresis[END_REF][START_REF] Henrich | Influence of surfactants in forced dynamic dewetting[END_REF][START_REF] Churaev | Interaction of Oil Droplets with Silica Surfaces[END_REF][START_REF] Stoebe | Enhanced Spreading of Aqueous Films Containing Ionic Surfactants on Solid Substrates[END_REF][START_REF] Starov | Spreading of Surfactant Solutions over Hydrophobic Substrates[END_REF][START_REF] Cachile | Spontaneous Spreading of Surfactant Solutions on Hydrophilic Surfaces: C n E m in Ethylene and Diethylene Glycol[END_REF][START_REF] Chaudhuri | Dynamic Contact Angles on PTFE Surface by Aqueous Surfactant Solution in the Absence and Presence of Electrolytes[END_REF] In literature, the wettability of surfaces by surfactant solutions was often characterized through measurements of equilibrium contact angles α e of droplets of surfactants solutions in air: the larger the angle, the lower the wettability. These macroscopic characterizations were interestingly related to the arrangement of surfactants on the solid surface depending on their concentration. [START_REF] Thiele | Equilibrium Contact Angle and Adsorption Layer Properties with Surfactants[END_REF][START_REF] Serrano-Saldanã | Wettability of Solid/Brine/ n-Dodecane Systems: Experimental Study of the Effects of Ionic Strength and Surfactant Concentration[END_REF][START_REF] Waghmare | Under-Water Superoleophobic Glass: Unexplored Role of the Surfactant-Rich Solvent[END_REF][12][START_REF] Stammitti-Scarpone | Solid-Liquid-Liquid Wettability of Surfactant-Oil-Water Systems and Its Prediction around the Phase Inversion Point[END_REF] Beyond the static case, the wetting dynamics of surfactants solutions is expected to involve complex interplay between transfers at both liquid and solid interfaces, liquid flows, and possibly specific behaviors at the contact line due to surfactants' adsorption or desorption. Over the past decades, the wetting dynamics of pure liquids over solid substrates, in air or in another liquid, without any surfactants, has been extensively studied both experimentally and theoretically. [START_REF] De Gennes | Wetting: Statics and Dynamics[END_REF][START_REF] Churaev | Wetting Films and Wetting[END_REF][START_REF] Grand | Shape and Motion of Drops Sliding down an Inclined Plane[END_REF][START_REF] Snoeijer | Moving Contact Lines: Scales, Regimes, and Dynamical Transitions[END_REF][START_REF] Blake | Kinetics of Liquid-Liquid Displacement[END_REF][START_REF] Cox | The Dynamics of the Spreading of Liquids on a Solid Surface. Part 2. Surfactants[END_REF][START_REF] Voinov | Hydrodynamics of Wetting[END_REF][START_REF] Petrov | A Combined Molecular-Hydrodynamic Approach to Wetting Kinetics[END_REF][START_REF] Goossens | Can We Predict the Spreading of a Two-Liquid System from the Spreading of the Corresponding Liquid-Air Systems?[END_REF] A moving contact line exhibits a dynamic contact angle α, which differs from its equilibrium value due to dissipation, and depends on the contact line velocity. Spontaneous wetting is agreed to be driven by the gain in surface energy, γ(cos α e -cos α), while several dissipative processes have been thought of, which involve very different lengthscales. [START_REF] Snoeijer | Moving Contact Lines: Scales, Regimes, and Dynamical Transitions[END_REF] Viscous dissipation in the spreading liquid, first, was modelled in the Stokes framework, using lubrication approximation for small-to-moderate contact angles [START_REF] Cox | The Dynamics of the Spreading of Liquids on a Solid Surface. Part 2. Surfactants[END_REF][START_REF] Voinov | Hydrodynamics of Wetting[END_REF][START_REF] De Gennes | Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves[END_REF] and is expected to apply at distances to the contact line ranging from a nanometer-sized length to the macroscopic system size. Second, at a microscopic scale, the contact line motion has been modeled in terms of dissipative molecular displacements between adsorption sites on the solid surface, where the molecular jumps are associated to a barrier activation energy. [START_REF] Blake | Kinetics of Liquid-Liquid Displacement[END_REF][START_REF] Goossens | Can We Predict the Spreading of a Two-Liquid System from the Spreading of the Corresponding Liquid-Air Systems?[END_REF][START_REF] Seveno | Predicting the Wetting Dynamics of a Two-Liquid System[END_REF] Experimentally, both models were shown to describe experimental data depending on the range of contact line velocities V. More precisely, a nondimensional capillary number is usefully defined as Ca = ηV/γ where γ is the liquid surface tension and η is the viscosity. [START_REF] De Gennes | Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves[END_REF] Hence, in most liquids, viscous dissipation was shown to control the wetting dynamics at large Ca numbers. Conversely, at smaller velocities or Ca numbers, the molecular kinetic theory was found to successfully describe experimental data, [START_REF] Fetzer | Dynamics of Liquid-Liquid Displacement[END_REF][START_REF] Ramiasa | Contact Line Friction in Liquid-Liquid Displacement on Hydrophobic Surfaces[END_REF][START_REF] Duvivier | Experimental Evidence of the Role of Viscosity in the Molecular Kinetic Theory of Dynamic Wetting[END_REF] even though some authors suggested other origins for friction at the contact line. [START_REF] Rolley | Dynamics and Hysteresis of the Contact Line between Liquid Hydrogen and Cesium Substrates[END_REF][START_REF] Carlson | Universality in Dynamic Wetting Dominated by Contact-Line Friction[END_REF][START_REF] Wang | Local Dissipation Limits the Dynamics of Impacting Droplets on Smooth and Rough Substrates[END_REF] A model combining both hydrodynamic dissipation and molecular theory was also developed to describe intermediate contact lines velocities and was successfully found appropriate in some cases. [START_REF] Petrov | A Combined Molecular-Hydrodynamic Approach to Wetting Kinetics[END_REF][START_REF] Primkulov | Microscale Liquid-Liquid Displacement Dynamics: Molecular Kinetic or Hydrodynamic Control[END_REF][START_REF] De Ruijter | Dynamic Wetting Studied by Molecular Modeling Simulations of Droplet Spreading[END_REF] However, this picture does not describe the wetting dynamics for all systems. [START_REF] Primkulov | Microscale Liquid-Liquid Displacement Dynamics: Molecular Kinetic or Hydrodynamic Control[END_REF][START_REF] De Ruijter | Dynamic Wetting Studied by Molecular Modeling Simulations of Droplet Spreading[END_REF][START_REF] Hoffman | A Study of the Advancing Interface[END_REF] Adding surfactants to the spreading liquid was shown to induce an important increase of the wetting speed of surfactant solutions on solid surfaces. This phenomenon is called superspreading and was observed with surfactants in the advancing phase. [START_REF] Stoebe | Enhanced Spreading of Aqueous Films Containing Ionic Surfactants on Solid Substrates[END_REF][START_REF] Cachile | Spontaneous Spreading of Surfactant Solutions on Hydrophilic Surfaces: C n E m in Ethylene and Diethylene Glycol[END_REF][START_REF] Karapetsas | On Surfactant-Enhanced Spreading and Superspreading of Liquid Drops on Solid Surfaces[END_REF][START_REF] Kabalnov | Monolayer Frustration Contributions to Surface and Interfacial Tensions: Explanation of Surfactant Superspreading[END_REF] The case of receding surfactant solutions, especially in a two-liquid problem, has been much less studied. [START_REF] Fell | Influence of Surfactant Concentration and Background Salt on Forced Dynamic Wetting and Dewetting[END_REF][START_REF] Chaudhuri | Dynamic Contact Angles on PTFE Surface by Aqueous Surfactant Solution in the Absence and Presence of Electrolytes[END_REF] In all cases, transfers of surfactants in the liquid phase and toward the air/liquid interface are regarded as the determining step controlling the contact line dynamics, [START_REF] Starov | Spreading of Surfactant Solutions over Hydrophobic Substrates[END_REF][START_REF] Wang | Surfactant-Enhanced Spreading of Sessile Water Drops on Polypropylene Surfaces[END_REF][START_REF] Chan | Surfactant-Assisted Spreading of a Liquid Drop on a Smooth Solid Surface[END_REF] with possible surfactant transport along the liquid/air interface through Marangoni effects. [START_REF] Fell | Influence of Surfactant Concentration and Background Salt on Forced Dynamic Wetting and Dewetting[END_REF] Yet, no clear picture of the effect of surfactants adsorbed to the solid interface on the wetting dynamics can be found in literature.

In the present work, we offer to investigate the dewetting dynamics of surfactant solutions at low capillary numbers, with surfactants added to the receding phase, and in a two-liquid situation. The low capillary number regime is expected to enhance the effect of surfactants adsorbed to the solid interface. To gain accurate knowledge of the behavior of adsorbed surfactants, we carefully characterized its adsorption to the solid at equilibrium. The ternary system studied here is silica as the solid, aqueous solutions of surfactants as the receding phase (hereafter called water), and oil as the advancing phase, as depicted in Figure 1. This system is of particular interest to applications where membranes are used to separate oil and water in waste water management processes. [START_REF] Asatekin | Oil Industry Wastewater Treatment with Fouling Resistant Membranes Containing Amphiphilic Comb Copolymers[END_REF][START_REF] Zhu | Surfactant-Stabilized Oil Separation from Water Using Ultrafiltration and Nanofiltration[END_REF][START_REF] Wang | Composite Membrane with Underwater-Oleophobic Surface for Anti-Oil-Fouling Membrane Distillation[END_REF] By experimentally studying the receding dynamics of aqueous solutions of surfactants on silica and in oil, we will determine the respective effects of surfactants adsorbed and transferred to the three interfaces at stake: solid/ water, solid/oil, and water/oil. The contact line dynamics will be analyzed both in terms of surface energy gain, viscous dissipation, and molecular friction at the contact line. In particular, since surfactants are in the receding phase only (Figure 1), the question of their trapping at the solid/oil interface or their possible desorption at the contact line will be tackled.

