M Guichon
email: maelle.guichon@enstimac.fr

C Boher

F Schmidt

An Understanding of Polymer/Mold Contact During Injection Molding Cycle

Injection molded parts often show several types of surface defects. Different authors mentioned that those defects are due to the interaction between the mold and the melt. This contact has a strong influence on the flow front behavior, and depends on processing parameters like melt and mould temperatures, ram speed during injection, mould surface properties and roughness, mould thickness and polymer melt rheological properties … After a literature review of "flow marks" defect, it appears that the "alternate flow marks" are caused by an instability of the Fountain flow front. An assumption proposed by some researchers is that the slip is the formation mechanism of this instability. We assume that this mechanism is the start of the flow front instability during the filling stage. We use numerical simulations performed with Forge2  commercial software, in order to generate non-symmetrical contact boundaries conditions. We introduce some sliding conditions at the wall during a flow between two parallel plates. Our preliminary computations confirm that the instability is created in this way.

Introduction

Injection molded parts often reveals several types of surface defects. These defects can appear under different forms on the surface of the parts. The general names of these defects are "flow marks", "tiger stripes", "ice lines", and "stick/slip defect". There is a mistake in the literature between the observation of these defects and their names. Yokoi [1] proposed a classification of the flow mark defects in three groups in terms of surface conditions: micro-grooved surface (also called micro flow marks, sharkskinning defect...); synchronous dull and gloss surface (also called halos for the parts injected by the center); alternate dull and gloss surface (called generally flow marks) This last defect manifests itself as a regular pattern of oriented dull and shiny stripes more or less perpendicular to the flow direction [2,3]. Experiments performed by previous researchers suggest that the defect results from an unstable flow near the free surface [2,3,4,[START_REF] Bulters | PPS 16 annual meeting Shangai China[END_REF][START_REF] Chang | [END_REF][START_REF] Grillet | PPS 16 annual meeting Shangai China[END_REF] Major studies of the filling stage consider that there is no slip at wall. Most authors mentioned that those defects are due to the interaction between the mold surface and the melt. This contact has a strong influence on the flow front behavior, and depends on processing parameters. The instrumentation during the process is very difficult to implement, and give only partial results like pressure and temperature, but no real data about the contact formation. Due to the limited availability of rheological data, there is no clear understanding of the rheological dependencies on the instability of the flow front. However, Chang [START_REF] Chang | [END_REF] found that there is a link between the defects formation and the recoverable shear stress, and Xu [9] found that the rheological characterizations (like the storage and less modulus of the complex viscosity, the first normal stress difference, the relaxation time...) have an influence on the defects formation. Thus, the molecular structure is having a strong effect on the elastic behavior of the polymer [START_REF] Chang | [END_REF]. The aim of this paper is to investigate the assumption of the slip at wall for the mechanism of the flow front instability.

Numerical simulation

Using Forge2 ® software, we compute flow between parallel rigid dies with discontinuous and nonsymmetrical contact conditions (figure1). Then, we investigate if flow front instabilities occur. This software is a forming process simulation based on Finite Element Method (FEM). At each time step, the thermo-mechanical equations are solved in a weak form (Galerkin integral formulation). For non-linear constitutive equations , a Newton-Raphson algorithm is used to compute the resulting non linear algebraic system. Due to the updating Lagrangian's procedure, an automatic remeshing procedure is used that allows to keep a fine mesh during flow computation (especially close to polymer flow front). The polymer melt behavior is represented by a Norton-Hoff law with a Arrhenius type thermal dependence:

    ij 1 m 0 T 0 ij 3 e K 2 s           (1)
For numerical simulations, we use an ABS NOVODUR P2H-AT, for which rheological parameters are referenced in table1.

V V e K 1 m T 0               (2)
Contact conditions are defined in figure1. The initial temperature of the polymer and the die are respectively 206°C, and 20°C. Thermal exchanges between the polymer and dies are defined in figure1.

Results and Discussion

The conventional measuring methods cannot reveal the actual cause of flow marks, so Yokoi and al. have used particular visualization experiments to observe the flow inside the mold cavity. The defects seem to be due, in according to Bulters experiments [START_REF] Bulters | PPS 16 annual meeting Shangai China[END_REF], to an oscillatory flow between the cavity walls. We assume that this instability results from a discontinuity of the boundaries contact conditions. We investigate the slip boundaries condition to know if they may produce the instability.

Figure 2 -Computed polymer temperature using nonsymmetrical contact conditions (Forge2 ® ). In figure2, we note that a discontinuity of contact conditions can create an instability flow front behavior. The variation of the contact conditions generates nonsymmetrical flow. When the slip is inserted at the cavity wall, the polymer swirls on the opposite cavity wall (when the slip is inserted at the inferior wall, the polymer swirls towards the superior wall). When the slip is changing at the other side, the polymer swirls on the opposite wall where there is the slip. We also find that the contact conditions influences the velocity profile (figure 2) in agreement with different experiments [9,[START_REF] Yokoi | PPS Annual Conference Presentation[END_REF][START_REF] Yokoi | [END_REF]12]. Yokoi [12] proposed the following mechanism for the formation of the flow marks:

-The polymer fractures/separates of one cavity wall -This fracture creates the unsymmetrical flow -The region on the surface of the molded part,

where the polymer has fractured, forms a dull region (we observe it in figure 3) Then, we assume that when the slip is inserted on a segment of cavity wall, it will create a dull region on the molded surface parts. They revealed a temperature gradient between the glossy and dull region. Yokoi affirmed that the glossy regions are hotter and dull regions are colder. (figure 3). [START_REF] Yokoi | PPS Annual Conference Presentation[END_REF] In our computations we observe a non-symmetrical gradient temperature created by the contact discontinuity (figure 2). This illustrates that when the polymer fractures/separates of the cavity wall, the temperature is low on the side where there has been the separation.

