Revealing the frictional transition in shear thickening suspensions

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Revealing the frictional transition in shear thickening suspensions

Cécile Clavaud a,1 , Antoine Bérut a , Bloen Metzger a , and Yoël Forterre a a Aix Marseille Univ, CNRS, IUSTI UMR 7343, 13453 Marseille, France. This manuscript was compiled on March 8, 2017 Shear thickening in dense particulate suspensions was recently proposed to be driven by the activation of friction above an onset stress arising from short range repulsive forces between particles. Testing this scenario represents a major challenge since classical rheological approaches do not provide access to the frictional properties of suspensions. Here we adopt a new strategy inspired by pressureimposed configurations in granular flows that specifically gives access to this information. By investigating the quasistatic avalanche angle, compaction, and dilatancy effects in different nonbuoyant suspensions flowing under gravity, we demonstrate that particles in shear-thickening suspensions are frictionless under low confining pressure. Moreover, we show that tuning the range of the repulsive force below the particle roughness suppresses the frictionless state and also the shear-thickening behavior of the suspension. These results, which link microscopic contact physics to the suspension macroscopic rheology, provide direct evidences that the recent frictional transition scenario applies in real suspensions. Discontinuous shear thickening occurs in suspensions whose viscosity dramatically increases, sometimes by several orders of magnitude, when the imposed shear-rate exceeds a critical value [START_REF] Barnes | Shear-thickening ("dilatancy") in suspensions of nonaggregating solid particles dispersed in newtonian liquids[END_REF]. The archetype of such suspensions is cornstarch immersed in water. When sheared vigorously or under impact, these fluids suddenly turn into solids [START_REF] Waitukaitis | Impact-activated solidification of dense suspensions via dynamic jamming fronts[END_REF]. Such remarkable properties play a key role in the flowing behavior of modern concrete [START_REF] Fernandez | From Tribology to Rheology: Impact of interparticle friction in the shear thickening of non-Brownian suspensions[END_REF] and have motivated applications ranging from soft-body protections to sports equipments [START_REF] Wagner | Shear thickening in colloidal dispersions[END_REF]. They also offer promising perspectives for the design of smart fluids with tunable rheology [START_REF] Lin | Tunable shear thickening in suspensions[END_REF]. However, the potential realm of development and applications remains largely under-explored due to the lack of understanding of this transition [START_REF] Brown | Shear thickening in concentrated suspensions: phenomenology, mechanisms and relations to jamming[END_REF].

This situation has moved on very recently owing to new theoretical and numerical works [START_REF] Seto | Discontinuous shear thickening of frictional hardsphere suspensions[END_REF][START_REF] Wyart | Discontinuous shear thickening without inertia in dense nonbrownian suspensions[END_REF]. Since non-Brownian suspensions of hard frictional particles immersed in a viscous fluid are Newtonian, as imposed by dimensional analysis [START_REF] Wyart | Discontinuous shear thickening without inertia in dense nonbrownian suspensions[END_REF][START_REF] Boyer | Unifying suspension and granular rheology[END_REF][START_REF] Mari | Shear thickening, frictionless and frictional rheologies in non-brownian suspensions[END_REF], the key idea of these studies is to add a short range repulsive force between particles besides hydrodynamics and contact forces. This repulsive force can for instance stem from electrostatic charges or from a specific coating of polymers on the surface of the particle [START_REF] Lee | Sweet, hairy, soft, and slippery[END_REF]. At small shear rate (or small stress), the repulsive force prevents the grains from touching; the suspension thus flows easily as if particles were frictionless. The viscosity of such a frictionless suspension would diverge at random close packing, whose volume fraction is φrcp = 0.64 for monodisperse spheres. Conversely, at large shear rate (or large stress), the repulsive force is overcome by the hydrodynamic forces and particles are therefore pressed into frictional contacts. The viscosity of such a suspension of frictional particles instead diverges at a lower critical volume fraction φc < φrcp, with typically φc 0.58 for monodisperse frictional spheres [START_REF] Boyer | Unifying suspension and granular rheology[END_REF][START_REF] Mari | Shear thickening, frictionless and frictional rheologies in non-brownian suspensions[END_REF][START_REF] Silbert | Jamming of frictional spheres and random loose packing[END_REF]. In essence, the frictional transition described above brings the suspension closer to its jamming point: this critical volume fraction shift suddenly increases its apparent viscosity.

This scenario has been successfully tested and analyzed in discrete numerical simulations performed for non-Brownian [START_REF] Seto | Discontinuous shear thickening of frictional hardsphere suspensions[END_REF][START_REF] Mari | Shear thickening, frictionless and frictional rheologies in non-brownian suspensions[END_REF] and Brownian [START_REF] Mari | Discontinuous shear thickening in brownian suspensions by dynamic simulation[END_REF] suspensions. Supporting results are also provided by recent experimental investigations. For instance, standard rheological measurements were performed on suspensions of small PMMA particles sterically stabilized by a coating of poly-12-hydroxystearic acid [START_REF] Guy | Towards a unified description of the rheology of hard-particle suspensions[END_REF]. The suspension was indeed found to follow two separate viscosity curves with distinct critical volume fractions, depending on what shear rate was applied. A similar suspension was investigated under shear reversal [START_REF] Lin | Hydrodynamic and contact contributions to continuous shear thickening in colloidal suspensions[END_REF], during which the viscosity first drops to a low value set by hydrodynamics interactions before increasing to a plateau dominated by contact interactions [START_REF] Blanc | Local transient rheological behavior of concentrated suspensions[END_REF]. As expected in such framework, only the contact contribution to the viscosity increases with increasing shear-rate, confirming the key role of contacts in shear thickening suspensions. Another study reported that in shear thickening suspensions, the first normal stress difference changes sign at the transition [START_REF] Royer | Rheological signature of frictional interactions in shear thickening suspensions[END_REF]. This behavior was interpreted as indicating the formation of frictional contacts between particles, although this point is still a matter of debate [START_REF] Mari | Shear thickening, frictionless and frictional rheologies in non-brownian suspensions[END_REF][START_REF] Cwalina | Material properties of the shear-thickened state in concentrated near hard-sphere colloidal dispersions[END_REF].

These experimental findings are encouraging, however they also reflect a major difficulty in testing the frictional transition put forward in the recent theoretical scenario. The standard rheological techniques used, performed under fixed volume fraction, provide information about the suspension shear rate, shear stress and viscosity. However they do not give access to the suspension friction coefficient, which is here the key quantity one needs to access. In this article, we propose a

Significance Statement

The sudden and severe increase in the viscosity of certain suspensions above an onset stress is one of the most spectacular phenomena observed in complex fluids. This shear thickening, which has major implications for industry, is a longstanding puzzle in soft-matter physics. Recently, a frictional transition was conjectured to cause this phenomenon. Using experimental concepts from granular physics, we provide direct evidences that such suspensions are frictionless under low confining pressure, which is key to understanding their shear thickening behavior.

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different approach inspired by pressure-imposed experiments in granular flows [START_REF] Forterre | Flows of dense granular media[END_REF], which specifically provides access to the friction coefficient of the suspension. By investigating the quasistatic avalanche angle, compaction, and dilatancy effects, in different nonbuoyant suspensions flowing under gravity, we provide the first direct proof that particles in shear thickening suspensions are frictionless under low confining pressure. We then bridge microscopic contact physics to the macroscopic rheology by tuning the short-range repulsive force in a model suspension of silica beads. We find that this shear thickening suspension, which has a frictionless state under low stress, no longer shear thickens when this frictionless state is suppressed.

Results

Steady avalanches. A simple way to probe the frictional behavior of a suspension is to measure its quasistatic avalanche angle in a rotating drum using non-buoyant particles [START_REF] Du Pont | Granular avalanches in fluids[END_REF][START_REF] Andreotti | Granular media: between fluid and solid[END_REF]. For sake of clarity, we compared the avalanche angle of a standard Newtonian suspension made of large frictional glass beads of diameter d = 500 µm (Fig. 1A left), to that of a typical shear-thickening suspension made of potato starch particles (d = 25 µm) immersed in water (Fig. 1A right). In both cases, the particle density ρp is larger than that of the suspending fluid ρ f and the fluid viscosity η f is chosen so that the Stokes number St is low and inertial effects can be neglected (St = ρp∆ρgd 3 /18η f ∼ 10 -2 where ∆ρ = ρp -ρ f and g stands for gravity) [START_REF] Andreotti | Granular media: between fluid and solid[END_REF]. Both suspensions are placed within a rotating drum as shown on the experimental set-up illustrated on figure 1B (center). By imposing a slow and constant rotation speed ω, the non-buoyant grains at the surface of the pile flow under their own weight forming a steady avalanche of angle θ on top of a region experiencing a rigid rotation with the drum [START_REF] Du Pont | Granular avalanches in fluids[END_REF]. In such a configuration, the confining pressure acting on the flowing layer of grains is P = φ∆ρgh cos θ where h is the height of the flowing layer and φ its volume fraction; the corresponding tangential stress is τ = φ∆ρgh sin θ. In the steady state, the macroscopic friction coefficient of the suspension µ is directly given by the avalanche angle since by definition µ = τ /P = tan θ. The avalanche angle θ thus provides access to the macroscopic friction coefficient of the suspension µ, which itself depends monotonically on the particle friction coefficient µp [START_REF] Chialvo | Bridging the rheology of granular flows in three regimes[END_REF]. For frictional grains, the macroscopic friction coefficient µ 0.4 has only a weak dependence on µp and yields a typical avalanche angle θ 25 • [START_REF] Andreotti | Granular media: between fluid and solid[END_REF]. However, when the interparticle friction µp becomes very small (below 0.1), the macroscopic friction µ sharply drops. Yet, because of steric constraints, µ remains finite as µp → 0. For frictionless spherical particles (µp = 0), discrete simulations predict a quasistatic macroscopic friction µ = 0.105, corresponding to a non-zero avalanche angle θ = 5.76 • [START_REF] Peyneau | Frictionless bead packs have macroscopic friction, but no dilatancy[END_REF]. Therefore, measuring the pile angle of steady avalanches constitutes a simple, yet decisive way to probe the interparticle friction coefficient in suspensions. Moreover, in this rotating drum configuration, the slope of the avalanche is set by the flowing layer of grains which is located near the free surface of the pile. For the low rotation speeds investigated here, the thickness of the layer h is of the order of a few particles diameters (h ∼ 10 d) [START_REF] Gdrmidi | On dense granular flows[END_REF]. This means that the measure of the avalanche angle gives access to the frictional state of the grains under very low confining pressure. Typically, for the potato starch particles, the confining pressure within the flowing layer is P ∼ 10φ∆ρgd 1 Pa.