■ EXPERIMENTAL SECTION

Materials. The two liquids were chosen to be immiscible: water and dodecane (Sigma-Aldrich, purity >99%). To guarantee a reproducible physico-chemistry, the solid substrates were uncoated UV-fused plano-convex silica lenses (SPX031) with focal lens 500 mm from Newport. To ensure an optimal cleanliness of the surface, the following procedure was used prior to each experiment. As received, the lenses were submitted to a heating cycle at 620 °C for 15 min in a furnace, to burn any organic impurity or surface coating. They were further dusted out under a nitrogen flux. Right before the experiment, each lens was exposed to an ozone atmosphere for 15 min and then immersed immediately into the work solution to avoid any contamination.

The surfactant was chosen with a good ability to adsorb on the negatively charged silica and very low solubility in oil. Consequently, we chose hexadecyltrimethylammonium bromide (CTAB) from Sigma-Aldrich (purity >96%), which meets these criteria. [START_REF] Rosen | Surfactants and Interfacial Phenomena[END_REF] It was dissolved as received in deionized water with an added background concentration of 10 -4 mol•L -1 of NaCl to set the value of the ionic strength in the water phase. The CTAB concentration [CTAB] was varied between 6 • 10 -7 and 4 • 10 -3 mol/L. In this range of concentration, the viscosity η of the aqueous solutions is found constant η = 0.89 mPa•s. The viscosity of dodecane is η oil = 0.75 mPa• s.

Adsorption at the Liquid/Liquid Interface. Tensiometry experiments were conducted to determine the interfacial tension of CTAB solutions with dodecane as a function of the concentration. Experimental details and results are shown in the Supporting Information. The interfacial tension decreases with bulk surfactant concentration until it reaches a plateau at the critical micellar concentration (CMC). [START_REF] Fainerman | Thermodynamics of Adsorption of Ionic Surfactants at Water/Alkane Interfaces[END_REF] We find CMC = 0.9 mmol•L -1 , in agreement with values from literature for CTAB with no added salt. [START_REF] Rosen | Surfactants and Interfacial Phenomena[END_REF][START_REF] Moulik | Micellar Properties of Cationic Surfactants in Pure and Mixed States[END_REF] Data from literature show that sorption equilibrium between CTAB in the bulk at concentration C and at the oil/water interface (surface concentration Γ i ) is well described by a Langmuir isotherm and Gibbs equation. [START_REF] Rosen | Surfactants and Interfacial Phenomena[END_REF] At saturation, the surface concentration is denoted Γ i ∞ and measured at 1.8μmol•m -2 , in agreement with existing data on CTAB at air or oil interfaces. [START_REF] Moulik | Micellar Properties of Cationic Surfactants in Pure and Mixed States[END_REF][START_REF] Zdziennicka | Activity and Thermodynamic Parameters of Some Surfactants Adsorption at the Water-Air Interface[END_REF][START_REF] Kedar | Effect of Salinity on the IFT between Aqueous Surfactant Solution and Crude Oil[END_REF] For the dodecane/pure water interfacical tension, we measure γ = 41.9 mN•m -1 and above CMC, γ = 7 mN•m -1 . We also checked, by fast swelling and deswelling of the oil drop, that the transport of surfactants at the oil water interface is governed by diffusion (data not shown).

Adsorption at the Solid/Liquid Interface. We characterized the adsorption of CTAB at the water-silica surface especially because it strongly depends on the nature and quantity of added salt, 46,47 using the depletion method described in the Supporting Information.

The adsorption isotherm, namely, the variations of the surface concentration Γ with CTAB concentration, is shown in Figure 2. The amount of CTAB adsorbed on silica increases with bulk concentration, or surfactant chemical potential, in three steps as follows: slow increase below Γ*, step-like increase above Γ*, and then saturation to a plateau value Γ ∞ of 2.4 μmol•m -2 similar to that measured in literature. [START_REF] Velegol | Counterion Effects on Hexadecyltrimethylammonium Surfactant Adsorption and Self-Assembly on Silica[END_REF][START_REF] Atkin | Adsorption Kinetics and Structural Arrangements of Cationic Surfactants on Silica Surfaces[END_REF][START_REF] Cases | Ionic Surfactants Adsorption on Heterogeneous Surfaces[END_REF][START_REF] Theodoly | A Combined Streaming-Potential Optical Reflectometer for Studying Adsorption at the Water/Solid Surface †[END_REF] The shape of the isotherm results from the arrangement of the surfactants on the solid surface, and the present picture emerging from literature is the following: [START_REF] Keḱicheff | Cationic-Surfactant-Coated Mica Surfaces below the Critical Micellar Concentration: 1. Patchy Structures As Revealed by Peak Force Tapping AFM Mode[END_REF][START_REF] Atkin | Mechanism of Cationic Surfactant Adsorption at the Solid-Aqueous Interface[END_REF] isolated aggregates are first detected around a bulk concentration 10 -5 mol• L -1 . As bulk concentration further increases, monolayered-like patches of surfactants progressively form from these aggregates, grow, and finally connect to form a network, until a complete monolayer is obtained at larger concentration. Further increase in bulk concentration leads to the formation of bilayer-like patches on top of the underlying monolayer until a complete bilayer covers the substrate, the top layer of which possibly being less dense than the monolayer. The complete bilayer corresponds to the plateau value Γ ∞ . In this picture, the sharp increase of Γ is attributed to adsorption mechanisms with low energetical cost compared to the electrostatically driven adsorption of isolated positively charged CTA + ions onto the negatively charged silica surface. Such mechanisms may be the tail-to-tail surfactants aggregation typically involved in the growth of bilayer-like patches on top of the monolayer [START_REF] Rosen | Surfactants and Interfacial Phenomena[END_REF] or earlier surfactants adsorbing with their counter-ion during the growth of monolayer-like patches. [START_REF] Theodoly | A Combined Streaming-Potential Optical Reflectometer for Studying Adsorption at the Water/Solid Surface †[END_REF][START_REF] Keḱicheff | Cationic-Surfactant-Coated Mica Surfaces below the Critical Micellar Concentration: 1. Patchy Structures As Revealed by Peak Force Tapping AFM Mode[END_REF] Altogether, the adsorption isotherm in Figure 2 reveals that CTAB adsorbs through strong interactions at low concentration, until a surface coverage denoted Γ* ∼ 0.4 μmol/m 2 . Above Γ*, the step-like isotherm reveals that further adsorption involves weaker interactions so that these additional surfactants are expected to be very labile.

Experimental determinations of the adsorption isotherm of surfactants on solid surfaces from literature [START_REF] Zhu | General Isotherm Equation for Adsorption of Surfactants at Solid/Liquid Interfaces. Part 2. Applications[END_REF] allowed the derivation of the empirical eq 1

Γ = Γ + + + ∞ - - k C n k C k C k C (1/ ) 1 (1 )
n n 1 2 1 1 2 1 (1)
where Γ ∞ is the surface concentration at saturation, and C = [CTAB]/CMC is the concentration relative to the CMC. Eq 1 was fitted to our experimental data Γ(C) in Figure 2 with k 1 , k 2 , and n as fitting parameters. It was later used to compute Γ at all concentrations. Squeezed Droplet Experiments. A homemade setup [START_REF] Bluteau | Water Film Squeezed between Oil and Solid: Drainage towards Stabilization by Disjoining Pressure[END_REF] was designed to observe the water/oil/silica contact line dynamics both within a water film trapped between a squeezed oil drop and silica and at the edge of the oil drop when it spreads on silica within water. A schematic representation is given in Figure 3, and a detailed description can be found in a previous work. [START_REF] Bluteau | Water Film Squeezed between Oil and Solid: Drainage towards Stabilization by Disjoining Pressure[END_REF] A transparent PMMA tank is filled with the aqueous solution. An oil drop (Figure 3c) of controlled volume ranging from 0.5 to 1 μL is created at the tip of a polymer tube (PEEK, ID 65 μm, OD 1.59 mm) connected to a syringe pump. Its radius is denoted R d . Both the tube with the drop and the tank are set to a motorized vertical stage (PI). The silica lens is held at the water surface and set to a 10× microscope objective (Zeiss Epiplan Apochromat). As depicted in Figure 3a, observations of the lens/water/oil interfaces were made through the lens with a microscope with episcopic monochromatic illumination (λ =615 nm). A typical image is shown in Figure 3b and will be discussed hereafter. Finally, millimeter-sized views of the oil droplet are imaged with a side camera (Sentech) at 10 fps and low magnification (2.8 μm per pixel) from which the oil drop radius R d was measured and the low velocity range was explored (Figure 3c).

The following procedure is used: First, the tank is filled with the surfactant+salt solution, an oil drop is created at the tip of the tube in the filled tank, and the silica lens is immersed in the tank also. Prior to any experiment, relaxation of the oil/water and water/silica interfaces is allowed for 30 and 15 min, respectively. Second, the drop is squeezed toward the surface at 15 mm•s -1 on a distance varying between 35 and 60 μm and then stopped. During the squeezing stage, water remains trapped between oil and silica. The oil/water interface is deformed in a well-known bell shape called a dimple 4,54-57 that subsequently drains. Here, the squeezed water film is pressurized by the oil drop and experiences a pressure equal to the drop capillary pressure 2γ/R d ranging from 20 to 120 Pa. Depending on the concentration in surfactants, the draining water film may either stabilize or spontaneously puncture, resulting in water dewetting from the silica surface in oil. We emphasize the squeezing stage is needed to trap a water film and nucleate the dewetting of water. However, once initiated, that process is spontaneous, and its dynamics is independent of the applied pressure. The dewetting case is the scope of the present paper.

First, after dewetting of water has occurred, the equilibrium angle α e in water at the triple contact line was measured as the static receding contact angles at vanishing velocity at the edge of the drop (Figure 3c). Vanishing velocities were obtained by low-rate injection of oil in the drop. This angle typically varies between 40°and 100°.