Conclusion

Using numerical simulations and specific contact conditions, we conclude that the slip at wall causes flow front instability during the filling stage. Nevertheless, it is necessary to perform different numerical simulations using other polymers in order to confirm this result. In order to reproduce this defect, we will realize molded parts on an industrial injection machine. We must verify slip hypothesis like a main mechanism of the formation of the surface defect by experimental means.

With all this considerations we can think that the sliding can be responsible of the surface defect.

Nevertheless, note that we don't know if this instability has been created by discontinuity of contact conditions (in practical) because Yokoi [12] and Chang [START_REF] Chang | [END_REF] used a geometrical discontinuity with a insert near the gate on the thickness of the mold cavity and created by this way the same instability of the flow. Perhaps the two mechanisms are linked, the geometrical discontinuity can generate some sliding. Whereas only a few simulations have performed to specifically investigate flow marks surface defects have been realized. And the extensional Fountain's flow near the advancing free surface (where the stagnation point instability has been postulated) has already been investigated [14]. We investigated some numerical simulation under the software FORGE2  . We investigated the slip to create the discontinuity boundaries contact conditions.

Figure 3 -

 3 Figure3-Thermal gradient temperature and development of the dull and glossy regions[START_REF] Yokoi | PPS Annual Conference Presentation[END_REF] In our computations we observe a non-symmetrical gradient temperature created by the contact discontinuity (figure2). This illustrates that when the polymer fractures/separates of the cavity wall, the temperature is low on the side where there has been the separation.


Sylvain Grangeon
email: s.grangeon@brgm.fr

Alain Manceau

Julien Guilhermet

Anne-Claire Gaillot

Martine Lanson

Bruno Lanson

Zn sorption modifies dynamically the layer and interlayer structure of vernadite

In surficial environments, the fate of many trace metals is influenced by their interactions with the phyllomanganate vernadite, a nano-sized and turbostratic variety of birnessite. To advance our understanding of the surface reactivity of vernadite, synthetic vernadite (d-MnO 2 ) was equilibrated at pH 5 or 7, reacted with dissolved Zn to produce Zn-sorbed d-MnO 2 with Zn/Mn atomic ratios from 0.003 to 0.156, and characterized structurally. The octahedral layers in the Zn-free vernadite contain on average $0.15 vacancies, $0.13-0.06 Mn 3+ and $0.72-0.79 Mn 4+ . The layer charge deficit is compensated in the interlayer by Mn 3+ bonded over Mn vacancy sites and Na + located in the interlayer mid-plane. The average lateral dimension of coherent scattering domains (CSDs) deduced from X-ray diffraction (XRD) modeling is $5 nm, consistent with that observed by transmission electron microscopy for individual crystals, indicating that the amounts of edge sites can be estimated by XRD. The average vertical dimension of CSDs is $1 nm, equivalent to 1.5 layers and less than the observed 3-4 layers in the particles. Zinc sorption at pH 5 and 7 on pre-equilibrated vernadite induced crystal dissolution reducing the lateral CSD size $15-20%. Zinc K-edge extended X-ray absorption fine structure (EXAFS) spectroscopy and XRD show that Zn occurs in the interlayer above vacancies as a triple-corner-sharing surface complex, which is fully tetrahedral at low Zn/ Mn ratios and increasingly octahedral at higher ratios. As Zn/Mn increases, the site density of layer Mn 3+ decreases from 0.13 ± 0.01 to 0.03 ± 0.01 at pH 5 and from 0.06 ± 0.01 to 0.01 ± 0.01 at pH 7, and that of layer vacancies correspondingly increases from $0.15 to 0.24 and 0.21 at pH 5 and 7, respectively. These changes likely occur because of the preference of Zn 2+ for regular coordination structures owing to its completely filled third electron shell (3d 10 configuration). Thus, sorption of Zn into the interlayer causes the departure of layer Mn 3+ , subsequent formation of new reactive layer vacancies, and an increase in surface area through a reduction in particle size, all of which dynamically enhance the sorbent reactivity. These results shed new light on the true complexity of the reactive vernadite surface, and pose greater challenges for surface-complexation modeling of its sorption isotherms.