t (s) t (s) γ (s -1 ) γ (s -1 ) (Pa s) η (Pa s) η ω (rev/s) ω (rev/s) θ s θ s θ ( • ) θ ( • ) θ s ( • ) θ s ( • ) θ µ = τ P =
For the Newtonian suspension of large glass beads, the avalanche angle θ shows classical hysteretic fluctuations [START_REF] Du Pont | Granular avalanches in fluids[END_REF] around a time averaged angle θs 25 °, see picture on figure 1B (left) and data on figure 1C (left). This angle corresponds to a suspension friction coefficient µ 0.47 which is a usual value for frictional particles. The striking result is that, under the same flowing conditions, the shear thickening suspension of potato starch particles yields a much lower avalanche angle, see picture on figure 1B (right) and data on figure 1C (right). The suspension can flow steadily with an angle of avalanche as small as θs 8.5 °. This angle corresponds to a suspension friction coefficient µ 0.15, showing that the friction coefficient between particles is nearly vanishing. The suspension friction coefficient (µ 0.15) here is slightly larger than the expected value for frictionless spheres (µ = 0.105) because potato starch particles are prolate, which geometrically increases the macroscopic friction coefficient [START_REF] Azéma | Stress-strain behavior and geometrical properties of packings of elongated particles[END_REF][START_REF] Guo | Granular shear flows of flat disks and elongated rods without and with friction[END_REF]. Importantly, in the range of drum rotation speeds ω investigated, the avalanche angles reported here do not depend on ω (Fig. 1C left and right insets). They thus characterize the frictional properties of the suspension in its quasistatic regime, i.e. when the suspension reaches its critical jamming state [START_REF] Boyer | Unifying suspension and granular rheology[END_REF].

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Compaction and dilatancy. Another robust way to probe the frictional behavior of a suspension is to investigate compaction and dilatancy effects [START_REF] Andreotti | Granular media: between fluid and solid[END_REF]. The protocol is the following: particles are first suspended entirely within the drum before letting them sediment (Fig. 2A). The sediment is then compacted by gently hitting the drum with a rubber head hammer Ntaps times. The volume fraction φ of the sediment (the ratio of the particles volume to the total volume of the sediment) is measured throughout this compaction process. Finally, the drum is quickly rotated by a fixed angle θs + 10 • above the steady state avalanche angle, to generate a transient avalanche whose angle θt is measured versus time.

A conspicuous feature of frictional systems, such as a pile of large glass beads, is that it compacts under vibrations. As shown on figure 2B (left), the packing fraction of the glass beads sediment, which right after sedimentation starts from a loose state (φ = 0.56 < φc), progressively increases with the number of taps to eventually reach a dense state (φ = 0.61 > φc). Remarkably, within this frictional system, very different transient avalanches are observed depending on the initial preparation of the sediment (Fig. 2C left). For an initial loose packing (0 tap), the avalanche rapidly flows until its angle relaxes to an angle much lower than θs (the steady state avalanche angle measured earlier). Conversely, for an initially compact sediment (120 taps), one observes a long delay during which the avalanche stays still. It then slowly flows, relaxing to θs. Such a drastic change in the avalanche dynamics with the packing of the initial sediment relies on a well known pore pressure feedback mechanism [START_REF] Iverson | The physics of debris flows[END_REF][START_REF] Pailha | Initiation of underwater granular avalanches: Influence of the initial volume fraction[END_REF][START_REF] Jerome | Unifying impacts in granular matter from quicksand to cornstarch[END_REF], which only applies for dilatant (i.e. frictional) systems [START_REF] Peyneau | Frictionless bead packs have macroscopic friction, but no dilatancy[END_REF]. As first described by Reynolds [START_REF] Reynolds | On the dilatancy of media composed of rigid particles in contact. With experimental illustrations[END_REF], deformation of a dense granular packing of frictional grains requires its dilation. Thus, as the drum is tilted for the avalanche to flow, the initially compact sediment must dilate. However, dilation in the presence of an incompressible interstitial fluid induces a fluid flow: some fluid is sucked within the granular network. This fluid flow presses the grains against each other, thereby enhancing friction. As a result, for a compact pile of frictional grains, the avalanche is strongly delayed and then flows slowly relaxing to θs [START_REF] Pailha | Initiation of underwater granular avalanches: Influence of the initial volume fraction[END_REF][START_REF] Rondon | Granular collapse in a fluid: role of the initial volume fraction[END_REF]. Conversely, a loosely packed granular bed tends to compact when it deforms. This time, the interstitial fluid is expelled from the granular packing, thereby resulting in a fluidization of the grains: the avalanche flows rapidly and relaxes to an angle smaller than θs.

The compaction and dilatancy effects observed for the large glass beads are the phenomenological signature of frictional grains. For frictionless particles, the situation is markedly different since there is only one possible state of compaction (φc = φrcp) and no dilatancy effects are thus expected under shear [START_REF] Peyneau | Frictionless bead packs have macroscopic friction, but no dilatancy[END_REF]. This is precisely what we observe with the shearthickening suspension of potato starch particles: tapping the settled bed of potato starch particles does not modify its packing fraction (Fig. 2B right) and hardly changes the dynamic of the transient avalanches which all relax to θs (Fig. 2C right). These experiments again show that, under low confining pressure, potato starch particles behave as if they were frictionless. Note that the maximum packing fraction of the potato starch particles, φ = 49 %, may seem small. However this low value can be explained by the anisotropic shape of the particles and also their tendency to swell when immersed in water [START_REF] Hellman | Starch granule swelling in water vapor sorption[END_REF]. Tuning microscopic friction using a model suspension. We have shown that potato starch particles immersed in water produce a shear thickening rheology and are frictionless under low confining pressure. These results are consistent with the frictional transition scenario for shear thickening presented in the introduction [START_REF] Seto | Discontinuous shear thickening of frictional hardsphere suspensions[END_REF][START_REF] Wyart | Discontinuous shear thickening without inertia in dense nonbrownian suspensions[END_REF]. They suggest the existence of a short range repulsion force or a microscopic pressure-dependent friction between the starch particles. However, the origin of this force and more generally the surface physico-chemistry of starch remain unclear [START_REF] Brown | Shear thickening in concentrated suspensions: phenomenology, mechanisms and relations to jamming[END_REF][START_REF] Freundlich | Dilatancy and its relation to thixotropy[END_REF][START_REF] Waduge | Exploring the surface morphology of developing wheat starch granules by using atomic force microscopy[END_REF]. To vary the interaction force between particles and investigate the frictional transition within a well-controlled system, we turn to a model suspension composed of silica beads immersed in water (Fig. 3A top). We use non-Brownian silica particles of diameter d = 24 µm comparable in size to the starch particles. When immersed in water, such silica particles spontaneously develop negative surface charges, which generates an electrostatic repulsive force between the grains [START_REF] Vigil | Interactions of silica surfaces[END_REF][START_REF] Israelachvili | Intermolecular and surface forces[END_REF][START_REF] Valmacco | Dispersion forces acting between silica particles across water: influence of nanoscale roughness[END_REF]. Moreover, this surface charge can easily be screened by dissolving electrolytes (salt) within the solvent. Increasing the salt concentration decreases the range of the repulsive force, i.e. the Debye length λ D (Fig. 3A bottom). This model system is thus particularly appealing to test the recent frictional transition scenario and clarify the link between microscopic interactions between particles, friction, and the suspension macroscopic rheology. We first use the rotating drum to systematically investigate steady avalanches, compaction and dilatancy effects on two suspensions of silica beads: one with silica beads immersed in pure water, and the second with the beads immersed in a solution of water and NaCl with a large concentration of salt ([NaCl]= 0.1 mol L -1 ) to fully screen the Debye layer.

φ c θ s θ s N taps θ t ( • ) θ t ( • ) φ (%) φ (%)
θ s θ s θ t ( • ) θ ( • ) θ s ( • ) (%)
Here again inertia is negligible (St ∼ 5 10 -3 ) and the flowing regime is quasistatic (ω → 0). As illustrated on figure 3B,C and D (green data), in the presence of a large concentration of salt which screens the repulsive force, the suspension behaves as frictional. The steady state avalanche angle is large: θs 27.5 °, the packing fraction of the sediment evolves from a loose packing right after sedimentation to a dense packing * * The absolute volume fraction is not reported in Fig. 3 since here it depends on the system size. This size effect can be explained by the large value of the Debye length in pure water (λ D 1 µm), which is not negligible relative to the silica particle diameter [START_REF] Watanabe | Nonlinear rheology of concentrated spherical silica suspensions: 3. concentration dependence[END_REF]. Here, particles may be thought of as a hard core of diameter d surrounded by a soft crust of thickness equal to the Debye length. The maximum packing of such system, when the confining pressure P → 0, is φmax ≈ φrcp(1 -3λ D /d) ≈ 0.48. However, due to the hydrostatic pressure within the after 80 taps, and the dynamics of the transient avalanche strongly depends on the initial packing, showing features related to the dilatancy effects discussed earlier. Conversely, the silica beads in pure water behave as frictionless particles (Fig. 3B,C andD, black data). The steady state avalanche angle is θs 6 °. This value is remarkably close to the quasistatic macroscopic friction angle obtained numerically for ideal frictionless spheres θs = 5.76 °± 0.22 [START_REF] Peyneau | Frictionless bead packs have macroscopic friction, but no dilatancy[END_REF]. Additionally, no compaction of the granular bed and no discernable effect of the initial packing on the transient avalanches are observed. These results clearly demonstrate that the presence of a short range repulsive force can lead under low stress to a frictionless behavior of the particles.