Second, when the squeezed water film punctures, the water film thickness profile is accurately measured over space and time and at the edge of the receding triple contact line, through optical interferometry, using the light reflected at the two interfaces and collected by the microscope. Typical microscopy images are shown in Figures 3b and4, where the rings are equal thickness fringes and the wetting of oil on silica appears as a black circular area. Contact line velocities are measured from images recorded with framerates ranging from 10 to 13,600 frames per second, thereby allowing a wide velocity range (from 10 -3 to 50 mm•s -1 ). To do so, a double camera system equipped with a microscope was used: a high speed camera (Photron Mini) with a resolution of 0.5 μm per pixel and a 10 fps camera (Sentech) with a resolution of 0.14 μm per pixel. A typical series of interferometry images is shown in Figure 4a-c for a CTAB solution at 0.001 CMC. The corresponding profile of the silica and oil/water interface is depicted in Figure 4d.

In the vicinity of the quasi-circular oil/silica contact zone, interference fringes accumulate, indicating a large thickness variation of the water film. They can be used to measure the thickness profile of the water film, in the vicinity of the contact line, as shown in Figure 4e. A dewetting rim is found to collect the water, as described in literature. [START_REF] De Gennes | Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves[END_REF] At the oil/water/silica contact line, water connects at an angle we denote α rim that can be measured from the thickness profiles. Typical results are plotted in Figure 4f at [CTAB] = 10 -3 .CMC. The contact angle is found to be small (around 6°in this case at long times), and for all aqueous solutions tested, it saturates to a steady value that will be taken as the dynamic contact angle value α rim in the following.

Finally, the growth rate of the dewetted area A is measured. Remarkably, the dewetted zone is quasi circular evidencing that the contact line velocities do not depend on the local thickness (Figure 4a-c). Typical time variations of its radius π = R A are shown in Figure 4f. A linear dependency of R with time is observed for all experiments, as reported in literature. [START_REF] Snoeijer | Moving Contact Lines: Scales, Regimes, and Dynamical Transitions[END_REF][START_REF] Bazazi | Wetting Dynamics in Two-Liquid Systems: Effect of the Surrounding Phase Viscosity[END_REF][START_REF] Redon | Dynamics of Dewetting[END_REF] The slope determines the dewetting velocity of the rim denoted V rim . Here, the sign of the dewetting velocity is chosen positive when water recedes and oil advances.

■ RESULTS

Dewetting Dynamics of Surfactant Solutions on Silica in Oil within a Trapped Water Film. First, for concentrations above 0.8 CMC, no water film puncture could be observed in our range of pressure value. For this reason, in this concentration range, shown in blue in Figure 5, no dynamic data was reported. At 5 CMC, the static receding contact angle α e is measured using a specific procedure: we initially approached an oil drop within pure water, which led to spontaneous dewetting of water on silica. Then, water was replaced in situ with a 5 CMC solution and α e was then measured: it is found lower than at 0.8 CMC, but of large finite value (40°). In the past, no occurrence of dewetting was interpreted as total wetting condition for water on silica in oil, [START_REF] Churaev | Interaction of Oil Droplets with Silica Surfaces[END_REF][START_REF] Waghmare | Under-Water Superoleophobic Glass: Unexplored Role of the Surfactant-Rich Solvent[END_REF] in apparent contradiction to the non-zero equilibrium contact angle we measure. Actually, zero occurrence of nucleation at 5 CMC is instead attributed to a larger amplitude energetic barrier for nucleation due to confined and possibly structured surfactants of high concentration in the water film. [START_REF] Danov | The Metastable States of Foam Films Containing Electrically Charged Micelles or Particles: Experiment and Quantitative Interpretation[END_REF][START_REF] Bergeron | Equilibrium Measurements of Oscillatory Disjoining Pressures in Aqueous Foam Films[END_REF] This will be the scope of the next article.

In the surfactant concentration range from 0 to 0.8 CMC, the aqueous film is observed to spontaneously puncture, and a rim always collects the dewetting aqueous solution, with an angle and velocity that are independent of time and squeezed water film thickness as soon as the dewetted zone is large enough. The rim dewetting angle and velocity are plotted as a function of the CTAB concentration in bulk in Figure 5. In addition, the edge of the dewetted area is observed to become all the more irregular that bulk concentration increases, as shown in Figure 6. As pointed out in the Introduction, dewetting of water in oil is driven by the gain in surface energy γ(cos α e -cos α rim ) between the equilibrium situation and dynamic one. We therefore systematically measured the equilibrium angle α e as the static receding contact angles at vanishing velocity at the edge of the drop (Figure 3c), after dewetting of water has occurred. Both angle values were averaged over two to six different experiments and are reported in Figure 5a. The equilibrium angle α e increases with bulk concentration from 40°to 100°, while the dynamic rim contact angle slightly decreases between 6°and 1°. Figure 5b displays the surface energy contributions to the driving energy term corresponding to γcos(α) for the two sets of angles. A monotonic decrease of both surface energies with concentration is obtained, but more importantly, we find that the driving capillary term γ(cos α e -cos α rim ) is roughly constant over the whole concentration range, in contrast with the contact line velocity displayed in Figure 5c: with no surfactant, it is close to 10 mm•s -1 and it abruptly decreases by three orders of magnitude as surfactant concentration increases between 10 -2 and 0.8 CMC.

Dewetting Dynamics of Surfactant Solutions on Silica at the Edge of an Oil Drop. To understand this apparent contradiction, supplementary data on the wetting dynamics are needed to characterize the dissipative processes at stake in the vicinity of the contact line, as pointed out in Introduction. To this end, the large angle and low velocity range were explored by using side views of oil drops in contact with silica (Figure 3c). After spontaneous dewetting of the water film, oil was injected in or removed from the drop at rates varying between 0.1 and 300 μL•min -1 and is depicted in Figure 7a. The contact angle α at the oil/water/silica contact line was measured as a function of its velocity V. Typical data are shown as an inset in Figure 7b for both advancing and receding cases. The receding case is plotted in Figure 7b for water and Figure 7c for CTAB solutions.

At all concentrations, in the small velocity range, the contact angle is independent of V and equal to α e . The plateau ends with a sharp decrease of the angle with velocity, at V ∼ 10 -2 m/s in pure water (Figure 7b), and at V-values, all the more low that more surfactants are added (Figure 7c). The angle α rim and velocity V rim of the rim are added to these graphs as stars. In all cases, the rim data nicely align with swollen drop data, demonstrating that both experiments explore the same physics. In the following, we offer to analyze the full contact line dynamics data to identify the relevant dissipative mechanisms, with and without surfactants. We will ultimately relate them to the adsorbed surfactant layers.

Dewetting Dynamics Driven by Friction at the Contact Line. Two contact lines dynamics models existing in literature are compared to the present data. In a purely hydrodynamic approach, the energy loss results from viscous dissipation in the corner formed by receding water in oil on silica, which yields the following relation between α and V 20,23,25,62

α α - = β β b a K Ca ln e i k j j j y { z z z (2)
α e is the receding equilibrium contact angle, Ca = η V/γ is the capillary number with η = 0.89 mPa•s the viscosity of the liquid wedge, γ = 41.9 mN•m -1 is the interfacial tension between the two liquids, a is the molecular-size length, and b is the macroscopic scale that we can assume to be the typical size of the drop. This leads to a factor ln(b/a) of order 15. The constants K and β depend on the viscosity ratio ϵ of the two liquid phases. Here, we have ϵ = η oil /η = 1.4. In the case of a viscosity ratio between the two fluids ϵ much smaller than 1 (e.g., a liquid drop in air) and α<3π/4, eq 2 reduces to the equation derived by Cox [START_REF] Cox | The Dynamics of the Spreading of Liquids on a Solid Surface. Part 2. Surfactants[END_REF] and Voinov [START_REF] Voinov | Hydrodynamics of Wetting[END_REF] with β = 3 and K = 9. For ϵ = 1.4 (which is the ratio we have here for water/ dodecane), Fetzer et al. [START_REF] Fetzer | Dynamics of Liquid-Liquid Displacement[END_REF] showed that Cox solution reduces to eq 2, but with β = 2.52 and K = 15.9. We will use these values in the following. Here, the capillary number Ca varies between 10 -5 and 10 -3 ; therefore, it is always much smaller than unity. For pure water, eq 2 is plotted as a dash-dotted line on Figure 7b with α e = 40°. We observe that the capillary number at the vanishing contact angle is predicted at Ca = 1.8 • 10 -2 (V = 810 -2 m•s -1 ), while in the present experiments, this velocity is measured to be V = 10 -2 m•s -1 , which is one order of magnitude smaller than predicted by the hydrodynamic model. Thus, viscous dissipation plays a negligible role on the motion of the contact line, and the dissipation likely originates from a contact line friction of other, microscopic, origin.

In literature, [START_REF] Blake | Kinetics of Liquid-Liquid Displacement[END_REF][START_REF] Goossens | Can We Predict the Spreading of a Two-Liquid System from the Spreading of the Corresponding Liquid-Air Systems?[END_REF][START_REF] Seveno | Predicting the Wetting Dynamics of a Two-Liquid System[END_REF] dissipation at the contact line has alternatively been offered to originate from a friction-like mechanism at a molecular scale, located at the contact line. The contact line displacement is associated to molecular jumps between adsorption sites on the solid, which are thermally activated, and the corresponding energy dissipation is denoted F(V) so that the equation relating α and V writes

α α γ = + F V cos cos ( ) e (3)
with = λ ( )

F V nk T h ( ) 2 arc sin V K B 2 0
, where K 0 is the jump frequency between two molecular sites, λ is the distance between them, n = 1/λ 2 , k B is the Boltzmann's constant, and T is the temperature. In the low Ca limit, eq 3 can be linearized [START_REF] Seveno | Predicting the Wetting Dynamics of a Two-Liquid System[END_REF][START_REF] Primkulov | Microscale Liquid-Liquid Displacement Dynamics: Molecular Kinetic or Hydrodynamic Control[END_REF] using a molecular friction coefficient ζ = k B T/ K 0 λ 3 . Eq 3 becomes (4) Eq 4 can be generalized to any friction mechanism whatever its physical or physico-chemical origin, provided that a friction coefficient ζ linearly relates the dissipative energy to velocity. [START_REF] Carlson | Universality in Dynamic Wetting Dominated by Contact-Line Friction[END_REF][START_REF] Wang | Local Dissipation Limits the Dynamics of Impacting Droplets on Smooth and Rough Substrates[END_REF][START_REF] Wang | Surface Structure Determines Dynamic Wetting[END_REF] Any kind of friction localized in the immediate vicinity of the contact line would lead to the same expression.