INTRODUCTION

Vernadite is the environmentally ubiquitous nano-sized and turbostratic variety of the well-crystallized phyllomanganate birnessite. Its formation is considered to be mediated dominantly by biota, because biogenic oxidation is approximately two orders of magnitude faster than heterogeneous oxidation catalyzed by mineral surfaces [START_REF] Crerar | Deposition of deep-sea manganese nodules[END_REF][START_REF] Tebo | Biogenic manganese oxides: properties and mechanisms of formation[END_REF][START_REF] Morgan | Kinetics of reaction between O 2 and Mn(II) species in aqueous solutions[END_REF]. Vernadite can be produced by bacteria [START_REF] Mandernack | Manganese mineral formation by bacterial spores of the marine Bacillus, strain SG-1: evidence for the direct oxidation of Mn(II) to Mn(IV)[END_REF][START_REF] Schulze | Manganese oxidation-states in Gaeumannomycesinfested wheat rhizospheres probed by micro-xanes spectroscopy[END_REF][START_REF] Villalobos | Characterization of the manganese oxide produced by Pseudomonas putida strain MnB1[END_REF][START_REF] Tebo | Biogenic manganese oxides: properties and mechanisms of formation[END_REF][START_REF] Toner | Spatially resolved characterization of biogenic manganese oxide production within a bacterial biofilm[END_REF][START_REF] Webb | Structural characterization of biogenic Mn oxides produced in seawater by the marine Bacillus sp. strain SG-1[END_REF][START_REF] Boonfueng | Zn sorption mechanisms onto sheathed Leptothrix discophoraand the impact of the nanoparticulate biogenic Mn oxide coating[END_REF], fungi [START_REF] Tani | Biogeochemistry of manganese oxide coatings on pebble surfaces in the Kikukawa River System, Shizuoka, Japan[END_REF][START_REF] Miyata | Enzymatic formation of manganese oxides by an Acremonium-like hyphomycete fungus, strain KR21-2[END_REF][START_REF] Miyata | Production of biogenic manganese oxides by repeated-batch cultures of laboratory microcosms[END_REF][START_REF] Santelli | Diversity of Mn oxides produced by Mn(II)-oxidizing fungi[END_REF], and higher-order organisms [START_REF] Lanson | Formation of Zn-Ca phyllomanganate nanoparticles in grass roots[END_REF]. Biogenic vernadite was reported or inferred to occur in soils and sediments (Hochella et al., 2005a;[START_REF] He | Bacterial communities inside and surrounding soil iron-manganese nodules[END_REF][START_REF] Lanson | Formation of Zn-Ca phyllomanganate nanoparticles in grass roots[END_REF], freshwater [START_REF] Bargar | Structural characterization of terrestrial microbial Mn oxides from Pinal Creek, AZ[END_REF], dry and cold deserts [START_REF] Dorn | Microbial origin of desert varnish[END_REF][START_REF] Dorn | Manganese-rich rock varnish does occur in Antarctica[END_REF][START_REF] Mckeown | Characterization of manganese oxide mineralogy in rock varnish and dendrites using X-ray absorption spectroscopy[END_REF], and marine deposits [START_REF] Crerar | Deposition of deep-sea manganese nodules[END_REF][START_REF] Bodeı | Formation of todorokite from vernadite in Ni-rich hemipelagic sediments[END_REF].

The crystal structure of vernadite and of its synthetic analog d-MnO 2 consists of randomly stacked layers of edge-sharing MnO 6 octahedra with a layer-to-layer distance of $7.2 A ˚ [START_REF] Giovanoli | A simplified scheme for polymorphism in the manganese dioxides[END_REF][START_REF] Drits | Structure of synthetic monoclinic Na-rich birnessite and hexagonal birnessite; I, Results from X-ray diffraction and selectedarea electron diffraction[END_REF]. Octahedral vacancies in the layer and Mn 4+ substitution by cations of lower valence (e.g. Mn 3+ ,N i 2+ ,C o 3+ ,o rC u 2+ ; [START_REF] Manceau | Structural mechanism of Co 2+ oxidation by the phyllomanganate buserite[END_REF]Manceau et al., , 2007a;;[START_REF] Silvester | Structure of synthetic monoclinic Na-rich birnessite and hexagonal birnessite; II. Results from chemical studies and EXAFS spectroscopy[END_REF][START_REF] Webb | Structural characterization of biogenic Mn oxides produced in seawater by the marine Bacillus sp. strain SG-1[END_REF][START_REF] Villalobos | Structural model for the biogenic Mn oxide produced by Pseudomonas putida[END_REF][START_REF] Peacock | Crystal-chemistry of Ni in marine ferromanganese crusts and nodules[END_REF][START_REF] Grangeon | Crystal structure of Ni-sorbed synthetic vernadite: a powder Xray diffraction study[END_REF][START_REF] Bargar | Structural characterization of terrestrial microbial Mn oxides from Pinal Creek, AZ[END_REF][START_REF] Sherman | Surface complexation of Cu on birnessite (d-MnO 2 ): controls on Cu in the deep ocean[END_REF]Zhu et al., 2010a) create a deficit of charge compensated for by interlayer cations. The density of layer vacancies, and hence the reactivity of vernadite with respect to cation sorption [START_REF] Zhao | Relationship between Pb 2+ adsorption and average Mn oxidation state in synthetic birnessite[END_REF], can be increased by the reduction of Mn 4+ and Mn 3+ to Mn 2+ by Cr 3+ [START_REF] Manceau | X-ray absorption spectroscopic study of the sorption of Cr(III) at the oxide/water interface. I Molecular mechanism of Cr(III) oxidation on Mn oxides[END_REF][START_REF] Silvester | The mechanism of chromium(III) oxidation by Na-buserite[END_REF] and by organic molecules and sunlight (Stone and Morgan, 1984a,b;[START_REF] Sunda | Oxidation of humic substances by manganese oxides yields low-molecular-weight organic substrates[END_REF][START_REF] Banerjee | Petrogenesis of ferromanganese nodules from east of the Chagos Archipelago, Central Indian Basin, Indian Ocean[END_REF][START_REF] Villatoro-Monzo ´n | Anaerobic biodegradation of BTEX using Mn(IV) and Fe(III) as alternative electron acceptors[END_REF][START_REF] Pizzigallo | Mechanochemical removal of organo-chlorinated compounds by inorganic components of soil[END_REF]Kwon et al., 2009a;[START_REF] Nasser | Mineral induced mechanochemical degradation: the imazaquin case[END_REF]. Vernadite surface reactivity is reinforced further by its nanometer size, which increases the amounts of border sites relative to birnessite.