To further inquire about the microscopic origin of this frictionless behavior under low stress, we measured the steady avalanche angle θs as a function of the salt concentration [NaCl]. Figure 4A shows that the suspension transits progressively from frictionless, with θs 6 °, in pure water to frictional with θs 30 °when the salt concentration [NaCl] is increased. Besides this macroscopic measurement, we also characterized the particle roughness with an AFM and found that the peak roughness of the silica particles is lr = 3.73 ± 0.80 nm. Since the Debye length is entirely set by the salt concentration: λ D = 0.304/ [NaCl] nm (at T = 25 • C) [START_REF] Israelachvili | Intermolecular and surface forces[END_REF], we can plot the steady avalanche angle θs as a function of lr/λ D (Fig. 4A top inset). Interestingly, the transition from frictionless to frictional occurs for lr/λ D ∼ 1. This result strongly supports the idea that the frictionless state arises from the interparticle repulsive force caused by the electrostatic double layer. When its range is smaller than the particle roughness, this force becomes ineffective to prevent the grains from touching and the system is frictional. According to the scenario described in the introduction [START_REF] Seto | Discontinuous shear thickening of frictional hardsphere suspensions[END_REF][START_REF] Wyart | Discontinuous shear thickening without inertia in dense nonbrownian suspensions[END_REF], the frictional transition should occur when the confining pressure P exerted by the weight of the granular layer equals the critical pressure Pc which the short range repulsive forces can sustain. Assuming that the repulsive force follows an exponential decay as Frep(z) = F0 exp(-z/λD) [START_REF] Israelachvili | Intermolecular and surface forces[END_REF], where z is the distance between granular bed which depends on the system size, grains deep in the bed must be closer from each other than those at the top. The absolute volume fraction may thus lie anywhere between the latter value and 0.64 (random close packing ), depending on the system size.

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the particles surfaces, the critical pressure at contact z = 2lr writes Pc ∼ Frep(2lr)/(πd 2 /4) ∼ (4F0/πd 2 ) exp(-2lr/λD). Matching it to the confining pressure P ∼ 10φ∆ρgd predicts a transition when lr/λD ∼ -(1/2) log(10πφ∆ρgd 3 /4F0). Using F0/d ∼ 1 mN/m as reported for silica surfaces in NaCl electrolytes [START_REF] Vigil | Interactions of silica surfaces[END_REF] yields lr/λD 1.9, in fair agreement with the transition observed on figure 4A.

Finally, we investigate whether for this model suspension, the existence of a frictionless state under low confining pressure leads to a shear thickening rheology and if the elimination of this state (by screening repulsive forces) restores a Newtonian behavior. Rheograms of the silica suspensions were obtained using the configuration sketched on the inset of figure 4B. Since silica particles are denser than the aqueous suspending fluid, we used a double-helix with tilted blades shearing the entire sample to avoid sedimentation and maintain the homogeneity of the suspension during the measurement. We then define an effective viscosity η eff = αΓ/(2πΩL 3 ) given by the ratio of the effective stress Γ/L 3 , where Γ is the torque and L the helix diameter, to the effective shear rate 2πΩ given by the revolution speed Ω of the helix. The constant α 2.07 is set to ensure that the effective viscosity matches the actual viscosity for a newtonian fluid. We performed rheological measurements on two suspensions of silica particles immersed in water with a salt concentration [NaCl]= 10 -4 mol L -1 and [NaCl]= 10 -1 mol L -1 respectively, i. e. just before and after the frictional transition observed on figure 4A. First, we find that the suspension which has a frictionless state under low confining pressure displays all the features of a shear-thickening suspension (Fig. 4B top): continuous shear thickening is observed at moderate volume fractions, while larger volume fractions lead to a dramatic increase of its effective viscosity (by about 4 orders of magnitude). Second, the striking result is that when the repulsive force is screened, so that no frictionless state exists under low confining pressure, the same suspension no longer shear-thickens (Fig. 4B bottom). These measurements corroborate previous rheological characterizations using Brownian silica microspheres [START_REF] Royer | Rheological signature of frictional interactions in shear thickening suspensions[END_REF][START_REF] Boersma | Shear thickening (dilatancy) in concentrated dispersions[END_REF][START_REF] Lootens | Dilatant flow of concentrated suspensions of rough particles[END_REF] and confirm the link between the existence of a repulsive force, friction and shear thickening rheology.

Discussion

In this article we propose a pressure-imposed approach, inspired from experiments in granular flows, to directly probe the microscopic frictional properties of non-Brownian shear thickening suspensions. By systematically investigating steady avalanches, compaction, and dilatancy effects, in rotating drums experiments, we provide the first direct proof that shear thickening suspensions have a frictionless state under low confining pressure. Unlike Newtonian suspensions of frictional particles [START_REF] Boyer | Unifying suspension and granular rheology[END_REF][START_REF] Du Pont | Granular avalanches in fluids[END_REF][START_REF] Pailha | Initiation of underwater granular avalanches: Influence of the initial volume fraction[END_REF][START_REF] Jerome | Unifying impacts in granular matter from quicksand to cornstarch[END_REF], shear thickening suspensions under low stress flow with a very small avalanche angle, do not compact and show no dilatancy effect. This phenomenology clearly indicates the absence of friction between particles [START_REF] Peyneau | Frictionless bead packs have macroscopic friction, but no dilatancy[END_REF]. Moreover, by using a model suspension of negatively charged silica beads, we find that lowering the range of the repulsive force below the particle roughness makes the suspension transit from a frictionless to frictional state. The elimination of this frictionless state under low confining pressure also suppresses the shear thickening behavior of the suspension. These experimental results, by linking microscopic contact physics to the suspension macroscopic rheology, provide strong evidences that the frictional transition scenario [START_REF] Seto | Discontinuous shear thickening of frictional hardsphere suspensions[END_REF][START_REF] Wyart | Discontinuous shear thickening without inertia in dense nonbrownian suspensions[END_REF] recently proposed to explain shear thickening, applies in real suspensions. For discontinuous shear thickening to occur, the presence of short range repulsive forces able to prevent inter-particle friction at low stress thus seems essential. This picture contrasts with other models of shear thickening in which idealized lubrication hydrodynamics [START_REF] Phung | Stokesian dynamics simulation of brownian suspensions[END_REF], confinement effects [START_REF] Brown | The role of dilation and confining stresses in shear thickening of dense suspensions[END_REF], particule migration phenomena [START_REF] Fall | Macroscopic discontinuous shear thickening versus local shear jamming in cornstarch[END_REF] or inertia [START_REF] Fall | Shear thickening and migration in granular suspensions[END_REF][START_REF] Fernandez | Microscopic mechanism for shear thickening of non-brownian suspensions[END_REF] were put forward.

The rotating drum configuration used in our study provides a simple, yet robust way to characterize inter-particle friction of dense non-buoyant suspensions. Nevertheless, this configuration also has some limitations. When slowly rotating the drum filled with a non-buoyant suspension, the thin flowing layer is on top of a pile experiencing solid rotation. Particles thus remain in static contact during long times. For microparticles coated with polymers, which are often involved in shear thickening, these enduring contacts may age and lead to cohesion between grains. In this case, the avalanche angle is no longer constant [START_REF] Alexander | Avalanching flow of cohesive powders[END_REF][START_REF] Liu | Dynamics of wet particles in rotating drums: effect of liquid surface tension[END_REF]. In our experiments performed with silica particles, small adhesive forces may have affected our results as they could for instance explain the slightly large avalanche angles measured at high salt concentrations (Fig. 3 and4). However, the transition from low to high avalanche angles must be dominated by frictional effects as (i) the steady avalanche angle saturates as the salt concentration is increased, (ii) the avalanches have a constant slope from the top to the bottom of the avalanche unlike adhesive powders, (iii) adhesion alone without friction would not lead to the dilatancy effects observed on figure 3D.

Finally, we emphasize that the rotating drum configuration gives access to the grains frictional properties in the limit of low confining pressure (P → 0) and in the quasistatic regime, i. e. when the viscous number of the suspension J = η f γ/P → 0. Interestingly, we were still able to evidence the frictional transition predicted in the recent model by lowering the critical pressure Pc while the confining pressure P remained fixed (see Fig. 4A). To fully explore the recent models, this transition should also be addressed by varying P while keeping Pc constant, and also by varying the viscous number J . Recently, promising devices have been developed opening the route to pressure-imposed rheometry of dense suspensions, but they are so far limited to the study of macroscopic particles [START_REF] Boyer | Unifying suspension and granular rheology[END_REF]. Extending such pressure-imposed approaches to suspensions of shear thickening and colloidal particles represents a challenging, yet very exciting issue for future studies.

Materials and Methods

Particles. The grains used in figure 1

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(Fig. 1B right) and silica particles (Fig. 3 and4) has a diameter of 12 mm and a depth of 3 mm with a coarsened side wall. It is filled with pure water or sodium chloride solutions. Note that to avoid aging of the potato starch, the small drum was surrounded by a thermal bath maintaining its temperature at 7 ℃. The drums were mounted on a precision rotating stage (M-061PD from PI piezo-nano positioning). To perform the experiment, the grains were first suspended by rotating the drum at 90 °s-1 . Then, the rotating speed ω was set to the desired value and pictures were taken using a Nikon D300S camera. Compaction experiments, in figures 2 and 3, consisted in dropping a rubber head hammer on the drum always from the same height in sequences of 10 taps. Between each sequence, a waiting time was respected to let the system relax. The relative variation of the packing fraction ∆φ was inferred by image analysis from the variation of the area of the granular bed.

Rheological measurements. The rheograms of figure 1 were obtained in the configuration sketched in the inset of that figure. To perform rheological measurements with a large gap (up to 10 mm required for the large glass beads) in a plane-plane geometry, the top plate (diameter 50 mm) is fully immersed in the suspension, which itself is contained in a cylindrical vessel (diameter 60 mm). In both cases, the particles were density matched with the suspending fluid to avoid sedimentation. For the large glass beads, the suspending fluid was a mixture of water (30 % wt), glycerol (13 % wt) and sodium polytungstate (57 % wt). For the potato starch, it was a mixture of water (45 % wt) and cesium chloride (55 % wt). The viscosity is obtained from increasing and decreasing ramps of shear rate after a pre-shear. No migration effects were noticable. The rheograms of figure 4B were obtained in a different configuration since the need to control physico-chemistry (salt concentration) does not allow us to match the suspending fluid density. The configuration, sketched in the inset of figure 4B, uses a double-helix with tilted blades shearing the entire sample to maintain the homogeneity of the suspension during the measurement. The suspension volume fraction is controlled by first letting the particles settle down and adjusting the liquid level at the pile interface, which defined the packing fraction in the loose state, then adding a given amount of liquid. For each measurement, the suspension is first thoroughly resuspended at a high rotation rate (1 rev/s) while vibrating the container to prevent shear thickening [START_REF] Lin | Tunable shear thickening in suspensions[END_REF]. The rotation rate is then set to a given value and the constat torque is measured before the effect of sedimentation is observed. In all cases, torques and rotation rates were measured using an Anton-Paar MCR 501 rheometer.