We have verified that in our case both eqs 3 and 4 give nearly the same values of ζ at all concentrations, demonstrating that friction dominates over viscous dissipation. Here, we first assume that the interfacial tension at the liquid interface can be taken as set by the bulk surfactant concentration. This hypothesis will be validated in the Discussion section. All data sets were successfully fitted to eq 4 with ζ as a fitting parameter: we find ζ ≃ 0.8 Pa•s for pure water, and ζ= 10 Pa•s at 0.1 CMC, in agreement with values from literature on other but close systems: for dodecane in water on thiol-coated gold surfaces, Fetzer et al. [START_REF] Fetzer | Dynamics of Liquid-Liquid Displacement[END_REF] In conclusion, we showed that, at all concentrations, the contact line dynamics is controlled by the balance between the gain of surface energy that acts as the driving force and a dissipation by friction at the contact line that cannot be reduced to hydrodynamics only. We further find that, although adding surfactants up to 0.8 CMC seem to hydrophobize the silica/water interface as revealed by an increase in α e , the dewetting of water from this hydrophobized interface is found to dramatically slow down because friction at the contact line considerably increases.

At this stage, a comment can be made on the shape of rim and the selection of its dewetting velocity, which is found independent of water film thickness. In Appendix, we solve this question in our very specific situation where friction at the contact line is several orders of magnitude larger than viscous dissipation. We show that the rims collecting the liquid are of constant curvature and geometrically constrained by both hydrodynamic dissipation and contact-line friction operating in parallel at the rear and front edges of the growing rim, as suggested by Bertrand et al. [START_REF] Bertrand | Dynamics of Dewetting[END_REF] in a simpler one-liquid situation. As we shall see, our description is in very good agreement with our experimental results.

■ DISCUSSION

We now consider the different effects, involving surfactants, from which the dramatic slowing down of water receding dynamics within the squeezed water film could result. We first address the question of the magnitude of the interfacial surface tension at the contact line, especially if surfactant desorb from the solid surface as contact line recedes: surfactant desorption may lead to an increase of surfactant concentration, localized in the wedge. In literature on triple contact line dynamics with surfactants, 1,2 the onset of a Marangoni flow at the liquid interface was discussed as a possible origin of the decrease of the contact angle with contact line velocity.

Surfactant-Induced Marangoni Effects at Oil/Water Interface Do Not Control the Dewetting Dynamics. The oil/water/silica triple line recedes and is depicted in Figure 4e. Note that the rim formed ahead of the contact line has a width over height aspect ratio of 100. Therefore, from a hydrodynamic point of view, the situation amounts to the sketch of Figure 9. As the triple phase contact line moves, surfactants can either remain adsorbed on the silica surface or desorb, either fully or partially.

That local increase can be opposed by three effects, namely, surfactant diffusion in the bulk, advection of the water solution in and out of the wedge (v x (z)), bulk diffusion, and interfacial advection at the oil/water interface (U). The latter arises when gradients of surfactant concentration at the liquid interface generate a Marangoni flow. A detailed modelling of these transfers is given in the Supporting Information. The main results are summarized here. First, in the liquid wedge, the advection-diffusion of surfactants in the bulk is shown to be driven by diffusion only. Indeed, the Pećlet number comparing surfactant transport by the flow and by diffusion writes: Pe = αhV/D. Given the typical values of velocity, between 10 -2 and 10 -5 m•s -1 , of the rim thickness h of 400 nm and D ∼ 10 -10 m 2 •s -1 , Pe remains smaller than 1, which means that surfactant concentration C obeys a diffusion equation: ΔC = 0. More precisely, transverse diffusion along z (Figure 9) feeds the liquid interface with surfactants from a subsurface layer, which extends over the depletion length λ: it is defined as the ratio Γ i ∞ /CMC (where Γ i ∞ is the liquid interface concentration at saturation, see the Supporting Information). For CTAB, λ ∼ 2μm, thus than larger than the rim height h. Hence, in the wedge, bulk concentration C is homogeneous along the transverse direction, and the bulk solution of concentration C(x) is in equilibrium with the liquid interface bearing a surface concentration Γ i (x). For CTAB, a Langmuir isotherm relates C and Γ i . In the following, we show that, in the wedge, the surfactants desorbed from the solid surface (flux ΓV) are mainly driven out of the wedge by a Marangoni flux at the liquid interface (flux Γ i U), which is predominent over the diffusive transport along the longitudinal direction x. The diffusion equation, written now as a function of the distance r to the contact line, is supplemented by two boundary conditions: no flux through the solid interface, and mass conservation of surfactants. The first condition imposes that C decreases logarithmically with the distance x to the contact line due to the wedge geometry. The second writes:

α Γ = Γ + V U D x C x d d i ( 5
)
where U is the velocity at the liquid interface. It is set by the hydrodynamic boundary condition that imposes that the viscous tangential stress in water is balanced by the Marangoni stress arising from the gradient in surface tension along the interface. Note that the viscous stress in oil can be neglected because shear in oil develops over the typical length R d , the radius of the drop, which is orders of magnitude larger than h = αx. The liquid/liquid interface boundary condition therefore

writes: η ∼ γ - U V h x / 2 d
d , which allows to derive the Marangoni interfacial velocity U. The mass conservation eq 5 becomes:

α η γ Γ = Γ + + Γ V V x C x D c /2 d d d d i i i k j j j j y { z z z z (6)
where we use = orders of magnitude larger than 1: surfactants desorbed from the solid interface are predominantly expelled from the wedge through the interfacial Marangoni flow. It follows that, at a distance r from the contact line, the increase in concentration in the wedge relative to the solution concentration C 0 set at large distance L can be written as

α Δ ∼ C C V V L r 1 ln 0 c (7)
where we assume Γ and Γ i are of the same order of magnitude, and we introduce the capillary velocity V c = (γ/η). More importantly, the resulting interfacial tension decrease can also be calculated:

γ Δ ∼ γ α ln V V L r c .
In our conditions, V c = 0.6 m•s -1 is orders of magnitude larger than the velocities V we measure. Consequently, even at a distance r as close as 1 nm to the contact line, we find Δγ ≃ 10 -8 N•m -1 is negligible.

The Supporting Information details the full calculation of the concentration profiles in the wedge, by taking into account the part of the wedge where C may become larger than CMC, and hence, no adsorption occurs at the liquid interface. It leads to the same conclusions: if surfactants desorb from the solid interface, they are expelled out of the wedge, and the oil/water Figure 9. Sketch of the water wedge receding in oil on silica, in the reference frame of the contact line, with an angle α and a velocity V. v x (z): water velocity profile in the lubrication approximation, U: velocity at the water/oil interface, Γ and Γ i : surfactant surface concentrations, respectively desorbed from the water/silica interface and adsorbed at the water/oil interface. h and L: characteristic length along the z-and x-axes, respectively (see text). For the sake of clarity, the surfactant molecules have not been represented. interfacial tension is not modified and set by the bulk concentration in the tank. Finally, the onset of a Marangoni flow at the liquid-liquid interface changes the boundary condition for the flow in the wedge, but it only affects the viscous dissipation term in the contact line dynamics and by a numerical factor of order unity. In the present study, we found that friction at the contact line dominates over the viscous terms so that surfactant transfers are not expected to alter significantly either the driving capillary term or the dissipation term in eq 2.

Friction at the Contact Line Increases with Strongly Adsorbed Surfactants at the Silica Surface. In the following, we offer to discuss the variations of ζ and α e in relation to the amount of CTAB adsorbed at the silica surface Γ, instead of bulk concentration. To do so, we first modify the adsorption isotherm of CTAB on silica (Figure 2) into a bulk concentration versus the surface concentration Γ curve in Figure 10a. As detailed earlier, the value Γ* ∼ 0.4 μmol•m -2 discriminates the adsorption of strongly bound surfactants from the weakly bound ones. The variations of ζ as a function of surface concentration on silica Γ are plotted in Figure 10b. The coefficient ζ first increases with Γ until it reaches a plateau above the threshold value Γ*, which is remarkably the same as for the CTAB adsorption isotherm on silica.

On the other hand, following the path of previous studies, [START_REF] Churaev | Interaction of Oil Droplets with Silica Surfaces[END_REF][START_REF] Waghmare | Under-Water Superoleophobic Glass: Unexplored Role of the Surfactant-Rich Solvent[END_REF] the affinity of silica for oil is characterized through the spreading parameter, denoted S, which compares the surface energies of silica wetted by water and of silica wetted by oil with water as a surrounding medium. A negative value of S corresponds to oil partially wetting silica within water. Water receding is therefore all the more favored that S is large. With our system and notations, S = -γ(cos α e + 1) can be computed from the measured interfacial tension and equilibrium angles. The results are plotted in Figure 10c as a function of surface concentration: S first increases with Γ, then also saturates at the same remarkable value Γ*. Below Γ*, first, the increase of S means that hydrophobicity of silica increases with the amount of surfactants adsorbed on the solid surface, in good agreement with a picture where CTAB tails are exposed to the liquids. In contrast, in the same Γ range, the friction coefficient increases, indicating that receding of water becomes slower as surface hydrophobicity is enhanced: no direct link is observed between the spreading parameter and friction coefficient in our case. Our observations are also at variance with results from literature where dynamic wetting of solids by liquids was analyzed using the adhesion energy defined as S + 2γ: [START_REF] Goossens | Can We Predict the Spreading of a Two-Liquid System from the Spreading of the Corresponding Liquid-Air Systems?[END_REF][START_REF] Seveno | Predicting the Wetting Dynamics of a Two-Liquid System[END_REF] the friction coefficient was found to increase exponentially with adhesion energy. [START_REF] Duvivier | Experimental Evidence of the Role of Viscosity in the Molecular Kinetic Theory of Dynamic Wetting[END_REF] In the present experiments, friction is found to decrease with adhesion energy. Clearly, in the present system, that picture is not adequate either.