The weak undersaturation of surface oxygens caused by the presence of di-and trivalent cations in the octahedral layer is usually balanced by exchangeable hydrated alkaline or alkali earth cations, such as Na + and Ca 2+ , forming outersphere complexes in the interlayer [START_REF] Drits | Substructure and superstructure of four-layer Ca-exchanged birnessite[END_REF]Lanson et al., 2002a). In contrast, the strong undersaturation of surface oxygens bordering layer vacancies is more permanently balanced by multivalent cations sorbed mainly as triple-corner-sharing surface complexes (TC configuration, Fig. 1;[START_REF] Silvester | Structure of synthetic monoclinic Na-rich birnessite and hexagonal birnessite; II. Results from chemical studies and EXAFS spectroscopy[END_REF][START_REF] Drits | Structure of heavy-metal sorbed birnessite: Part 2. Results from electron diffraction[END_REF]Manceau et al., 2002a;Lanson et al., 2002b;[START_REF] Jurgensen | The structure of the manganese oxide on the sheath of the bacterium Leptothrix discophora: an XAFS study[END_REF][START_REF] Li | EXAFS studies on adsorption-desorption reversibility at manganese oxide-water interfaces. II. Reversible adsorption of zinc on d-MnO 2[END_REF][START_REF] Webb | Structural characterization of biogenic Mn oxides produced in seawater by the marine Bacillus sp. strain SG-1[END_REF][START_REF] Peacock | Crystal-chemistry of Ni in marine ferromanganese crusts and nodules[END_REF][START_REF] Peacock | Physiochemical controls on the crystalchemistry of Ni in birnessite: genetic implications for ferromanganese precipitates[END_REF][START_REF] Kwon | Surface complexation of Pb(II) by hexagonal birnessite nanoparticles[END_REF]Pen ˜a et al., 2010;Zhu et al., 2010b). The deficit of layer charge may also be balanced partly by the formation of double-corner-sharing and triple-edge-sharing surface complexes (DC and TE configurations, respectively, Fig. 1; Lanson et al., 2002b;Manceau et al., 2002aManceau et al., , 2007a;;[START_REF] Kwon | Surface complexation of Pb(II) by hexagonal birnessite nanoparticles[END_REF].

As a result of both its ubiquity and high surface reactivity, vernadite is often associated with transition metals, including Zn, rare-earth elements, and actinides in surface, subsurface, and marine environments, such as in ferromanganese crusts, nodules and grain coatings [START_REF] Ostwald | Chemical and mineralogical investigations on deep sea manganese nodules from the Southern Ocean[END_REF][START_REF] Mckenzie | The adsorption of lead and other heavy metals on oxides of manganese and iron[END_REF][START_REF] Aplin | Ferromanganese oxide deposits from the Central Pacific Ocean, I. Encrustations from the Line Islands Archipelago[END_REF][START_REF] Chukhrov | Crystal structure of birnessite from the Pacific ocean[END_REF][START_REF] Bogdanov | Ferromanganese nodules of the Kara Sea[END_REF][START_REF] Koschinsky | Sequential leaching of marine ferromanganese precipitates: genetic implications[END_REF][START_REF] Lei | Mineralogical control on transition metal distributions in marine manganese nodules[END_REF][START_REF] Friedl | Solid phases in the cycling of manganese in eutrophic lakes: new insights from EXAFS spectroscopy[END_REF][START_REF] Duff | Mineral associations and average oxidation states of sorbed Pu on tuff[END_REF][START_REF] Exon | Ferromanganese nodules and crusts from the Christmas Island Region, Indian Ocean[END_REF][START_REF] Koschinsky | Uptake of elements from seawater by ferromanganese crusts: solid-phase associations and seawater speciation[END_REF][START_REF] Manceau | Molecularscale speciation of Zn and Ni in soil ferromanganese nodules from Loess soils of the Mississippi Basin[END_REF][START_REF] Manceau | Natural speciation of Zn at the micrometer scale in a clayey soil using X-ray fluorescence, absorption, and diffraction[END_REF]Manceau et al., , 2007a,b;,b;Marcus et al., 2004a;Hochella et al., 2005b;[START_REF] Isaure | Zinc mobility and speciation in soil covered by contaminated dredged sediment using micrometer-scale and bulk-averaging X-ray fluorescence, absorption and diffraction techniques[END_REF][START_REF] Bodeı | Formation of todorokite from vernadite in Ni-rich hemipelagic sediments[END_REF][START_REF] Peacock | Crystal-chemistry of Ni in marine ferromanganese crusts and nodules[END_REF][START_REF] Takahashi | Chemical and structural control of the partitioning of Co, Ce, and Pb in marine ferromanganese oxides[END_REF][START_REF] Vane | Combined chemical and mineralogical evidence for heavy metal binding in mining-and smelting-affected alluvial soils[END_REF][START_REF] Bargar | Structural characterization of terrestrial microbial Mn oxides from Pinal Creek, AZ[END_REF]. Phyllomanganates have been reported to influence Zn mobility also in wetlands [START_REF] Olivie-Lauquet | Release of trace elements in wetlands: role of seasonal variability[END_REF], in areas affected by atmospheric fallout from smelting activities [START_REF] Manceau | Quantitative Zn speciation in smelter-contaminated soils by EXAFS spectroscopy[END_REF], and in the hyporheic zone of rivers contaminated by mining operations [START_REF] Fuller | Reactive uptake of trace metals in the hyporheic zone of a mining-contaminated stream, Pinal Creek, Arizona[END_REF]. Laboratory experiments indicate that when Zn, and other metals such as Ni, are introduced into a bacteria-rich medium with microbially produced vernadite and biofilms, sorption predominantly occurs on vernadite [START_REF] Toner | Zinc sorption to biogenic hexagonal-birnessite particles within a hydrated bacterial biofilm[END_REF]Pen ˜a et al., 2010Pen ˜a et al., , 2011;;Zhu et al., 2010b), consistent with its close association with trace metals in natural systems.