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  soft matter | shear thickening | dense suspensions | friction |

  C.C., A.B., B.M. and Y.F. designed the research, performed the research, analyzed data and wrote the paper.The authors declare no conflict of interest.

Fig. 1 .

 1 Fig. 1. Steady avalanches in (left) Newtonian and (right) shear thickening suspensions. (A) Picture and rheograms (viscosity η versus shear-rate γ) of (left) a Newtonian suspension of large glass beads and (right) a shear thickening suspension of potato starch particles. Rheograms were obtained in the configuration sketched on the figure using density matched suspensions. (B) (center) sketch of the rotating drum. Pictures of a typical steady avalanche for (left) the glass beads immersed in a mixture of Ucon oil and water and (right) the potato starch immersed in water. (C) Angle of avalanche θ versus time for (left) the glass beads (right) the potato starch. Insets: steady state avalanche angle θs versus drum rotation speed ω (see Materials and Methods for the detailed description of particles, fluids and experimental protocol).

gFig. 2 .

 2 Fig. 2. Compaction and transient avalanches in (left) Newtonian and (right) shear thickening suspensions. (A) Sketch of the experimental protocol to study compaction and dilatancy effects. (B) Volume fraction of the sediment φ versus number of taps Ntaps (left) for the large glass beads and (right) for the potato starch particles. (C) Angle of the transient avalanche θt versus time obtained for different initial compactions of the sediment (left) for the large glass beads and (right) for the potato starch particles.

Fig. 3 .

 3 Fig. 3. Steady avalanches, compaction and dilatancy effects in suspensions of silica beads in pure water (black) or ionic solution (green). (A) Picture of the silica particles and sketch of a silica bead immersed in an ionic solution. Silica particles spontaneously carry negative charges on their surface when immersed in water. The range of the resulting repulsive force, i.e. the Debye length λD, can be tuned by changing the ionic concentration of the solvent. (B) Pile slope avalanche angle θ versus time, (C) relative packing fraction of the sediment ∆φ = φ(Ntaps) -φ(Ntaps = 0) versus number of taps and (D) transient avalanche angle θt versus time for the silica beads in (green) a sodium chloride solution with [NaCl]= 0.1 mol L -1 and (black) in pure water.

Fig. 4 .

 4 Fig. 4. Frictional transition in silica suspensions when varying the range of the repulsive force and link with macroscopic rheology. (A) Steady avalanche angle θs versus salt concentration [NaCl]. Top inset: steady avalanche angle θs versus particle roughness normalized by the Debye Length lr/λD. Bottom inset: AFM scan of a silica particle surface. The peak roughness is lr = 3.73 ± 0.80 nm. (B) Rheograms of silica beads suspensions obtained for different volume fractions in solutions of water and NaCl with salt concentration (top) [NaCl]= 10 -4 mol L -1 and (bottom) [NaCl]= 0.1 mol L -1 . The effective viscosity is η eff = αΓ/(2πΩL 3 ), where Γ is the torque, Ω the revolution speed and α 2.07 is a calibration constant. Inset: sketch of the experimental configuration used to obain the rheograms.

  and 2 (left) for the Newtonian suspension are large glass beads of diameter d = 487 ± 72 µm and density ρp = 2500 kg m -3 . The grains used in figure 1 and 2 (right) for the shear thickening suspension are potato starch particles of major axis d = 25±15 µm and (dry) density ρp = 1500 kg m -3 . The silica beads used in figure 3 and figure 4 are commercial particles from Microparticles GmbH with diameter 23.46 ± 1.06 µm and density ρp = 1850 kg m -3 . Rotating drums experiments. The drum used for the large glass beads (Fig. 1B left) has a diameter of 52 mm and a depth of 10 mm with a coarsened side wall. It is filled with a mixture of Ucon oil and pure (micro-filtered) water of viscosity η f = 57 mPas and density ρ f = 1005 kg m -3 . The drum used for potato starch

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Clavaud et al.

Clavaud et al.

ACKNOWLEDGMENTS.

We are thankful to Sarah Hormozy and Pauline Dame for helping us with preliminary experiments, Alain Rangis from CINAM for performing the AFM measurements and our technical staffs at IUSTI for building the experiments. This work was supported by the European Research Council under the European Union Horizon 2020 Research and Innovation programme (ERC grant agreement No. 647384 ) and by the Labex MEC (ANR-10-LABX-0092) under the A*MIDEX project (ANR-11-IDEX-0001-02) funded by the French government program Investissements d'Avenir.


Wanli Gao

Ozlem Sel
email: ozlem.sel@upmc.fr

Hubert Perrot
email: hubert.perrot@upmc.fr

Electrochemical and viscoelastic evolution of dodecyl sulfate-doped polypyrrole films during electrochemical cycling

Keywords: Polypyrrole, electrochemical quartz-crystal microbalance (EQCM), ac-electrogravimetry, ionic flux, electroacoustic measurements

The correlation between electrochemical and viscoelastic properties of electrodeposited dodecylsulfate-doped polypyrrole (PPy-DS) during electrochemical cycling process was described through combining electrochemical quartz-crystal microbalance (EQCM), ac-electrogravimetric characterizations and electroacoustic measurements. As the PPy-DS electrode evolves during the course of consecutive cycling in aqueous NaCl electrolyte, the film exhibits (i) an obvious ion-selective transition from cations to anions in the charge compensation process; (ii) an inferior electrochemical performance accompanied with increased stiffness (increased storage moduli, G´); and (iii) depleted capability of ionic exchange through film/electrolyte interface. PPy-DS conducting polymer electrodes (CPEs) are of interest in energy storage and the relationship between electrochemical and viscoelastic properties during electrochemical cycling process is essential for promoting the performance of these devices. In this perspective, ac-electrogravimetry combined with electroacoustic measurements can be suggested as an alternative method to synchronously probe the electrochemical and mechanical evolution and has the potential to offer a generalized route to study aging mechanism of CPEs.

Introduction

Species transfer in conducting polymer electrodes (CPEs) plays a key role in numerous applications, such as electrochemical sensors [START_REF] Knopfmacher | Highly stable organic polymer field-effect transistor sensor for selective detection in the marine environment[END_REF][START_REF] Ramanavičius | Electrochemical sensors based on conducting polymer-polypyrrole[END_REF], batteries [START_REF] Gracia | Polymers with redox properties: materials for batteries, biosensors and more[END_REF][START_REF] Li | A mechanically robust and highly ion-conductive polymer-blend coating for high-power and long-life lithium-ion battery anodes[END_REF] and supercapacitors [START_REF] Wang | Conducting polymer nanowire arrays for high performance supercapacitors[END_REF][START_REF] Ghenaatian | High performance hybrid supercapacitor based on two nanostructured conducting polymers: Self-doped polyaniline and polypyrrole nanofibers[END_REF]. Up to date, significant attention has been drawn to enhance the ionic transfer/transport and cycling stability of CPEs to devise electronics with effective energy storage capability [START_REF] Han | Hierarchical Co3O4@PPy@MnO2 core-shell-shell nanowire arrays for enhanced electrochemical energy storage[END_REF][START_REF] Liu | Polyaniline and polypyrrole pseudocapacitor electrodes with excellent cycling stability[END_REF][START_REF] Holze | Intrinsically conducting polymers in electrochemical energy technology: Trends and progress[END_REF][START_REF] Xia | Highly Stable Supercapacitors with Conducting Polymer Core-Shell Electrodes for Energy Storage Applications[END_REF], thereby demanding a thorough understanding of the ion transfer behavior at the CPEs/electrolyte interface. Another issue is that the CPEs experience inevitable structural changes in practical applications primarily due to the electrochemical aging of the polymer. The latter may aggravate the mechanical properties of CPEs which can be reflected in the viscoelastic variations of polymer electrodes during electrochemical cycling [START_REF] Agrisuelas | Viscoelastic potential-induced changes in acoustically thin films explored by quartz crystal microbalance with motional resistance monitoring[END_REF][START_REF] Mohamoud | The effect of anion identity on the viscoelastic properties of polyaniline films during electrochemical film deposition and redox cycling[END_REF][START_REF] Shpigel | Non-invasive in situ dynamic monitoring of elastic properties of composite battery electrodes by EQCM-D[END_REF]. Many CPEs have been studied for their appealing electrochemical properties [START_REF] Wang | A review of electrode materials for electrochemical supercapacitors[END_REF], such as poly(3,4-ethylenedioxythiophene) (PEDOT) [START_REF] Zhan | PEDOT: Cathode active material with high specific capacity in novel electrolyte system[END_REF][START_REF] Mo | Electrochemical synthesis and capacitance properties of a novel poly(3,4-ethylenedioxythiophene bis-substituted bithiophene) electrode material[END_REF], polypyrrole (PPy) [START_REF] Feng | Polypyrrole/hexadecylpyridinium chloride-modified graphite oxide composites: Fabrication, characterization, and application in supercapacitors[END_REF][START_REF] Tang | Growth of polypyrrole ultrathin films on MoS(2) monolayers as high-performance supercapacitor electrodes[END_REF][START_REF] Inzelt | Electrochemical quartz crystal microbalance study of ion transport accompanying charging-discharging of poly(pyrrole) films[END_REF], polyaniline (PANI) [START_REF] Liu | Polyaniline and polypyrrole pseudocapacitor electrodes with excellent cycling stability[END_REF][START_REF] Wang | Flexible Solid-State Supercapacitor Based on a Metal-Organic Framework Interwoven by Electrochemically-Deposited PANI[END_REF] and polythiophene (PHT) [START_REF] Ambade | Polythiophene infiltrated TiO2 nanotubes as high-performance supercapacitor electrodes[END_REF][START_REF] Snook | Conducting-polymer-based supercapacitor devices and electrodes[END_REF]. PPy has been exploited in considerable amount of researches, due to its relatively higher pseudocapacitance and lower cost, as well as its particularly supreme flexibility in morphology and structure [START_REF] Zhou | Construction of high-capacitance 3D CoO@polypyrrole nanowire array electrode for aqueous asymmetric supercapacitor[END_REF]. However, inferior cycle stability caused by significant dimensional changes during charge-discharge process greatly hinders their applications. Therefore, the relationship between internal structure and film properties has been scrutinized with the purpose of promoting the performance of CPEs in applications (i.e. energy storage).