Instead, combining our results on adsorption at the silica surface (Figure 10a), friction (Figure 10b), and spreading parameter (Figure 10c) allows us to offer the following picture. Both S and ζ increase with Γ below Γ*, that is, when only strongly adsorbed surfactants are increasingly covering the silica surface. Then, both S and ζ saturate to a plateau value above Γ*, namely, when any adsorbed additional surfactant is bound to the surface through low energy interactions. Note that the S-value measured at Γ ∞ = 2.4 μmol•m 2 where the surfactant forms a complete bilayer also belongs to this plateau. In other words, the strongly bound surfactants, of concentration Γ<Γ*, do contribute to both the oil/silica interactions and the friction at the contact line. In contrast, for Γ>Γ*, weakly bound surfactants, therefore at a surface concentration equal to Γ -Γ*, neither contribute to oil/silica interactions nor to friction at the contact line, which are both set by the strongly bound surfactant at a concentration Γ*. This suggests that, as water recedes on the adsorbed layer of CTAB, the strongly bound CTABs are trapped between oil and silica and do not desorb, while the weakly bound CTABs are desorbed and removed from the wedge by a Marangoni flow at the oil/ water interface. We conclude that both the kinetics and thermodynamics of dewetting ignore the weakly adsorbed surfactants that desorb from silica. Conversely, surfactants that are adsorbed through strong electrostatic interactions change the silica surface from hydrophilic to hydrophobic, but this enhanced affinity for oil that should accelerate water dewetting plays a negligible role. Instead, strongly bound surfactants impair the dewetting dynamics through a strong increase of the contact line friction. By combining our observations that contact lines becomes all the more irregular that concentration increases in Figure 6, with the description from literature of the patterns progressively formed by adsorbed CTAB (see Experimental Section), we offer to ascribe the contact line friction increase to the growth of surface heterogeneities: as the surface concentration of strongly bound surfactants increase, monolayered-like patches of surfactants progressively form, grow, and connect, and the silica surface exhibits more complex patterns on which the contact line gets pinned.

■ CONCLUSIONS

The receding dynamics of water on silica in oil is shown to be controlled by the gain in surface energy, which is dissipated through friction at the contact line. Upon the addition of cationic surfactants in the water phase, up to approximately 0.8 CMC, water spontaneously dewets, and the affinity of oil for silica is found to increase while the dewetting dynamics of water is heavily impaired: it can be described by a huge increase of the friction coefficient at the contact line. We show that these effects are fully described by the quantity of surfactants adsorbed at the silica surface and their transfers. We show that: (i) Only electrostatically bound surfactants at the silica surface contribute to friction at the contact line, through contact line pinning on surfactants patterns. [START_REF] Keḱicheff | Cationic-Surfactant-Coated Mica Surfaces below the Critical Micellar Concentration: 1. Patchy Structures As Revealed by Peak Force Tapping AFM Mode[END_REF] (ii) Surfactant bound to silica through weaker interactions desorbs as the contact line recedes, without contributing to friction. (iii) The gain in affinity for oil of surfactant-covered silica has much less positive impact on the water dewetting dynamics than does heterogeneity-induced contact friction in a negative way. From a practical point of view, our results show that cationic surfactants efficiently control the wetting of oil drops on silica in water up to a threshold concentration above which additional surfactants desorb and no longer contribute. In the present case, threshold concentration values are Γ = 0.4 μmol•L -1 and [CTAB]∼ 0.5 CMC. We believe that such systems could be interestingly used to relate the empirical macroscopic friction coefficient to the patterns formed by adsorbed surfactants and elucidate its origin. Finally, we find that, in our experimental conditions, at CTAB concentrations larger than 0.8 CMC, the water film squeezed between oil and silica is never found to puncture. These cases will be detailed in a forthcoming paper, but still, we find altogether that CTAB added to the water delays the formation of oil wet silica zones by either dramatically slowing down the water dewetting dynamics or preventing their nucleation.

■ APPENDIX A

In the present state of literature, no available theory describes the dewetting velocity selection in the present case, namely, two liquids on a solid with triple line friction. The sole available references hold, in principle, for a single liquid in air. [START_REF] Redon | Dynamics of Dewetting[END_REF][START_REF] Bertrand | Dynamics of Dewetting[END_REF][START_REF] Snoeijer | Asymptotic Analysis of the Dewetting Rim[END_REF] We build here a specific model that is not far from the one offered by Bertrand et al., [START_REF] Bertrand | Dynamics of Dewetting[END_REF] at least in the limit of large molecular over viscous dissipation ratio ζ/η. In the present experiments, this ratio varies between 10 3 and 10 6 and is indeed large. The physical ingredients are as follows: (i) the oil/water/solid triple line recedes as described above, with a dynamics controlled by the difference between dynamic contact angle and equilibrium contact angle and a friction mechanism at the triple contact line: the dynamics at the rear follows eq 4. On the other hand, the rim advances on a water film so that (ii) the "equilibrium" contact angle of the rim on the film is zero, while the only relevant dissipative mechanism is viscous: the dynamics at the advancing front is described by eq 2 with α e = 0. Here, we assume that the two-liquid model holds, and we take K = -15.9, β = 2.52. Furthermore, inspired by available works on "effective" contact lines sliding on a liquid film or prewetted surface, [START_REF] Snoeijer | Asymptotic Analysis of the Dewetting Rim[END_REF][START_REF] Voinov | Inclination angles of the boundary in moving liquid layers[END_REF][START_REF] Chen | The effects of thin and ultrathin liquid films on dynamic wetting[END_REF][START_REF] Eggers | Characteristic lengths at moving contact lines for a perfectly wetting fluid: the influence of speed on the dynamic contact angle[END_REF] we assume that the logarythmic term ln(b/a) is approximately equal to ln(Ca 1/3 w/ h f ), where Ca = ηV/γ is the capillary number, w is the rim width, and h f is the water film thickness. Following the path of Redon et al., [START_REF] Redon | Dynamics of Dewetting[END_REF] the hypothesis is further made that (iii) the front and rear velocities of the rim are equal. In the present experiment, this hypothesis holds as soon as the hole is large enough (typically 40 μm in Figure 4f). (iv) Finally, the shape of the rim is assumed to be a spherical cap of uniform curvature set by Laplace pressure. [START_REF] Redon | Dynamics of Dewetting[END_REF][START_REF] Bertrand | Dynamics of Dewetting[END_REF] From this, the triple line contact angle α and front angle connecting the rim to the film α front are equal provided that the film thickness h f is negligible compared to the rim height h.

As shown in Figure 4f, the front angle can be measured at the inflexion point where the rim connects to the film: we find α front = 4 o ± 1 while α = 6 o . The data are reported in Figure 11 for all CTAB concentrations. Note that the front angle is measured with high uncertainty due to the bell shape of the dimple. Nevertheless, the front and rear angles are found almost equal within experimental uncertainty, as soon as the rear and front velocities are measured equal, and in all the concentration range tested. Hence, hypotheses (iii) and (iv) are experimentally verified. It follows that the rim velocity V should obey both eqs 4 and 2 with α ≃ α front

α α ζ γ = + V cos cos e (8)
α η γ η γ = β K V V w h ln 1/3 f Ä Ç Å Å Å Å Å Å Å Å Å Å Å Å i k j j j j y { z z z z É Ö Ñ Ñ Ñ Ñ Ñ Ñ Ñ Ñ Ñ Ñ Ñ Ñ (9)
For equilibrium contact angles α e smaller than 50°, eq 8 can be linearized and V obeys the following implicite equation Eq 10 was solved for each CTAB concentration, using measured values of the width of the rim w and the film height h f . Over the whole range of concentration tested, w over h f Figure 11. ▲ (red), contact angle α rim measured at the rear of the rim as a function of CTAB concentration; ■ , measured front angle α front between the rim and the film; □ , angle solution to eq 9 using measured values of V, w/h f , γ, η = 0.9 mPa•s, K = -15.9, and β = 2.52

Figure 1 .

 1 Figure 1. Sketch of a triple contact line between silica, water, and oil. Water recedes at velocity V. Water-added surfactants adsorb at the oil-water and water-silica interfaces. Dotted circle: As water recedes, surfactants may remain adsorbed at silica/oil interface or desorb from silica (either partially or totally).

Figure 2 .

 2 Figure 2. Adsorption isotherm of CTAB on silica. Dotted line: Γ* = 0.37 μmol•m -2 . Dashed line: Γ ∞ = 2.4 μmol•m -2 . Full line: fit to eq 1 with k 1 = 30, k 2 = 2.7, and n = 8.5.

Figure 3 .

 3 Figure 3. (a) Experimental setup. (b) Interference microscopy image within the squeezed water film between oil and silica. (c) Side image of the oil droplet of radius R d immersed in water and squeezed against a silica lens. After complete dewetting of the water film, oil connects to silica in the aqueous solution at a static receding contact angle α e .

Figure 4 .

 4 Figure 4. (a)-(c) Microscopy images: top views of the dewetting of water on silica within a water film trapped between oil and silica. [CTAB]/ CMC = 10 -3 . Time interval between images: 2.8 ms. Contact zones between oil and silica appear as black disks of radius R. Rings are equal thickness fringes. (d) Sketch of the oil/water interface when water recedes on silica against oil around an oil/silica contact zone. (e) Profile of the oil/water interface at the contact line from interferometry data (asterisks) evidencing a dewetting rim advancing on a trapped water film of thickness h f = 250 nm. The line is a fit to a parabola. [CTAB]/CMC = 0, time after nucleation = 17 ms. The water wedge recedes with a velocity V rim and connects silica at an angle α rim . (f) Triangle, rim contact angle α rim vs time; circle, radius R of the dewetted zone vs time. The slope determines V rim = 12.1 mm•s -1 , [CTAB]/CMC = 10 -3 .

Figure 5 .

 5 Figure 5. Dewetting dynamics at the triple line of the rim as a function of CTAB concentration (a) ▲, dynamic contact angle α rim ; ■ (red), equilibrium contact angle α e . (b) Surface energy contributions: ▼, γcos α rim ; ⧫ (red), γcos α e . Values are averages. (c) Contact line receding velocity measured at the edge of the rim. The blue zone corresponds to concentrations where the water film remains metastable at the level of pressure applied here.