Previous structural studies of Zn sorption on synthetic hexagonal birnessite containing $0.17 vacancy and $0.11 layer Mn 3+ per octahedral layer site (E site, Fig. 1) showed that Zn coordination varies with surface loading: Zn is dominantly tetrahedral at low Zn/Mn atomic ratios ( IV Zn/ VI Zn % 2 for Zn/Mn % 0.008), and octahedral at higher Zn loading [START_REF] Drits | Structure of heavy-metal sorbed birnessite: Part 2. Results from electron diffraction[END_REF]Manceau et al., 2002a;Lanson et al., 2002b). Recent quantum mechanical calculations suggested that VI Zn is stabilized by H-bonding between neighboring H 2 O molecules located near the interlayer mid-plane and belonging to the coordination spheres of two Zn 2+ cations each adsorbed on one side of the interlayer space (Kwon et al., 2009b). If this is the case, the IV Zn/ VI Zn ratio should vary not only with the surface coverage, but also with the layer stacking order because disruption of the layer periodicity should hinder the formation of H-bonds. To verify this hypothesis, two series of d-MnO 2 were equilibrated at pH 5 and 7, then equilibrated with Zn solutions to achieve a final solid Zn/Mn mole ratio of 0.003-0.156, and characterized structurally. Interest was further whetted by the finding from X-ray diffraction (XRD) simulations that the density of Mn 4+ vacancies increased and the layer size decreased with increasing Zn loading. Thus, the crystal chemistry of Zn at the surface of vernadite appeared to be influenced by the stacking order of the sorbent, while the defective structure of the phyllomanganate layers was in return modified dynamically by Zn.

MATERIALS AND METHODS

2.1. Sample synthesis and zinc sorption protocol d-MnO 2 was synthesized using stoichiometric amounts of KMnO 4 and MnCl 2 as described by [START_REF] Villalobos | Characterization of the manganese oxide produced by Pseudomonas putida strain MnB1[END_REF]. Two suspensions were prepared at I = 0.1 M NaNO 3 using $1.5 g L À1 of d-MnO 2 powder and deionized water (resistivity > 18 MX cm À1 ), which was boiled and degassed by bubbling argon for 30 min before use. One batch was equilibrated at pH 5.0 ± 0.1 and another at pH 7.0 ± 0.2 (T =25°C). Zinc was introduced next by dropwise addition (0.2-1.0 mL min À1 depending on the Zn/Mn ratio) with intense stirring of 5.0 Â 10 À3 M (pH 5) and 5.0 Â 10 À4 M (pH 7) Zn(NO 3 ) 2 solutions. Solution concentrations were chosen to maximize the concentration of free aqueous Zn 2+ while avoiding metal precipitation, and their volumes varied to obtain the desired Zn/Mn ratios. Ionic strength and pH were kept constant during the addition of Zn(NO 3 ) 2 . Finally, the pH was re-adjusted after the last addition of Zn(NO 3 ) 2 solution until fully stabilized (usually for $12 h). Then samples were filtered, rinsed with deionized water, and freeze-dried. Sample codes are ZnXdBiY, where X stands for the pH and Y for the atomic ratio of Zn to Mn (Table 1).

Chemical analysis

Total Mn, Na and Zn contents were measured by Inductively Coupled Plasma -Atomic Emission Spectrometry (ICP-AES, Perkin-Elmer Optima 3000) on aliquots of solutions obtained from $5 mg Mn oxide digested in $15 mL NH 3 OHCl (0.7 mol L À1 , pH 1.9). Average Mn oxidation states were measured in triplicate by potentiometric titration, using (NH 4 ) 2 FeSO 4 (Mohr salt) and Na 4 P 2 O 7 (Table 1; [START_REF] Lingane | New method for determination of manganese[END_REF][START_REF] Vetter | Potentialausbildung an der mangandioxid-elektrode als oxidelektrode mit nichtstochiometrischemoxid[END_REF][START_REF] Gaillot | Caracte ´risation structurale de la birnessite: Influence du protocole de synthe[END_REF]. This method requires only the measurement of three equivalence volumes (see Supplementary information) to provide a fast, accurate, and robust estimate of this parameter. In contrast, titration methods using potassium or sodium iodide [START_REF] Murray | The oxidation state of manganese in marine sediments and ferromanganese nodules[END_REF][START_REF] Villalobos | Characterization of the manganese oxide produced by Pseudomonas putida strain MnB1[END_REF], sodium oxalate [START_REF] Freeman | An improved oxalate method for the determination of active oxygen in manganese dioxide[END_REF][START_REF] Silvester | Structure of synthetic monoclinic Na-rich birnessite and hexagonal birnessite; II. Results from chemical studies and EXAFS spectroscopy[END_REF][START_REF] Villalobos | Characterization of the manganese oxide produced by Pseudomonas putida strain MnB1[END_REF], or oxalic acid [START_REF] Feng | Li + extraction/ insertion with spinel-type lithium manganese oxides. Characterization of redox-type and ion-exchange-type sites[END_REF] require the accurate determination of both sample mass and concentrations of titrating solutions. Additional uncertainties come from the analytical determination of the amount of Mn 2+ resulting from the reductive dissolution of the phyllomanganate.