Electrochemical quartz-crystal microbalance (EQCM) and its coupling with electrochemical impedance spectroscopy (the so-called ac-electrogravimetry) have proved themselves as baseline analytical tools to probe electrochemical processes, with tremendous benefits in in situ capturing ionic fluxes in various electrodes, including carbon based electrodes [START_REF] Escobar-Teran | Gravimetric and dynamic deconvolution of global EQCM response of carbon nanotube based electrodes by Ac-electrogravimetry[END_REF][START_REF] Griffin | In situ NMR and electrochemical quartz crystal microbalance techniques reveal the structure of the electrical double layer in supercapacitors[END_REF][START_REF] Tsai | Electrochemical quartz crystal microbalance (EQCM) study of ion dynamics in nanoporous carbons[END_REF] and CPEs [START_REF] Gabrielli | Ac-electrogravimetry study of electroactive thin films. II. Application to polypyrrole[END_REF]28]. Considerable amount of work has focused on the exploration of electrochemical properties of CPEs, which has been regarded as a prerequisite for improving performances of electrochemical devices [START_REF] Levi | Application of a quartz-crystal microbalance to measure ionic fluxes in microporous carbons for energy storage[END_REF][START_REF] Patrice | Materials for electrochemical capacitors[END_REF]. However, their physical or viscoelastic properties are of equal importance especially for the electrode cycling stability and should not be neglected. The ionic fluxes accompanied the free solvent molecules transfer during charging-discharging process may bring about the periodic potential-dependent volumetric changes of the electrodes (i.e., swelling and shrinking) [START_REF] Wang | A review of electrode materials for electrochemical supercapacitors[END_REF][START_REF] Snook | Conducting-polymer-based supercapacitor devices and electrodes[END_REF]. These processes are likely to result in a wide variety of unpredictable mechanical defects, i.e. polymer electrode fatigue, stress concentration and delamination from current collector. Thus, a measurement methodology capable of capturing the ionic transfer as well as viscoelastic evolution of the CPEs synchronously is highly desirable.

The viscoelastic properties of CPEs have been extensively investigated through the electroacoustic impedance method [START_REF] García-Jareño | Validation of the mass response of a quartz crystal microbalance coated with Prussian Blue film for ac electrogravimetry[END_REF][START_REF] Hillman | Dynamics of regioregular conducting polymer electrodes in response to electrochemical stimuli[END_REF][START_REF] Koehler | Shear moduli of anion and cation exchanging polypyrrole films[END_REF], by which the storage (G´) and loss moduli (G") of the polymer film can be determined. As the film ages, the viscoelastic changes may occur inside the film due to polymer chain rearrangements and species transfer through film/electrolyte interface [START_REF] Hillman | Dynamics of regioregular conducting polymer electrodes in response to electrochemical stimuli[END_REF]. Hillman and co-workers have reported an increase in the stiffness of PANI films due to insertion of anions and the expulsion of the solvent molecules [START_REF] Mohamoud | The effect of anion identity on the viscoelastic properties of polyaniline films during electrochemical film deposition and redox cycling[END_REF][START_REF] Hillman | Time-temperature superposition and the controlling role of solvation in the viscoelastic properties of polyaniline thin films[END_REF]. Bund et al. observed that the influx of anions may increase the stiffness of PEDOT film and the variations of G´ and G" were correlated with concentrations of charged species within film [START_REF] Ispas | On the p-doping of PEDOT layers in various ionic liquids studied by EQCM and acoustic impedance[END_REF][START_REF] Lyutov | An acoustic impedance study of PEDOT layers obtained in aqueous solution[END_REF]. It is considered that such viscoelastic changes are somewhat associated with the electrochemical performance of the film, as the flux of ions and solvent during the charge-discharge process can modify the intermolecular interactions between polymer chains, which in turn substantially

Experimental

Film preparation and characterization

Pyrrole solution (Py), sodium dodecyl sulphate (NaDS) and NaCl salts were purchased from Sigma Aldrich. The Py monomer was distilled before use and kept at -20 o C. All the solutions were prepared with bi-distilled water.

Polypyrrole films doped with DS -anions were electrodeposited on the gold electrode (0.2 cm 2 ) of a quartz crystal resonator (9 MHz-AWS, Valencia, Spain) where a platinum grid and a saturated calomel electrode (SCE) are used as counter and reference electrode, respectively. The PPy-DS films were electrodeposited by cyclic voltammetry (2 cycles) from 0.675 V to 0 V vs. SCE at 10 mV·s -1 in a solution of 0.1 M pyrrole and 0.05 M NaDS [START_REF] Gabrielli | Ac-electrogravimetry study of electroactive thin films. II. Application to polypyrrole[END_REF][START_REF] Gabrielli | Charge compensation process in polypyrrole studied by ac electrogravimetry[END_REF]. The average film thickness of the electrogenerated PPy-DS film and 175-cycled film was analyzed using a field emission gun scanning electron microscope (FEG-SEM, Zeiss, Supra 55). Fourier transform infrared (FTIR) spectra were recorded on VERTEX 70 spectrometer (BRUKER Co., USA) from 2000 to 650 cm -1 with a 4 cm -1 resolution. Ultraviolet-visible (UV-vis) spectra were recorded with a U-4001 spectrophotometer. The films used for FTIR and UV-vis were prepared on ITO coated glass slides and cycled under the same conditions as those on gold electrode of the quartz resonators.

Electrogravimetric measurements

All of the electrochemical experiments were carried out using an Autolab potentiostat-galvanostat electrochemical workstation (PGSTAT302). After the PPy-DS film electrogeneration, the ac-electrogravimetry cannot be conducted immediately because the film composition is not under equilibrium. So it was stabilized by 15 scan cycles from -1.3 V to 0.5 V vs. SCE at 50 mV·s -1 in a 0.25 M NaCl aqueous electrolyte.

This stabilized film was deemed as fresh film. Subsequently, ac-electrogravimetric investigation of fresh PPy film was performed at two different potentials -0.6 V and -0.2 V vs. SCE, respectively. The ac-electrogravimetric measurements of the film were tracked after each 25 CV cycles up until 175 cycles were reached, where the electrogravimetric response is too weak to be analyzed. The procedure is illustrated schematically in Figure 1 (a). Two key potentials were selected: (i) -0.6 V, located between the reduction (-0.68 V) and oxidation (-0.5 V) peak for fresh film and thus, can be regarded to be a representative potential of the Faradic process. (ii) -0.2 V, approximately a constant current response was observed for fresh film in the vicinity of this potential, therefore, it can be considered to be indicative of a non-Faradaic process.

In order to have coherent comparison it is decided to keep monitoring the changes at these two potentials, even slight shifts of potential may occur during the electrochemical cycling.

For ac-electrogravimetry, a four-channel frequency response analyser (FRA, Solartron 1254) and a lab-made potentiostat (SOTELEM-PGSTAT) were used. The QCM was used under dynamic regime, the working electrode (WE) was polarized at previously selected potentials, and sinusoidal small amplitude potential perturbation (80 mV rms) was superimposed. The microbalance frequency change (Δf m ) related with the mass response (Δm) of the modified working electrode was measured simultaneously with the charge response (Δq) of the electrochemical system. The resulting signals were sent to the four-channel FRA, which allowed the electrogravimetric transfer function (

( )   m E  )
and the charge/potential transfer function ( ( )

   q E
) to be obtained simultaneously at the given potential and frequency modulation, f (pulsation =2f). The charge/potential transfer function ( ( )   q E  ) and mass/potential transfer function (

( ) m E   
) can be theoretically calculated by using the eq. ( 1), ( 2) and ( 3), where Δc i presents the change of the concentration of each species (ions and free solvent) in the film,  the pulsation, d f the film thickness (here 200 nm estimated through QCM measurements), K i and G i are the partial derivatives of the flux (J i ) with respect to the concentration and the potential, respectively. K i describes the kinetics of transfer. G i is the reciprocal of the transfer resistance (Rt i ), exhibiting the ease or difficulty in the transfer at the film/electrolyte interface for respective species.

( ) ( )

i i f i c G E j d K       (1) ( ) ( )
i f i f i G q Fd E j d K        (i: ions) (2)
( ) ( )

i f i i f i G m d M E jd K       



(i: ions and non-charged species) [START_REF] Gracia | Polymers with redox properties: materials for batteries, biosensors and more[END_REF] On the basis of the above parameters, the characteristic frequency of transfer (f i ), the transfer resistance (Rt i ) and the instantaneous capacitance (C i ) of each species are further considered and calculated using eq. (4) to eq. ( 6).

2 i i f K f d   (4) 1 i i Rt FG   ( 5
)
f i i i Fd G C K   (6)
After the ac-electrogravimetry measurements, the experimental data obtained from fresh film, 100 and 175-cycled films were fitted with the theoretical functions given in eq. ( 2) and (3) by using the Mathcad software.

Electroacoustic impedance measurements

The viscoelastic properties of the PPy-DS film during electrochemical aging were explored through the electroacoustic admittance method. To track the viscoelastic variation of our films and to corroborate with the ac-electrogravimetry results, electroacoustic measurements were performed at the same stationary potentials (-0.6V and -0.2V) after each 25 cycles up to the 175th cycle was reached (Figure 1b). To perform the electroacoustic admittance measurements under polarization, an Agilent 4294A impedance analyzer associated to a lab-made potentiostat (SOTELEM-PGSTAT) was used.

A software developed in our laboratory (Simad) was used for fitting the experimental data for extracting the storage moduli (G´) and loss moduli (G") of the film. The real component (G´) describes the energy storage capability of the polymer chains and the imaginary part (G") is associated with the energy dissipation of the film due to irreversible deformation of polymer chains [START_REF] Hillman | Time-temperature superposition for viscoelastic properties of regioregular poly(3-hexylthiophene) films[END_REF] .