Figure 6 .

 6 Figure 6. Microscopy images: top views of the dewetting of aqueous solutions of CTAB on silica within a film trapped between oil and silica. [CTAB]/CMC= (a) 10 -3 , (b) 0.5, (c) 0.8. The contact line is increasingly irregular as concentration increases. The white line represents 50 μm.

  found ζ values ranging from 1.6 to 3.7 Pa•s; for a CTAB solution receding in air on either a polymer sealant substrate or polystyrene, Fell et al. 1 found ζ values ranging from 4 to 6 Pa•s. Figure 8 displays the variations of ζ with the CTAB concentration: ζ values were averaged over two to six experiments for each concentration. We find that the friction coefficient strongly increases with concentration, reaching almost 10 3 Pa•s close to CMC.

Figure 7 .

 7 Figure 7. (a) Sketch of the swollen drop experiment: oil is injected to measure V and α at the drop scale. (b, c) Dynamic receding contact angle α as a function of contact line velocity V (log scale): ▲, swollen drop experiment; * , rim data. (b) Pure water, α e = 40°(c) (blue) [CTAB]/CMC= 0.1, α e = 70°(cyan) [CTAB]/CMC= 0.7, α e = 130°. (b) -•-•-, Hydrodynamic model, eq 2 with β = 2.52, K = 15.9. (b,c) , Molecular kinetic model, eq4 with (red) ζ = 0.8 Pa•s; (blue) ζ = 9.9 Pa•s; (cyan) ζ = 400 Pa•s. ---, hydrodynamic model eq 9 for the front angle of the rim (see Appendix) (β = 2.52, K = 15.9, w/h f = 100, and value of oil/water interfacial tension γ depends on CTAB concentration). (b) Inset: pure water: advancing and receding dynamic angle vs velocity V (linear scale) from swollen/deswollen drop experiments.

Figure 8 .

 8 Figure 8. Friction coefficient ζ of the contact line receding on silica in CTAB solutions as a function of CTAB concentration normalized by CMC. The full line is a guide for the eyes.

.3

  6 evidences longitudinal surfactant transfers result from two mechanisms, diffusion and Marangoni, that can be compared through the Marangoni number Ma For CTAB, and close to CMC, Γ i ∼ Γ i ∞ ∼ 2 μ m o l • m -3 a n d t h e G i b b s e q u a t i o n y i e l d s : Nm 2 mol -1 . We find Ma ∼10 5

Figure 10 .

 10 Figure 10. Variations with the CTAB surface concentration at water/ silica interface Γ of (a) bulk surfactant concentration normalized by CMC, (b) friction coefficient ζ, and (c) spreading parameter S =γ(cos α e + 1). Dashed lines: guides to the eyes evidencing an increase and a plateau above Γ* ∼ 0.4 μmol•m -2 .

Notes

The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

This work benefited from meetings within the French working group GDR CNRS 2019 "Solliciter LA Matiere Molle" (SLAMM).


Giorgia Scetta

Jianzhu Ju

Nathan Selles

Patrick Heuillet

Matteo Ciccotti
email: matteo.ciccotti@espci.psl.eu

Costantino Creton
email: costantino.creton@espci.psl.eu

Dr G S Author

J J Author

Prof. M C Author

Prof C C Author

Dr N S Author

Dr P H Author

Strain Induced Strengthening of Soft Thermoplastic Polyurethanes Under Cyclic Deformation

Keywords: thermoplastic elastomers, cyclic behavior, damage, stiffening, Young modulus

We investigate the cyclic mechanical behavior in uniaxial tension of three different commercial thermoplastic polyurethane elastomers (TPU) often considered as a sustainable replacement for common filled elastomers. All TPU have similar hard segment contents and linear moduli but sensibly different large strain properties as shown by X-Ray analysis. Despite these differences, we found a stiffening effect after conditioning in step cyclic loading which greatly differs from the common softening (also referred as Mullins effect) observed in chemically crosslinked filled rubbers. We propose that this self-reinforcement is related to the fragmentation of hard domains, naturally present in TPU, in smaller but more numerous subunits that may act as new physical crosslinking points. The proposed stiffening mechanism is not dissimilar to the strain-induced crystallization observed in stretched natural rubber, but it presents a persistent nature. In particular, it may cause a local reinforcement where an inhomogeneous strain field is present, as is the case of a crack propagating in cyclic fatigue, providing a potential explanation for the well-known toughness and wear resistance of TPU.

Introduction

Soft TPU are well known for their outstanding combination of reversible elasticity, abrasion resistance and easy processability. They are multiblock copolymers characterized by alternating soft segments (SS) and hard segments (HS) forming a two-phase microstructure where the soft phase is the majority. The microphase separation is driven by the ability of the hard segments to form inter and intra-chain hydrogen bonds between carbonyl and amine groups developing therefore small and stiff lamellae domains surrounded by the soft phase.

These hard domains (HD) have a typical size of 5-30 nm and are stiffer than soft segment domains (SD) acting both as nanoscale fillers and physical crosslinks [START_REF] Petrovic | POLYURETHANE ELASTOMERS[END_REF], [START_REF] Bonart | Thermoplastic Elastomers[END_REF]. The versatile processing, recyclability and comparable reversible elasticity make TPU a serious competitor to replace elastomers in a number of technical applications despite the higher material cost.

Unsurprisingly, several studies on TPU focused on the correlation between their composition and mechanical properties at small and large strain [START_REF] Petrovic | POLYURETHANE ELASTOMERS[END_REF], [START_REF] Buckley | Elasticity and inelasticity of thermoplastic polyurethane elastomers: Sensitivity to chemical and physical structure[END_REF]- [START_REF] Russo | Phase Separation in Linear and Cross-Linked Polyurethanes[END_REF] with the target to further explore the field of applications of this class of materials. In particular, the presence of a mechanical behavior with the same characteristics as those of the Mullins effect classically observed in filled rubbers [START_REF] Diani | A review on the Mullins effect[END_REF] (higher energy losses and stress softening during the first loading-unloading cycle), was reported in several TPU with different composition of hard and soft segments [START_REF] Buckley | Elasticity and inelasticity of thermoplastic polyurethane elastomers: Sensitivity to chemical and physical structure[END_REF], [START_REF] Drozdov | Mullins' effect in thermoplastic elastomers: Experiments and modeling[END_REF], [START_REF] Yi | Large deformation rate-dependent stress-strain behavior of polyurea and polyurethanes[END_REF].

The Mullins effect was originally detected in filled (or crystallizing) chemically crosslinked rubbers [START_REF] Mullins | Softening of rubber by displacement[END_REF] and despite its relevance for final rubber properties, its origin is still debated and may depend on the detailed structure of the material. Nevertheless, it is generally accepted, that the first cycle hysteresis comes in particular from structural rearrangements of filler aggregates [START_REF] Diani | A review on the Mullins effect[END_REF]. In the case of unfilled TPU, the change in mechanical behavior after the application of strain is due to structural rearrangements of the multiphase structure. This mechanical effect has been often qualitatively investigated and compared to that observed in filled rubbers [START_REF] Bonart | Thermoplastic Elastomers[END_REF], [START_REF] Buckley | Elasticity and inelasticity of thermoplastic polyurethane elastomers: Sensitivity to chemical and physical structure[END_REF], [START_REF] Yi | Large deformation rate-dependent stress-strain behavior of polyurea and polyurethanes[END_REF], [START_REF] Qi | Stress-strain behavior of thermoplastic polyurethanes[END_REF], but to the best of our knowledge, has not yet been discussed quantitatively and in detail with a consistent methodology. Given the relevance of cyclic loading for the durability of materials and the renewed push to replace permanently crosslinked elastomers with thermoplastic reprocessable alternatives, we felt that the question of the evolution of the structure and mechanical properties of TPU with cyclic loading should be revisited.

Recently, Merckel and co-workers [START_REF] Merckel | Characterization of the mullins effect of carbon-black filled rubbers[END_REF] proposed an easy methodology to quantify and compare the contribution of the structural changes to mechanical damage in filled elastomers after the application of a given strain. They proposed to use two damage parameters: one to account for the reduction in linear modulus and the other to account for the change in the onset of strain hardening in large strain. As they point out, these two parameters overlap for filled elastomers, and suggest that the same type of structural modification affects small strain stiffness and strain hardening [START_REF] Merckel | Characterization of the mullins effect of carbon-black filled rubbers[END_REF]. However, mechanical damage is inherently related to the structural modifications induced by deformation which is a material-specific property and may be fundamentally different between TPU and filled crosslinked rubbers.

Using the above-mentioned methodology, we carried out here a quantitative evaluation of the structural changes occurring under cyclic loading in TPU and more importantly of the changes in mechanical properties induced by this cyclic loading. In order to be representative, we carried out all experiments with three commercially available TPU of the Elastollan™ series kindly provided by BASF AG.

Finally, within the framework of the possible substitution of conventional filled rubbers with TPU we also compared the mechanical behavior of our soft TPU with that of a typical crosslinked elastomer made from a random copolymer of styrene-butadiene (SBR) filled with reinforcing carbon black, emphasizing similarities between these two classes of materials in terms of small strain elasticity, and differences in structural evolution and large strain behavior.

Experimental results

Uniaxial tensile test

The different large strain behavior for all three TPU: TPU_XTAL, TPU_HARD and TPU_SOFT, can be appreciated in Figure 1 (a), reporting the engineering stress-stretch curves in uniaxial tension at different temperatures. All TPU are characterized by a high extensibility at failure. The linear regime is only observed for a few percent of deformation (λ < 1.2) where we calculated the Young modulus E Table 1 for 23 and 60°C). Above this limit, all three materials initially show a strain softening regime. Then TPU_XTAL and TPU_HARD present a marked strain hardening that is less intense in TPU_SOFT. Only in case of TPU_XTAL, as we reported in another work [START_REF] Scetta | Self-organization at the crack tip and cyclic fatigue in TPU[END_REF], the strain hardening is accompanied by the formation of a new crystalline phase (strain induced crystallization), which is partially retained in unloaded samples. The effect of increasing the temperature is mainly that of reducing the stress at break for all materials, and in the case of TPU_SOFT also to reduce its maximum extensibility. Interestingly this reduction of strain at break with temperature was already observed for multiblock thermoplastic elastomers (TPE) based on poly-butadiene terephthalate (PBT) as hard segment as reported by Aime [START_REF] Aime | A model for failure in thermoplastic elastomers based on Eyring kinetics and network connectivity[END_REF].  Large hysteresis between the first load-unload cycle.