EXAFS spectroscopy

All EXAFS spectra, including previously acquired reference spectra (Marcus et al., 2004a), were collected on beam-line 10.3.2 at the Advanced Light Source (Berkeley, USA; Marcus et al., 2004b). Because Zn can be tetrahedral and octahedral at medium to high Zn/Mn ratio and EXAFS spectra represent the weighted average of all bonding environments of the target element, the fraction of each coordination species was determined by linear combination fitting of chalcophanite as VI Zn reference (ZnMn 3 O 7 .3H 2 O; [START_REF] Wadsley | The crystal structure of chalcophanite, ZnMn 3 O 7 .3H 2[END_REF][START_REF] Post | Chalcophanite, ZnMn 3 O 7 .3-H 2 O; new crystal-structure determinations[END_REF], and IV ZndBi from a marine ferromanganese nodule of Baltic Sea as IV Zn reference (Marcus et al., 2004a). Zinc is sorbed at vacancy sites in both references. It is fully octahedral in chalcophanite [START_REF] Post | Chalcophanite, ZnMn 3 O 7 .3-H 2 O; new crystal-structure determinations[END_REF]Manceau et al., 2002a), and fully tetrahedral, within the 7% precision, in IV ZndBi (Marcus et al., 2004a). Spectra were reconstructed in k 3 v(k) space initially with one component, and the regression evaluated over the 1.8-10.6 A ˚À1 k range with the normalized sum-squared residual

NSS = R(k 3 v exp -k 3 v cal ) 2 /R(k 3 v exp ) 2 .
A second component was considered statistically significant if NSS decreased by at least $10% and if its fractional contribution was >10% (e.g. [START_REF] Manceau | Quantitative Zn speciation in smelter-contaminated soils by EXAFS spectroscopy[END_REF]Manceau et al., , 2002b;;[START_REF] Isaure | Quantitative Zn speciation in a contaminated dredged sediment by l-PIXE, l-SXRF, EXAFS spectroscopy and principal component analysis[END_REF]. The weights of reference spectra in the linear fits to the data were the only adjustable parameters. The sum of VI Zn and IV Zn species was not constrained to 1, but should be close to this value if the local environment of Zn is well described with the end-members for octahedral and tetrahedral Zn.

Powder XRD

XRD patterns were collected on a Bruker D5000 diffractometer, equipped with a SolX solid-state detector (Baltic Scientific Equipments) and CuKa radiation (k = 1.5418 A ˚), over the 5-80 °2h angular range (17.6-1.2 A ˚) with 40 s counting time per 0.04 °2h step. Usual structure refinement methods such as the Rietveld method are inapplicable because of the turbostratic stacking of vernadite (100% of random stacking faults). Simulations were performed using the formalism described by [START_REF] Drits | X-ray Diffraction by Disordered Lamellar Structures: Theory and Applications to Microdivided Silicates and Carbons[END_REF], and successfully applied previously to both natural and synthetic phyllomanganates (see for example [START_REF] Chukhrov | Crystal structure of birnessite from the Pacific ocean[END_REF][START_REF] Manceau | Structural mechanism of Co 2+ oxidation by the phyllomanganate buserite[END_REF][START_REF] Drits | Substructure and superstructure of four-layer Ca-exchanged birnessite[END_REF][START_REF] Lanson | Structure of H-exchange hexagonal birnessite and its mechanism of formation from Na-rich monoclinic buserite at low pH[END_REF]Lanson et al., , 2002b;;[START_REF] Gaillot | Structure of birnessite obtained from decomposition of permanganate under soft hydrothermal conditions. 1. Chemical and structural evolution as a function of temperature[END_REF][START_REF] Gaillot | Structure of the synthetic K-rich phyllomanganate birnessite obtained by high-temperature decomposition of KMnO 4 : Substructures of K-rich birnessite from 1000 °C experiment[END_REF][START_REF] Villalobos | Structural model for the biogenic Mn oxide produced by Pseudomonas putida[END_REF][START_REF] Grangeon | Crystal structure of Ni-sorbed synthetic vernadite: a powder Xray diffraction study[END_REF][START_REF] Grangeon | Structure of nanocristalline phyllomanganates produced by freshwater fungi[END_REF].

The layer and interlayer structure (nature, position and quantity of layer and interlayer species) and the dimension [START_REF] Grangeon | Crystal structure of Ni-sorbed synthetic vernadite: a powder Xray diffraction study[END_REF], which is essentially insensitive to other structural parameters. These parameters were obtained from the simulation of the high-angle tail of the 11, 20 band [START_REF] Villalobos | Structural model for the biogenic Mn oxide produced by Pseudomonas putida[END_REF][START_REF] Drits | Birnessite polytype systematics and identification by powder X-ray diffraction[END_REF][START_REF] Grangeon | Crystal structure of Ni-sorbed synthetic vernadite: a powder Xray diffraction study[END_REF][START_REF] Lanson | Formation of Zn-Ca phyllomanganate nanoparticles in grass roots[END_REF]. Atomic positions were considered to be invariant among samples, and Na to be coordinated always to three water molecules, to reduce the number of adjustable parameters [START_REF] Post | Crystal structure determinations of synthetic sodium, magnesium, and potassium birnessite using TEM and the Rietveld method[END_REF][START_REF] Villalobos | Structural model for the biogenic Mn oxide produced by Pseudomonas putida[END_REF][START_REF] Grangeon | Crystal structure of Ni-sorbed synthetic vernadite: a powder Xray diffraction study[END_REF].