The complete theoretical electrical admittance, ( )

V th Y  , of the loaded quartz resonator is:

1 1 ( ) ( ) ( ) V th p V V th m Y i C Z Z          (7)
where

2 f      Cp is the parasitic capacitance and V m
Z is the motional impedance of the loaded quartz resonator calculated with a viscoelastic model.

The motional impedance, V m Z , can be completely modelled according to the work of Martin et al. [START_REF] Granstaff | Characterization of a thickness-shear mode quartz resonator with multiple nonpiezoelectric layers[END_REF]. If the characteristics of the quartz and of the liquid are considered as constants, the motional electrical impedance, V m Z of the coated resonator is:

2 2 tanh( ) ( ) 4 tanh( ) q s f f f V m f q f s f f h Z Z h Z Z e A Z Z h               (8)
where q h is the quartz thickness, q e is the quartz piezoelectric constant, A is the active mass area, f Z is the acoustic impedance of the film, s Z is the acoustic impedance of the liquid, f  is the complex propagation constant of the film and f h is its thickness. Moreover, f Z and f  can be described as:

f f f Z G    (9) f f f G    (10)
where f  is the film density and f G is the shear thickness modulus of the film, which can be written as a complex number with a real and imaginary part,

´"

f G =G jG  , where j 2 =-1.
The acoustic impedance of the solution, s Z , is defined as eq. ( 9) except that G´ becomes negligible and for a Newtonian liquid, G"=2πf s , where f is the frequency and s  the liquid viscosity.

Results and discussion

Cyclic electrogravimetric behavior

The cross-sectional morphology of electrodeposited PPy-DS films were observed by FEG-SEM (Figure 1c and1d). The average film thickness is ~130 nm and ~110 nm for the fresh and 175-cycled film, respectively. These values correspond to the shrunken state of the film under the vacuum conditions of the measurements. Parallelly, the Concerning the 100 times-cycled film, both cations and anions can participate in the charge compensation and they may play an equal part in the electrochemical response without consideration of solvent exchange. Thus, the mass contribution from cations and anions may offset which leads to this almost "no mass response" for 100-cycled film, which is illustrated in Figure 2c-zone II.

The maximum mass change (M max ) during a redox cycle was tracked after every 25 scan cycles, as depicted in Figure 2c. The M max value of the film decreases and reaches to a minimum after 100 cycles, i.e. 0.23 g.cm -2 , which is approximately 7 times less than that of a fresh film. After that, M max values gradually increase to 1.4 g.cm -2 for 175-cycled film. This "quasi-U" shape describes an obvious transition where the predominance of cation participation is gradually replaced by anion participation in the charge compensation process as the film is electrochemically cycled.

The above discussion considers the ionic species as the major contribution but the free solvent contributions cannot be excluded. It has been widely reported that the ion exchanges during redox reactions are commonly accompanied with flux of solvent [START_REF] Arias | New Insights into Pseudocapacitive Charge-Storage Mechanisms in Li-Birnessite Type MnO2Monitored by Fast Quartz Crystal Microbalance Methods[END_REF][START_REF] Sel | Determination of the diffusion coefficient of protons in Nafion thin films by ac-electrogravimetry[END_REF]. To get insights into the nature of the ionic species and possible free solvent molecules' contribution, the EQCM results are further analyzed. The molar mass, M i , of each species involved in the charge compensation process can provide a better understanding of the species transfer as a function of the number of cycles.

To do this, the m F q   function was calculated as a function of applied potential using the current and the mass response of the film (Figure 2a andb), as follows:

1 ( )    i dm dm M F F dq dt i (11)
This function provides a global estimation of the molar mass of the species (M i ) that may participate in the charge compensation process. The m F q   function was calculated from the reduction branch of the EQCM data and Figure 2d compares M i of the species involved in the reduction process as the film is electrochemically cycled. It is evident that M i presents a potential and cycling dependence. For fresh film, M i exhibits a negative value reaching -88 g.mol -1 at -0.7 V without an evident plateau in the reduction sweep regime. It should be kept in mind that the ions present in the electrolyte are only sodium cations (Na + , 23 g.mol -1 ) and chloride anions (Cl -, 35.5 g.mol -1 ). In the m F q   function, negative and positive values are characteristic of cations and anions, respectively [28,[START_REF] Arias | New Insights into Pseudocapacitive Charge-Storage Mechanisms in Li-Birnessite Type MnO2Monitored by Fast Quartz Crystal Microbalance Methods[END_REF]. The values higher than expected molar mass of the cations suggest that cations are inserted into the fresh film accompanied with water in either free form with the same flux direction or in the hydration shell of Na + . After the film is 100

times-cycled, the potential corresponding to the max M i value is moved to more cathodic potential (from -0.7 V to -1.05 V). When the film is further cycled up to 175 cycles, the peak intensity dramatically increases approximately 5 times up to 479 g.mol -1 compared to that observed after 100 times cycling. This indicates that the nature of the species involved in the charge compensation are dependent on the film cycling state. The film exhibits unexpected behavior: the cations dominate charge balance when the film is fresh, while anion's contribution increases as the film is electrochemically cycled and predominates in charge balance in the end. Since the estimated molar mass values are much higher than the theoretical ones (Na + , 23 g.mol -1 and Cl -, 35.5 g.mol -1 ), the water molecules are speculated to play a significant role in the electrochemical process.

However, it is not straightforward to separate each species contribution and the possible synergistic effect among them. Indeed, the deconvolution of the global cyclic electrogravimetry response into gravimetric and dynamic components is quite challenging since the measurements are done at a certain scan rate. Therefore, coupling of the QCM with electrochemical impedance spectroscopy (ac-electrogravimetry) was suggested [START_REF] Gabrielli | Ac-electrogravimetry study of electroactive thin films. II. Application to polypyrrole[END_REF]. To shed light on the subtleties of the charge compensation process during electrochemical aging, an ac-electrogravimetric study was performed to understand the relationship between film cycling and charge compensation process.

Ac-electrogravimetric investigations

To gain insights into the dynamic behavior of the species transfer at the film/electrolyte interface at the temporal scale, ac-electrogravimetry was performed to probe the influence of film cycling on the transfer of charged and non-charged species. Figure 3 compares the charge/potential transfer function ( )

   q E
TF, obtained at -0.6V and -0.2V at different cycled state of the film, respectively.

Theoretically, the ( )

   q E
TF in Figure 3 appears as a single loop if there is only one charged species transferred. In this study, the ( )

   q E
TF shows mainly one suppressed loop (a composition of several loops) at both potentials at different cycled state of the film, suggesting the presence of more than one species participating in the charge compensation. It is also likely that their time constants are not significantly different to have them appear as separate loops. The experiment data were fitted using theoretical equation 2 and two ionic species were involved. Their corresponding values of K i and G i , obtained through the fitting process are given in Table 1. As the film is electrochemically cycled, the diameter of the global loop gets smaller, which may indicate that the population of the ions involved in the charge compensation is reduced as clearly shown in figure 3 g and h for both potentials. This result is coherent with the decrease of the current observed in Figure 2a.

Apart from the charge/potential TF, the electrogravimetric response, ( )

m E   
, which can provide information on both the charged and non-charged species transfer, was simultaneously obtained (Figure 4). For all

( ) m E   
fittings (except Figure 4f), three species, Na + (hydrated or not), free water molecules and Cl -were identified, which led to a good agreement between the experimental and theoretical curves. Our data presented in Figure 4 indicate that the cations appear at high frequencies, followed by free water molecules at intermediate frequencies and anions at low frequencies, independently of the cycled degree of the film at both potentials. At -0.2 V, the electrogravimetric response is rather constant and only desolvated sodium at high frequencies, free water contribution at intermediate frequencies and chloride at low frequencies were detected (Figure 4 a, c and e). At -0.6V, a fairly good agreement between the experimental and theoretical ( )

m E   
data was obtained by considering the molar mass of hydrated cations (Na + · 2H 2 O) for fresh film (Figure 4b). It seems that the solvation shell of the Na + is gradually removed at -0.6V as the film is electrochemically cycled (Figure 4 d andf). It is interesting to note that a small loop appears in the first quadrant at very high frequencies for the 175-cycled film (Figure 4f). It is supposed that some of the DS -anions anchored on the polymer chains are removed and start to participate in the charge compensation process, as the molar mass of DS -was determined. This is probably related to the periodic swelling-shrinking process of the film cycling which modifies the film structure and permits the exchange of DS -. It will be further explored in the electroacoustic part (3.3).

The ( ) m E   
TFs at both potentials for all cycled films (Figure 4 g and h) present one big loop in the third quadrant at high and intermediate frequencies (HF and IF), and another one in the fourth quadrant at lower frequencies (LF). It is worth mentioning here that the loops in the third quadrant are characteristic of contributions originated from cations and/or free solvent with the same flux direction as cations [START_REF] Gabrielli | Ac-electrogravimetry study of electroactive thin films. II. Application to polypyrrole[END_REF].These loops in the third quadrant are reduced in diameter as the film is electrochemically cycled (Figure 4 (a-e)) which indicates either a decrease of the cation/free solvent contributions or a decrease of the molar mass of the cations by losing their solvation shell.

The characteristic frequencies, f i , in Figure 5(a) and (b) display that cations (hydrated or not) have the highest kinetics of transfer at the electrode/electrolyte interfaces, followed subsequently by H 2 O molecules and Cl -anions (f c > f s > f a ) at both potentials as the film is electrochemically cycled. Additionally, it is noted that only for the 175-cycled film at -0.6 V, the DS -anions are observed in the charge compensation process where they possess the highest kinetics of transfer (DS -anions were not taken into account in Figure 5b, d and f as they are only detected for 175-cycled film at -0.6 V).

At -0.2V (Figure 5a), the f i of H 2 O molecules is enhanced nearly 3 times up to 1.75 Hz in the region II, accompanied with a decrease in cation transfer kinetics (from 3.45 Hz to 2.15 Hz). When the film is electrochemically cycled up to region III, the f i value of the cation and solvent molecules approaches and they eventually exhibit equivalent transfer kinetics. The transfer of anions remain as the slowest contribution at both potentials over the course of film cycling, which is in agreement with the higher R t value of anions compared to that of cations and water molecules, as shown in Figure 5c.