 Very pronounced softening after the first loading, and recovery of the monotonic test behavior envelope only when the material is stretched to higher values than those previously applied (Mullins effect).

 Marked residual deformation after unloading.

This large residual deformation is consistent with literature data on TPU [START_REF] Buckley | Elasticity and inelasticity of thermoplastic polyurethane elastomers: Sensitivity to chemical and physical structure[END_REF], [START_REF] Prisacariu | Effect of the hydrogen bonding on the inelasticity of thermoplastic polyurethane elastomers[END_REF] and can be attributed to the absence of chemical crosslinks as well as to the plastic deformation of the hard domains following the application of large strains. Interestingly, we found that for the same value of maximum applied stretch , all TPUs present a similar fraction of residual Table 1 Young modulus for all TPU at 23 and 60°C TPU_XTAL, TPU_HARD and TPU_SOFT respectively. All curves are characterized by a maximum in the intensity, due to microphase separation in TPU, which can be associated to the average distance between hard-domains (or long period L) [START_REF] Bonart | X-ray investigations concerning the physical structure of cross-linking in segmented urethane elastomers[END_REF] . The data of the long period L calculated from Bragg's law in both pristine and unloaded samples are reported in Table 2. The lower value of L for strained samples was already observed in similar multiphase systems [START_REF] Wang | Transient microstructure in long alkane segment polyamide: Deformation mechanism and its temperature dependence[END_REF]- [START_REF] Koerner | Transient microstructure of low hard segment thermoplastic polyurethane under uniaxial deformation[END_REF] and was generally associated to a fragmentation of HD into smaller units as sketched in Figure 2 (e). Additionally, TPU_SOFT has an elliptical SAXS pattern indicating the presence of a preferential orientation in the HD (probably induced by injection molding) that contrasts with the random orientation of HD in the other two TPU (circular pattern).

Structural investigations

WAXS 1D intensity profile are shown in

We adopted the lamellar model proposed by Strobl and Schneider [START_REF] Strobl | Direct Evaluation of the Electron Density Correlation Function of Partially Crystalline Polymers[END_REF], which requires random orientation of HD, in order to evaluate some structural parameters in TPU_XTAL and TPU_HARD. Both materials present the same calculated values of thickness of hard domains (C) and hard segment volume fraction ϕ (Table 2) suggesting a very similar microstructure between TPU_XTAL and TPU_HARD. On the other hand, the higher value of L and the semi-crystalline character of HD in TPU_SOFT, indicates the presence of some major structural difference compared to TPU_XTAL and TPU_HARD. Table 2 Long period L between HD for pristine and unloaded samples (according to Bragg's law). Domains thickness and hard segment volume fraction for pristine TPU_XTAL and TPU_HARD calculate using the lamellar model.

Damage analysis in cyclic loading

We used the approach proposed by Merckel et al. [START_REF] Merckel | Characterization of the mullins effect of carbon-black filled rubbers[END_REF] to estimate the damage in both unfilled TPU and filled SBR in terms of large strain damage and small strain damage ( ) as detailed in the following. First, we expressed the data of cyclic loading experiments in terms of true stress vs. Hencky strain as reported in Figure 3 (a) for TPU_HARD and SBR. We would like to stress that in cyclic deformation of TPU, the engineering stress-strain representation (Figure 1 (b)), that seems to suggest a cyclic softening, is misleading. The engineering representation of strain in fact, only compares the final state with the initial state and, in the case of materials with high residual strain it introduces a non-negligible bias on the measurement. Contrarily, the Hencky strain accounts for all the incremental steps of deformation (considering the value of the sample length just before each strain increment). The value of for each increasing step of maximum strain h k , is obtained from the ratio between the linear modulus E k for the cycles of step k and that of the pristine material (E 0 ) as follows:

(1) Hencky strain at which the modulus was evaluated for TPU are justified by their higher maximum extensibility compared to SBR. While in the case of SBR, E always decreases with maximum applied strain, in all TPU E initially decreases and, for Hencky strains larger than 1.5 ( 4), E increases again, reaching the pristine value or even larger values in the case of TPU_XTAL. A similar result was also found by Koerner [START_REF] Koerner | Transient microstructure of low hard segment thermoplastic polyurethane under uniaxial deformation[END_REF] The large strain damage, or , is associated to the onset of strain hardening in cyclic loading at different maximum strain and is defined as:

(

) 2
where α is a re-scaling factor on the Hencky strain and it is obtained as follows:

1) Each unloading curve is shifted to the origin to compensate for the residual strain (Figure 4(a, c)).

2) A master-curve is built by performing a superposition fit using a least square minimization of each unloading curve using the first unloading curve as a reference (Figure 4(b,d)). This is mathematically equivalent to write:

h virgin = α*h shifted .
The first step is very important especially for materials such as TPU, which present a significant residual strain when unloaded. Shifting the stress-strain curve at the origin in fact, we obtain the same curve which a user, unaware of the previous strain history, would measure experimentally. Moreover, the shifted curves reported for TPU_HARD and SBR in Figure 4(a,c) demonstrate the different effect of maximum applied strain on the onset of strain hardening (approximatively indicated as λ hard ) between TPU_HARD and SBR. Unlike SBR, in TPU_HARD the onset of strain hardening in each unloading curve for the step k+1 appears at comparable or lower strain than step k. This has a strong influence on the previously described rescaling procedure as shown by the different values of the damage parameter D ls obtained for SBR and for all TPU. ,c). The trend is substantially different between SBR (where both and similarly increase with strain) and TPU. In all TPU, and have a dependence on the maximum Hencky strain that is qualitatively similar to the one we just discussed for the linear modulus. Both damage parameters first increase (softening) and then decrease (stiffening), eventually becoming negative in case of TPU_XTAL. At 60°C this trend is even more evident and all damage values are negative. Moreover, the damage in small and large strain are decoupled.

Discussion

Differences between TPU and SBR

In the case of SBR, the analysis of damage shows that both damage parameters ( and )

nearly overlap and have a monotonically increasing dependence on the applied strain, meaning that the damage in the material increases with deformation. Merckel and coworkers [START_REF] Merckel | Characterization of the mullins effect of carbon-black filled rubbers[END_REF] interpreted this as an indication that, in filled SBR, the application of a cyclic strain generates some kind of physical damage on the filled rubber that affects in a similar way both the small and large strain properties of the polymer itself. In other words, they argued that in SBR the change in the small and large strain mechanical response with applied strain have the same origin. On the other hand, although in all three TPU and have similar trends, they do not superimpose well and, above a threshold value of strain, they decrease with increasing maximum strain. In certain cases, and may assume even a negative value, especially at 60°C. Finally, it is important to underline that, the main difference between TPU and SBR, which leads to a different trend in the calculated damage, is the amount of residual deformation λ res . In the case of SBR, λ res is mostly negligible while, in the case of TPU, λ res accounts for almost one third of λ max and has a great effect on the rescaling procedure.

Interpretation of the estimated damage in TPU

The decrease of in TPU at large applied strains is associated with a permanent increase in the initial modulus E with applied deformation for all samples (Figure 3 (d)). In particular, TPU_XTAL, which can crystallize under strain at 23°C, shows the highest values of E that eventually becomes even higher than in the pristine material, for large values of maximum applied strain, which results in a 'negative damage'. This inversion of trend is not typical of classical damage theories, where the damage parameter increases monotonically up to failure, as observed for SBR. The inversion of trend observed for TPU suggest that both estimators and reveal the competing effect of a strain induced damage mechanism with a strong strain induced stiffening mechanism that permanently affects both the initial modulus and the strain hardening properties of TPU. This unusual increase in the initial modulus with applied strain must depend on the specific multi-phase structure of each TPU that gets re-arranged with applied strain [START_REF] Bonart | X-ray investigations concerning the physical structure of cross-linking in segmented urethane elastomers[END_REF]. The reduction of the long period L in highly strained TPU was reported by several authors [START_REF] Wang | Transient microstructure in long alkane segment polyamide: Deformation mechanism and its temperature dependence[END_REF]- [START_REF] Kojio | Simultaneous small-angle X-ray scattering/wide-angle X-ray diffraction study of the microdomain structure of polyurethane elastomers during mechanical deformation[END_REF] and interpreted as a fragmentation of the original HD into smaller units. We believe that the breakdown of the original bigger hard domains into smaller, but probably more homogeneously dispersed and more numerous domains, has the same effect of increasing the density of physical crosslinking points, as schematically showed in Figure 6 , thus causing an increase of the stiffness. In the case of TPU_XTAL, which crystallizes under strain, the increase in physical crosslinking (attributed to the fragmentation of hard domains) is enhanced by the intrinsic stiffness of the crystallites (that act as additional hard domains and crosslinking points), explaining the enhanced trend in E(h) for TPU_XTAL.

Figure 6 Schematic illustration of HD restructuration with strain. The fragmentation of original HD in smaller but more numerous units provides additional physical crosslinking to the network.

Conclusions

We analyzed the cyclic mechanical behavior at small and large strain of three TPU which share a similar linear modulus ( 7-8 MPa at 23°C), but have different large strain properties, related to subtle differences in composition and microstructure. As common to most TPU, all of these multiblock copolymers self-organize into a microphase separated structure of hard domains that act as physical crosslinks into a softer matrix. This conveys to TPU their remarkable mechanical behavior, combining the classical elastomeric reversible elasticity with high extensibility, considerable strain hardening, damage softening limited to the first loading cycle (Mullins like), and contained plastic creep under large strain. We developed here a consistent methodology to assess these different components of the complex behavior of TPU, inspired from the work of Merckel and co-workers [START_REF] Merckel | Characterization of the mullins effect of carbon-black filled rubbers[END_REF] on filled rubbers. This allowed us to identify the occurrence of a strain induced permanent stiffening in TPU, which is shown to increase progressively with applied strain in uniaxial cyclic loading, overcoming the damage softening effect that is common with filled rubbers.