The average number of layers stacked coherently in diffracting crystallites was determined next from the simulation of the low angle-region (5-30 °2h) which contains basal (0 0 l) reflections. The CSD size along the c * axis was optimized, while keeping all other structural parameters to their optimal values derived from the simulation of the high-angle region. Fit quality was evaluated with the usual R wp and Goodness of Fit (GoF = R 2 wp /R 2 exp ) factors [START_REF] Howard | Profile fitting of powder diffraction patterns[END_REF]. The trial-and-error approach used here by necessity prevents the calculation of a covariance matrix. The precision on parameter values obtained from the simulation of turbostratic phyllomanganates, was estimated previously [START_REF] Villalobos | Structural model for the biogenic Mn oxide produced by Pseudomonas putida[END_REF][START_REF] Drits | Birnessite polytype systematics and identification by powder X-ray diffraction[END_REF][START_REF] Grangeon | Crystal structure of Ni-sorbed synthetic vernadite: a powder Xray diffraction study[END_REF][START_REF] Lanson | Formation of Zn-Ca phyllomanganate nanoparticles in grass roots[END_REF]. The uncertainty on the b lattice parameter is ±0.001 A [START_REF] Grangeon | Crystal structure of Ni-sorbed synthetic vernadite: a powder Xray diffraction study[END_REF], and the uncertainty on the sum of DC and TC site occupancy is ±0.01 atom per octahedral site. Note that diffraction does not allow the differentiation of DC and TC complexes, because their positions are crystallographically equivalent [START_REF] Grangeon | Crystal structure of Ni-sorbed synthetic vernadite: a powder Xray diffraction study[END_REF]. When CSDs include 2-4 layers, as in vernadite, the precision from XRD on their size is likely better than 0.2 layer, a fivefold intensity increase being observed for the 0 0 1 reflection when the average number of layers in CSDs increases from 2.1 to 3.4 [START_REF] Grangeon | Structure of nanocristalline phyllomanganates produced by freshwater fungi[END_REF]. The precision of the CSD size in the a-b plane is estimated to ±10%. The sensitivity of XRD to this parameter was demonstrated in Fig. 6 of [START_REF] Villalobos | Structural model for the biogenic Mn oxide produced by Pseudomonas putida[END_REF], which shows that reducing the CSD size from 60 to 30 A ˚dramatically modifies the XRD profile.

Transmission electron microscopy

Transmission electron microscopy (TEM) images were acquired on a Hitachi H9000 NAR microscope equipped with a LaB 6 cathode, operated at 300 kV, and a Multiscan GATAN charge-coupled device (CCD) camera. Highly diluted aqueous suspensions of the samples were dried on a copper mesh grid covered with a 20 nm thick holey carbon membrane. The extremely limited dimensions of individual particles restrained their observation above the carbon membrane.

RESULTS

Chemical analysis

The average Mn oxidation state is between 3.76 ± 0.01 (Zn5dBi03) and 3.88 ± 0.01 (Zn7dBi156) instead of nominally 4.0 for stoichiometric d-MnO 2 , meaning that all samples contain mixed-valent states of Mn (Table 1). Lowvalence Mn may substitute for Mn 4+ in d-MnO 2 layers (Mn 3+ only) or be sorbed at vacancy sites (Mn 2+ and Mn 3+ ; see for example [START_REF] Jurgensen | The structure of the manganese oxide on the sheath of the bacterium Leptothrix discophora: an XAFS study[END_REF][START_REF] Tebo | Biogenic manganese oxides: properties and mechanisms of formation[END_REF][START_REF] Webb | Structural characterization of biogenic Mn oxides produced in seawater by the marine Bacillus sp. strain SG-1[END_REF][START_REF] Toner | Zinc sorption to biogenic hexagonal-birnessite particles within a hydrated bacterial biofilm[END_REF][START_REF] Villalobos | Structural model for the biogenic Mn oxide produced by Pseudomonas putida[END_REF]. It was concluded from the interlayer Mn-O bond length [d( DC/TC/TE Mn-O)] derived from XRD that the interlayer does not contain Mn 2+ [START_REF] Grangeon | Structure of nanocristalline phyllomanganates produced by freshwater fungi[END_REF]. In the two pH series, the average oxidation state was 0.05 ± 0.02 higher and the amount of Na lower at high Zn/Mn ratio (Zn5dBi153 and Zn7dBi156). This variation suggests that Zn replaces both Mn 3+ and interlayer Na + , at least at high loading.