On the contrary, the cation transfer kinetics become faster in the end of region II at -0.6V (Figure 5b), which can be attributed to the dehydration process of hydrated cations (Na + · 2H 2 O) on the course of film cycling as depicted in Figure 6a. Meanwhile, it also demonstrates higher transfer capability of dehydrated Na + relative to the hydrated counterparts due to its smaller size.

An interesting phenomenon is observed in the transfer of H 2 O molecules at -0.6V (Figure 5b) as follows. The f i of H 2 O molecules experience a slight decrease (from 0.90Hz to 0.35Hz) in region I, followed by a surge up to 3.9Hz at the beginning of region II. Afterwards, it progressively decreases to 0.21Hz at the end of region III.

Correspondingly, the R t of H 2 O molecules (Figure 5d) shows an approximate mirror symmetry, except that the peak value of f i is reached after 75 cycles whereas the minimum value of R t appears after 125 cycles (i.e. ~50 cycles lag between the f i and R t ).

In fact, this is not contradictory because the f i is related with the transfer kinetics of the species, while the R t is correlated to the ease/difficulty of their transfer. As the film is 75 times-cycled, the hydration shell of cations becomes smaller (one H 2 O molecule removed), and the cation motion is somewhat released from the restriction of H 2 O shell, resulting in an increase of f c . Meaningwhile, much more steric spaces inside the film would become accessible for free H 2 O molecules due to the smaller size of cations. This can lead to an ease in the solvent transfer which is translated into a decrease of R t (H 2 O) values. After that, the cations completely remove their hydration shell towards the 125 times-cycled state (the end of region II), i.e. bare cations (Figure 6a). Due to the relatively smaller size of bare cations, free H 2 O molecules inside the film may be better accommodated leading to a minimum of R t (H 2 O) value observed at around 125 cycles (Figure 5d). In this case, H 2 O molecules possess the greatest potential to be transferred at the film/electrolyte interface, which can be further confirmed in Figure 6b. For the measurements at -0.6V, the proportion of free H 2 O transferred through the film/electrolyte interface (calculated using eq. 12 and 13) reaches maximum at the end of region II, i.e. 80% after 125 cycles (Figure 6b). This observation can be discussed by consideration of an increased amount of space available inside the film provided by the dehydration process of the cations in region II. This results in a minimum value of the Rt s lagging behind ~50 cycles to the peak of f s (Fig. 5b and5d). Additionally, the film at -0.6V undergoes more H 2 O exchange than that at -0.2V for the major portions of the cycling period (Figure 6b). This finding may indicate a relatively higher swollen state and porosity of the film when polarized at -0.6V. It can facilitate the transfer of bigger ions and may be the reason for (i) the transfer of hydrated cations (Na + · 2H 2 O) at -0.6V rather than at -0.2V as the film is electrochemically cycled in region I, and (ii) the transfer of bigger anions (DS -) after the film is cycled ~ 175 times.

| | | | | | | | H O H O H O Na xH O Na Cl H O Na Na xH O Cl G K H O free G G G G K K K K                  (12) 2 2 2 2 2 2 2 2 2 | | | | ( ) | | | | | | | | H O Na xH O H O Na xH O H O Na xH O Na Cl H O Na Na xH O Cl G G x K K H O global G G G G K K K K                        (13)
The Rt i and C i (instantaneous capacitance) of cations and anions (Cl -, without consideration of DS -) possess a similar dependence on the electrochemical cycling (Figure 5c-f). When the data obtained at -0.2V is taken as an example, the Rt i of ions shows a progressive increase with electrochemical cycling, indicating that the more the film is cycled, the more difficult the ionic transfer becomes. Accordingly, the ionic capacitance, C i decreases for both cations and anions. This observation may indicate that transfer process of ions progressively degrades. Hence, it can be suggested that the periodic charging-discharging process can weaken the capability of CPEs to exchange ions at the film/electrolyte interface as a function of cycle number.

Viscoelastic property changes upon film aging

Numerous studies have reported that the viscoelastic properties of the electroactive polymer play a crucial role in the electrogravimetric response if the film is not sufficiently thin or rigid [START_REF] Levi | In Situ Electrochemical Quartz Crystal Admittance Methodology for Tracking Compositional and Mechanical Changes in Porous Carbon Electrodes[END_REF]. More importantly, the viscoelastic change with electrochemical cycling is supposed to have a great influence on the electrochemical performance of the film primarily because volumetric changes during the redox process (insertion or expulsion of charged and non-charged species) are strongly associated with the viscoelastic properties of the polymer chains. Thus, the variation of the viscoelastic properties of the film during electrochemical cycling process was examined and the correlation between electrochemical and viscoelastic properties was further considered with regard to long term performance of CPEs.

Figure 7a displays a similar change of G´ and G" at the two selected potentials.

Taking the film measured at -0.6 V for example, the storage modulus (G´) is increased by approximately 200% as the film is electrochemically cycled. However, G" shows an entirely opposite tendency with film cycling, decreasing from 0.77×10 5 N.m -2 to 0.19×10 5 N.m -2 at -0.6V. It has been revealed that the G´ is correlated with the film stiffness, while G" is a measure of the film viscosity [START_REF] Mohamoud | The effect of anion identity on the viscoelastic properties of polyaniline films during electrochemical film deposition and redox cycling[END_REF][START_REF] Hillman | Time-temperature superposition for viscoelastic properties of regioregular poly(3-hexylthiophene) films[END_REF]. The progressively increased G´ and decreased G" suggest that the periodical cycling renders the PPy-DS film stiffer and less viscous. Nevertheless, this should not be attributed to the overoxidation of PPy because it starts at potentials greater than 0.7V vs. SCE [START_REF] Christensen | In situ spectroscopic investigations of the growth, electrochemical cycling and overoxidation of polypyrrole in aqueous solution[END_REF][START_REF] Beck | Organic Electrochemistry in the Solid State-Overoxidation of Polypyrrole[END_REF].

Additionally, FTIR spectra of the fresh and cycled PPy-DS films (Fig. S1 in supporting information) exhibit the characteristic vibrational bands associated with the doped polypyrrole structure. The spectra of the fresh, 100-and 175-cycled film do not show remarkable differences which suggests the absence of polymer crosslinking phenomena upon electrochemical cycling. The absence of a band at ~1700 cm -1 (corresponding to C=O functions) further indicates that there is no overoxidation of the polymer film [START_REF] Lu | Polypyrrole micro-and nanowires synthesized by electrochemical polymerization of pyrrole in the aqueous solutions of pyrenesulfonic acid[END_REF].

In this work, we hold that the reconformation of the polymer chains resulted from cycling process embows the film more rigid (increased G´) and less viscous (decreased G"). It has been reported that the requirement of co-planarity of π orbitals for long conjugation leads to the stiffness of poly (3-alkylthiophene)s through the reconfiguration and rearrangements of polymer chains [START_REF] Hillman | Dynamics of regioregular conducting polymer electrodes in response to electrochemical stimuli[END_REF]. Briefly, redox process of PPy-DS films involves a sequence of events: (i) electrons transferred between the film and the working electrode, (ii) exchange of cations and/or anions between the film and electrolyte to satisfy electroneutrality which is often coupled with free solvent transfer to meet the volumetric confinement of the viscoelastic film and lastly, (iii) difficult for ionic species not only to be transferred at the film/electrolyte interface but transported in the film bulk as well, which is in agreement with results obtained from the cyclic electrogravimetric and ac-electrogravimetric part, i.e. i) fading of the pseudocapacitive capability ii) increase of the ionic transfer resistance, Rt i, and iii) decrease of the instantaneous capacitance, C i , of each charged species.

As a matter of fact, the volume of the PPy-DS film can be varied from cathodic to anodic potentials within one cycle (Figure 8-Route I) and also at the same potential after many cycles (Figure 8-Route II). As Figure 8-Route I shows, the PPy-DS film undergoes successive swelling and shrinking cycles during the redox process. In addition, a dehydration process of cations for freshly prepared films has been reported

during anodic potential sweep due to the lower porosity of PPy-DS film in a relatively shrunken state [START_REF] Hillman | Time-temperature superposition for viscoelastic properties of regioregular poly(3-hexylthiophene) films[END_REF]. As for route II which is explored in this work, the volumetric change capability of the film can become poorer upon cycling, and the solvation shell of cation at -0.6 V is removed during the cycling process.

Conclusions

The combination of EQCM, ac-electrogravimetry and electroacoustic measurements was proposed to track the electrochemical and viscoelastic evolution during the electrochemical cycling of PPy-DS films. An obvious ion-selective transition from cations to anions for charge compensation is observed during film cycling process.

A predominant role is played by cations for fresh and slightly cycled films, whereas anions dominate the charge balance in older films.

The electrochemical performance was investigated at two different potentials. At -0.6V, the film presents a relatively more swollen state than that at -0.2V due to the higher amount of H Note: cm · s -1 and mol · s -1 · cm -2 · V -1 are for the units of K and G parameters, respectively.

Cation, anion and solvent in the Table refer to Na + or hydrated Na + , Cl -and free H 2 O.

For 175-cycled film at -0.6V, the fitting parameters for DS -are K=2.815×10 -3 cm · s -1 and G=-2.815×10 -8 mol · s -1 · cm -2 · V -1 .

  affect the film viscoelasticity. Herein, a methodology which combines the EQCM, ac-electrogravimetry and electroacoustic measurements was proposed to get a broader view of the physico-chemical interactions inside the CPEs over the course of electrochemical aging. The particularity of this methodology stems from the utility of EQCM together with ac-electrogravimetry and electroacoustic impedance for electrogravimetric evaluation and for viscoelastic tests, respectively.With the aim of synchronous description of the relationship between electrochemical properties and viscoelastic evolution during PPy electrode electrochemical cycling, the combined methodology (involving EQCM, ac-electrogravimetry and electroacoustic impedance measurements) was applied to characterize PPy film doped with DS -anions (PPy-DS) after every 25 charge/discharge cycles in aqueous electrolytes until 175 th cycle was reached. Due to the nanometric film thickness, film/electrolyte configuration can be considered as a zoom of a real macroscopic electrochemical system. During the limited number of cycles, various phenomena might be observed which can permit to predict an eventual degradation of CPEs in energy storage devices. This systematic study is expected to provide insights into the relationship between the internal structure of the CPE film and the ability to maintain its electrochemical and mechanical performance. To the best of our knowledge, such systematic study has not yet been reported. In previous works of ourgroup (ref. 11 and 27), either materials and dopants or the methods to explore the mechanical properties were different. The influences of aging degree and applied potential on the species transfer (charged or uncharged), hydration/dehydration of ions and free solvents motion and intimately related viscoelastic changes of PPy-DS electrode were investigated during film aging upon cycling and a model was proposed to illustrate the electrochemical cycling process.