A major focus of our work is the quantitative comparison of the different components of the mechanical behavior between three different commercially available TPU that were chosen to discriminate between role of macroscopic large strain behavior and the microscopic mechanisms involved in the structural modifications induced by cyclic loadings at large strain. While TPU_XTAL and TPU_HARD have similar fractions of HD and a remarkable strain-hardening, TPU_SOFT contains evidence of the presence of crystallized PBT and has a considerably less intense strain hardening before fracture. While the macroscopic large strain behavior of TPU_XTAL and TPU_HARD is quite similar, its microscopic origin for TPU_XTAL can be partly attributed to strain induced crystallization, that only occurs in this material. Despite their differences, we showed a surprising linear relationship between residual and maximum strain during cycles at different temperatures and all three TPU resulted in a pronounced change in mechanical properties after cyclic loading. However, the most remarkable and potentially impactful result of the present work lies in the discovery of strain induced stiffening in TPU with applied strain in cyclic loading. While the molecular origin of this peculiar behavior in TPU has not been clarified unambiguously yet, we propose that it originates from the fragmentation of original HD into smaller, but more numerous sub-units that may themselves act as additional physical crosslinking points [START_REF] Zhang | Strain induced nanocavitation and crystallization in natural rubber probed by real time small and wide angle X-ray scattering[END_REF]. This straindependent stiffening, can be compared to the strain-induced crystallization observed in stretched natural rubber. However, while NR melts when the strain is released, the SIC stiffening of TPU has a persistent nature and adds to the effect of HD fragmentation, which we propose as a more general mechanism of permanent strain stiffening in TPU. We believe that this peculiar strain induced permanent strain stiffening plays a major role in determining the remarkable resistance of TPU to cyclic fatigue, that we investigated in a companion paper [START_REF] Scetta | Cyclic fatigue failure of TPU using a crack propagation approach[END_REF] , due to the enhanced local stiffening of the crack tip region where the strains are locally concentrated by the presence of a notch.

Materials and methods

Materials

The three TPU used in this work are polyester based polyurethanes of the Elastollan™ series with commercial names EC 60 A 10P, LP9 277 10 and 565 A 12P and were kindly provided by BASF. We labelled them TPU_HARD, TPU_SOFT and TPU_XTAL respectively, to underline the difference in their large strain behavior as will be discussed in the experimental part. TPU_SOFT also differs from the others because it contains a small percentage of crystallized poly-butadiene terephthalate (PBT), while the other two are completely amorphous. Their glass transition temperature T g measured by differential scanning calorimetry (DSC at 10°/min) is reported in [START_REF] Mzabi | Caractérisation et analyse des mécanismes de fracture en fatigue des élastomères chargés[END_REF]). Note that N347 is a type of carbon black, Sulfur is a crosslinking agent, Struktol™ and N-Cyclohexyl-2-benzothiazole sulfenamide (CBS) are accelerators to vulcanize the rubber, and N-(1,3-dimethylbutyl)-N'-phenyl-pphenylenediamine (6PPD) is an anti-oxidant

Step-Cycle Tests

The dog-bone shaped samples were strongly fixed between mechanical clamps since TPU are very tough. An optical system was used to measure the local stretch in the gauge area of the sample and to check the absence of slippage from the clamps during the test. The samples were strained in uniaxial conditions at the stretch rate of = 4 s -1 . The elongation was performed in a stepwise mode: 5 or 10 cycles were performed for each increasing value of maximum applied stretch for SBR and TPU respectively. The stress was reduced to σ = 0 between two successive steps in order to prevent buckling. Strain ε, stretch λ, Hencky strain h, stress σ and true stress T are defined as below.

l 0 and l indicate the initial length and instantaneous length respectively, A 0 the initial cross section area and F the measured force.

Structural study

Information on the physical structure of nanodomains was obtained by X-Ray analysis using the facilities of the materials science center of DSM, Netherlands. The beam wavelength was 0.154 nm. The 2D data were integrated using "FIT-2D" software [START_REF] Hammersley | FIT2D[END_REF]. All data were corrected by subtracting background scattering and circularly integrated to obtain 1D profile. SAXS data was expressed in terms of wave vector where 2θ is the scattering angle and  is the wavelength. 1D SAXS profile were fitted with Gaussian curves to determine the central position q* of the peak. According to Bragg's law the long period L or inter-hard domain distance was evaluated as . The 2D SAXS profiles were obtained for all three TPU in relaxed conditions for two sets of samples: pristine and previously strained for several times at = 2.25.

An approach based on two-phase, lamellar morphology [START_REF] Strobl | Direct Evaluation of the Electron Density Correlation Function of Partially Crystalline Polymers[END_REF] and correlation function analysis was used to identify the crystalline layer thickness (C) and bulk volume crystallinity () (graphically indicated in Figure 7) for those TPU presenting random orientation of HD.

The correlation function has the form:

(3)

This approach requires the extrapolation of the data at and . The data were extrapolated using Porod's law I ≈ and Guinier's law: I≈A+Bq respectively.

Figure 1 Figure 1

 11 Figure 1 Uniaxial stress-stretch curves at different temperatures (a) and cyclic stretch-stress curve at 23°C (b) for three TPU. (c) Residual vs. maximum applied deformation during the last cycle for: . The stress-stretch curves of uniaxial step-strain cyclic test for all TPU at 23°C are reported in

stretch ( Figure 1

 1 (c)). In contrast, in SBR the fraction of residual stretch is considerably lower for all values of tested maximum stretch compared to TPU because the chemical crosslinking prevents plastic deformation.

Figure 2 (

 2 a) for all three soft TPU. The absence of any crystalline reflection in TPU_XTAL and TPU_HARD indicates a completely amorphous hard phase in the pristine material. The crystalline peaks (indicated by the arrows) in TPU_SOFT are compatible with the crystalline structure of PBT as reported in literature [14], [15]. 2D SAXS images and the corresponding integrated profiles for pristine and unloaded samples (previously strained for several cycles at = 2.25) are shown in Figure 2 (b,c,d) for

Figure 2

 2 Figure 2 (a) WAXS pattern for pristine TPU_XTAL, TPU_SOFT and TPU_HARD (data were vertically shifted for the sake of readability). (b) 2D SAXS Pattern and 1D integrated profile for pristine and unloaded TPU_XTAL(b), TPU_HARD (c), TPU_SOFT (d). Schematic illustrating the aggregation of HS in HD and definition of L (long period between hard domain) before and after loading (e).

Figure 3

 3 Figure 3 True stress-Hencky strain representation of cyclic experiment for TPU_HARD (a) and filled SBR (b). Example of linear fitting for the calculation of E for TPU_HARD (c). E vs. Hencky strain for all TPU and for SBR (d).

Figure 3 (

 3 Figure 3(c) shows an example of linear fitting used to calculate E, and the values of the fitted

Figure 4

 4 Figure 4 Example of true stress vs. Hencky Shifted (a-c) and true stress vs. Hencky Virgin (b-d) respectively for TPU_HARD and SBR. The dotted lines represent an estimation of the onset of strain hardening and are used as a guide for the eyes.

Figure 5

 5 Figure 5 reports the calculated values of and for SBR at 23°C (a) and for all three

Figure 5

 5 Figure 5 Damage vs. Hencky strain calculated for SBR (a) and TPU at 23°C (b) and 60°C (c) . The symbols indicate D ss for: SBR: , TPU_HARD: , TPU_SOFT : , TPU_XTAL: and D ls for SBR : ,TPU_HARD: ,TPU_SOFT: ,TPU_XTAL: .

Figure 7

 7 Figure 7 Example of correlation function and interpretation of its features for TPU_HARDbased on the analysis of Strobl and Schneider[START_REF] Strobl | Direct Evaluation of the Electron Density Correlation Function of Partially Crystalline Polymers[END_REF]

Table 3 .

 3

	Sample	TPU_HARD	TPU_SOFT	TPU_XTAL
	Tg a 10°/min °C	-50°C	-48°C	-34°C

Table 3

 3 Glass transition temperature for all TPU measured by DSC TPU specimens were injected by the Laboratoire de Recherche et Contrôle des Caoutchoucs et Plastiques (LRCCP) into 2 mm thick large square-plate, from which tensile dog-bone samples (cross section of 2x4 mm) were cut. The temperatures used in the injection molding procedure are summarized in the appendix for all samples.The SBR rubber is filled with carbon black (CB) and all data concerning that rubber comes from the work of Mzabi et al.[START_REF] Mzabi | Caractérisation et analyse des mécanismes de fracture en fatigue des élastomères chargés[END_REF],[START_REF] Mzabi | A critical local energy release rate criterion for fatigue fracture of elastomers[END_REF]. The unvulcanised SBR has a mass M w of 120 kg/mol and a polydispersity of 1.94 and was provided by Michelin. Its styrene content is 15 wt% and the glass transition temperature T g measured by differential scanning calorimetry (DSC at 10°/min) is -48°C. The detailed composition is reported in Table4as provided by Michelin.All samples were prepared, molded and cured by Michelin. For tensile tests, samples were cut in a dog-bone shape and cross section of 2x4 mm and loaded with a strain rate of 4 s -1 .

		20CB_19XL
	SBR	100
	N347	5
	6PPD	1
	Struktol	3
	CBS	1.5
	Sulfur	1.5
		0.03
		8.1•10 -5

Table 4

 4 SBR composition in PHR. Filler content () and crosslinking density () are reported in volumetric fraction (data from

Acknowledgements

The PhD work of G. Scetta was jointly funded by the French ANRT and the LRCCP. We are grateful to Aude Belguise for her support with correlation function analysis. We are indebted to Dr. Matthias Gerst, Dr. Elke Marten and Mr. Stephan Dohmen from BASF AG for kindly providing the TPU samples. We thank Stephane Delaunay for injecting the samples. CC was partially funded by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program under grant agreement AdG No 695351.

Table of Content Appendix

The temperature used in the injection procedure is summarized in A 1 and schematically showed in A 2