  Fig.2a are likely to be related to creation of the polarons and bipolarons in agreement

Figure 8

 8 elucidates the two different ways which can stiffen the PPy-DS film, i.e. anodic sweep and film cycling, both of which prohibit the transfer of hydrated Na + . On the course of electrochemical cycling, the film would hardly experience volumetric change any more, which is accompanied with a fading of the electrochemical performance as seen in CV responses (Figure2a) and charge/potential response (Figure3 g and h). The electrochemical activity loss upon cycling is further investigated by UV-vis spectroscopy. FigureS2in supporting information indicates the presence of a distinct band appearing below ~480 nm which is due to π-π* transitions[START_REF] Jeon | Spherical polypyrrole nanoparticles as a highly efficient counter electrode for dye-sensitized solar cells[END_REF]. When the PPy-DS films are cycled for 100 and 175 times, a decrease of the intensity and a shift to lower wavelength values of this characteristic band are observed. A blue shift and a decrease in the intensity of this band indicate an increase in the band gap of the PPy-DS films and a decrease in the conjugation length of the conducting polymer upon electrochemical cycling. This observation is in agreement with (i) the cyclic voltammetry investigations showing a considerable electrochemical activity loss and (ii) with the viscoelastic property investigations indicating a stiffening of the polymer which is likely to render the charge transfer more difficult. To the best of authors' knowledge, it is the first time that the correlation between electrochemical and viscoelastic properties in an electrochemical cycling process has been systematically investigated.

Figure 1 .

 1 Figure 1. Schematic illustration of the measurement procedures for (a) ac-electrogravimetry and (b) electroacoustic tests during film electrochemical cycling as

Figure 2 . 25 MFigure 3 .Figure 4 .Figure 5 .Figure 6 .Figure 7 .

 22534567 Figure 2. Cyclic voltammetry (a), mass change (Δm) (b), the maximum mass change (c) and F(dm/dq) function calculated from the reduction branch (d) of PPy-DS film in 0.25 M NaCl aqueous solution between -1.3V and 0.5V vs. SCE at a scan rate of 50 mV·s -1 .

Figure 8 .

 8 Figure 8. Schematic of volumetric evolution of PPy electrode during film cycling, without considering the exchange of free H 2 O molecules.

Table 1 .

 1 2 O molecules insertion, facilitating the transfer of bigger ions, i.e., prohibiting H 2 O transfer). At -0.2V, desolvated Na + is the only form of cations participating in the charge compensation. The cation is the fastest species (except the DS -at -0.6V for 175-cycled film) transferred at the film/electrolyte interface followed by free H 2 O molecules at intermediate frequencies and anions are the slowest species at both potentials irrespective of cycled degree of the film.For PPy-DS electrodes, the ionic transfer becomes more difficult upon electrochemical cycling process examined in the present work. It should be noted that this evolution can also be influenced by the film thickness, the nature and the concentration of electrolytes, and the scan rate. The observed ionic transfer change is not only due to the loss of electroactive sites inside the film but also due to the increasing stiffness of the polymer chains. It is attributed to the reconformation of the PPy chains which consequently result in the deterioration of the conjugated π systems. Fitting parameters, K i and G i , obtained from ac-electrogravimetry.

	Na + with two H 2 O molecules in the hydration shell and DS -anions. Kinetics of H 2 O
	molecule in region II (50-125th cycle in Figure 5b) show a complex and
	cycling-dependent property due to the competitive relationship between availability for
	accommodation inside the film provided by cation's dehydration process (favoring H 2 O
	transfer) and polymer chain's increasing stiffness during film cycling (increased G´,

Acknowledgments

Wanli Gao acknowledges China Scholarship Council (CSC) for Ph.D. grant. F. Pillier is thanked for the FEG-SEM measurement.

reconformation of polymer chains to be compatible with such new spatial architecture of the film. In a redox process, PPy chain's reconformation takes place to keep sufficient π orbital overlaps for conduction structure, where a co-planarity of π orbitals is required within 40 o [START_REF] Brédas | Organic polymers based on aromatic rings (polyparaphenylene, polypyrrole, polythiophene): Evolution of the electronic properties as a function of the torsion angle between adjacent rings[END_REF]. Therefore, upon electrochemical cycling process, the structure of the polymer chains can be progressively altered due to such conformational changes. Specifically, for fresh PPy-DS film, pyrrole rings possess a coplanar conformation [START_REF] Beck | Organic Electrochemistry in the Solid State-Overoxidation of Polypyrrole[END_REF], and the movement of DS -ions is greatly restricted by strong interactions from large conjugated π systems. During film cycling process, the coplanar conformation of PPy is gradually forced to approach a non-coplanar one by means of PPy chain's motions, giving rise to a progressive deterioration of long conjugated systems and consequently loss of electroactive sites or electronic conductivity, as it is approved by the fading electrical response of cyclic voltammetry in Figure 2a or charge/potential TF in Figure 3g andh. When the film is further electrochemically cycled (175 cycles), the DS -ions are released out of the film and embark on the charge compensation process, as supported by Figure 4f. Altogether, the electrochemical cycling process causes the reconformation of the polymer chains, which brings about the stiffness of the film with fading electronic conductivity.

The film loss tangent, G"/G´ was further used for describing the viscoelastic evolution of the film upon cycling process. As depicted in Figure 7b, the film loss tangent shows a comparable decrease upon cycling at the two different potentials. It indicates that the cycling process confers increasing stiffness on the film. Namely, region I can be generally regarded as viscous region, region II becomes viscoelastic while region III is fairly elastic in the film electrochemical cycling evolution.

The stiffness of the film can restrict the volumetric changes and make it more

AUTHOR INFORMATION

Corresponding Author

 E-mail addresses: ozlem.sel@upmc.fr (O. Sel), hubert.perrot@upmc.fr (H. Perrot).

Notes

The authors declare no competing financial interest.


Konstantinos Raftopoulos
email: konstantinos.raftopoulos@cnam.fr

Klimis Ntalianis

Paraskevi Tzouveli

Nicolas Tsapatsoulis
email: nicolas.tsapatsoulis@cut.ac.cy

Aleatha Parker-Wood
email: aleatha@soe.ucsc.edu

Marin Ferecatu
email: marin.ferecatu@cnam.fr

Watermark Resynchronization: An Efficient Approach based on Eulerian Tours around a Robust Skeleton

Keywords: Object-based Watermarking, Resynchronization, Skeleton Transform, Global-Local Transformation, Eulerian Tours

The existing block-based approaches, albeit successful in resisting frequency domain attacks, are sensitive to geometric distortions due to the lack of reference in repositioning the block grid. In this paper an RST-invariant block-based approach is proposed, aiming at protecting image objects. The term "image object" refers to semantically contiguous parts of images that have a specific contour boundary. The proposed approach is based on shape information, since the watermark is embedded in image blocks, the location and orientation of which are defined by Eulerian tours that are appropriately arranged in layers, around an object's robust skeleton. Images from the Polymathic project are used to illustrate the technique.

Introduction

Block-based watermarking approaches using spread spectrum modulation of pseudorandom signals, even though successfully improving watermark resistance to various frequency domain attacks, cannot withstand rotation, because the rectangular grid arrangement is changed and thus synchronization is lost. A reference point for placing the rectangular block-grid for watermark recovery is not easy to obtain after image/object rotation, if a priori registration information is not available. The situation is illustrated in [START_REF] Lin | Rotation, scale, and translation resilient watermarking for images[END_REF] where elaborate methods of high complexity are proposed to alleviate this problem. The main contribution of this paper is that it incorporates a certain noise resistant method of extracting shape information [START_REF] Raftopoulos | The Global-Local transformation for noise resistant shape representation[END_REF] during the block-based watermark embedding process in such a way that the watermarked block's location is readily identifiable at the retrieval phase, even after RST transformation, cropping or Gaussian boundary noise. The proposed system is tested in its ability to provide geometrically resistant copyright protection of semantic objects having an explicit boundary, most suited for protecting certain objects in an image, or explicit creations of artists that have to be distributed and reused in different contexts. Another application is inferring image provenance, allowing artists to find source images quickly by examining watermarks in derivative files, similar to activity inference [START_REF] Gaugaz | Activity based links as a ranking factor in semantic desktop search[END_REF].

The method

A robust skeleton of each object is initially extracted in a vector form. To introduce enhanced noise resistance to the extracted skeleton, we use the Global-Local transformation [START_REF] Raftopoulos | The Global-Local transformation for noise resistant shape representation[END_REF] to map the noise contour back to a smoothed version. Starting then from the skeleton endpoints (marked as small circles in the images below), the pseudorandom watermark sequence is embedded in the DCT domain of the blocks along the skeleton's Eulerian tour. When the first tour is completed the Eulerian tour is extended outwards, in consecutive layers towards the object's boundary until the watermark sequence is spread to the whole object. During watermark detection, initially the skeleton of the candidate object is extracted and the potentially watermarked blocks that are located along the extended Eulerian tour are matched against the respective blocks around the initial skeleton. Only tours starting from the skeleton endpoints are examined. The success of the method stems from the fact that based on the Global-Local transformation, the robust skeleton is extracted from a smooth version of the original contour that retains certain metric information.

Figure 1 3 ExperimentsFigure 2 .

 132 Figure 1 Watermarked blocks arranged across the Eulerian tours around the skeleton of the Superman top view.

Figure 3 .

 3 Figure 3. A closer view of the Eulerian tours at the back view of the Superman image. Some overlap has been allowed for better illustration.

  4

Acknowledgements

This research has been supported by the Project FUI Polymathic, financed by the French government.