EXAFS spectroscopy

At low Zn/Mn ratio and pH 5 (Zn5dBi13), the EXAFS spectrum is nearly identical to that of the IV Zn reference (Fig. 2). At intermediate (Zn5dBi61) and even more so at high (Zn5dBi156) Zn/Mn ratio, a shoulder appears at k % 3.8 A ˚À1 and the splitting of the second oscillation at k % 6.1 A ˚À1 becomes less deep. Linear combination fits to both spectra indicate that the relative contributions of the IV Zn and VI Zn coordination species are about (89 ± 10)% and (14 ± 10)% for Zn5dBi61, and about (73 ± 10)% and (26 ± 10)% for Zn5dBi156. The high quality of the reconstructions indicates that the bonding environment of Zn can be described as a binary mixture of Zn sorbed in DC/ TC configuration (Fig. 1), apparently on the same type of surface site, but with two coordinations, tetrahedral at low surface coverage then octahedral. The EXAFS spectra at medium Zn concentration are statistically indistinguishable at pH 5 and 7 (Zn5dBi61 and Zn7dBi53, Fig. 3), and thus fitted with the same proportions of IV Zn and VI Zn. Because Zn5dBi61 corresponds to a mixture of IV Zn and VI Zn bonding environments, this spectral similarity suggests that the relative contribution of each complex is essentially independent of pH. This hypothesis is confirmed below by XRD.

Qualitative description of XRD patterns

Layer symmetry and Mn 3+ content

The XRD patterns (Fig. 4) show only broad basal reflections and asymmetric hk bands characteristic of d-MnO 2 [START_REF] Giovanoli | Vernadite is random-stacked birnessite[END_REF][START_REF] Drits | Birnessite polytype systematics and identification by powder X-ray diffraction[END_REF]. The ratio of the peak positions measured for the 11, 20 and 31, 02 bands ($1.72) is close to ffiffi ffi 3 p and the 31,02 band is nearly symmetrical, which is indicative of hexagonal layer symmetry [START_REF] Drits | Birnessite polytype systematics and identification by powder X-ray diffraction[END_REF]. Despite the sixfold layer symmetry, the structure will be described with a C-centered orthogonal unit cell and a = ffiffi ffi 3 p  b for consistency with previous structural studies of phyllomanganates. The b dimension is 2.840 ± 0.002 A ˚, indicative of a low Mn 3+ content in the hexagonal layer ($0.00-0.10 per layer octahedron; [START_REF] Villalobos | Structural model for the biogenic Mn oxide produced by Pseudomonas putida[END_REF][START_REF] Grangeon | Crystal structure of Ni-sorbed synthetic vernadite: a powder Xray diffraction study[END_REF][START_REF] Lanson | Formation of Zn-Ca phyllomanganate nanoparticles in grass roots[END_REF]. In comparison, lithiophorite, which contains 32% layer Mn 3+ [START_REF] Manceau | Natural speciation of Mn, Ni and Zn at the micrometer scale in a clayey paddy soil using X-ray fluorescence, absorption, and diffraction[END_REF], has a b dimension of 2.925 A ˚ [START_REF] Post | Crystal structure refinement of lithiophorite[END_REF].

Structural evolution with Zn loading

The width and amplitude of the 0 0 1 and 0 0 2 reflections are similar for all samples, thus the CSD dimension in the c * direction is independent of the Zn/Mn ratio and pH. From the broadening of basal reflections, the diffracting crystallites contain approximately 1.5 layers on average, therefore many constitutive layers from the d-MnO 2 nanoparticles are either monodispersed, not strictly parallel, or parallel but not spaced regularly (Fig. 4; [START_REF] Lanson | Formation of Zn-Ca phyllomanganate nanoparticles in grass roots[END_REF]. The two lowest Zn/Mn patterns are similar at pH 5 (Zn5dBi03 and Zn5dBi13) and pH 7 (Zn7dBi03 and Zn7dBi11) with a scattering tail that decreases almost monotonically from 40 to 60 °2h. A dip at $47 °2h followed by a hump at $52 °2h are clearly observed for Zn5dBi61 and Zn7dBi53 and become more prominent at highest Zn loading. This evolution is a signature of increasing amounts of high-Z atoms in DC/TC configuration [START_REF] Villalobos | Structural model for the biogenic Mn oxide produced by Pseudomonas putida[END_REF][START_REF] Drits | Birnessite polytype systematics and identification by powder X-ray diffraction[END_REF][START_REF] Grangeon | Crystal structure of Ni-sorbed synthetic vernadite: a powder Xray diffraction study[END_REF][START_REF] Lafferty | Arsenite oxidation by a poorly crystalline manganeseoxide. 2. Results from X-ray absorption spectroscopy and X-ray diffraction[END_REF], consistent with EXAFS results.

XRD modeling

The XRD simulations are shown in Fig. 5 and results summarized in Tables 2 and3. The model structures for low-Zn d-MnO 2 are close at pH 5 and 7. At low Zn loading, the layers have $0.15 vacancy per octahedral site, and the deficit of charge is approximately equally compensated for by DC/TC Mn 3+ (0.085 Â 3+) and Na + (0.24/ 0.30 Â 1+). The best model was obtained by adding 0.01-0.02 Mn above the tridentate cavities formed by three layer octahedra (TE position, Fig. 1). EXAFS spectroscopy did not allow differentiation of the relative contributions of DC Mn and TC Mn nor confirmation of the presence of TE Mn owing to the multiplicity of Mn sites having similar local environments (DC, TC, TE, E sites), and in particular a similar first oxygen shell. The average DC/TC Mn-O and TE Mn-O distances are $2.05 A ˚, which supports the conclusion that interlayer Mn is trivalent based on bond valence calculations (for more details, see [START_REF] Grangeon | Structure of nanocristalline phyllomanganates produced by freshwater fungi[END_REF].

The density of layer vacancies is $0.10 (pH 5) and $0.05 (pH 7) higher at high Zn content than at low Zn content, values that match the decrease in the number of layer Mn 3+ (0.10 and 0.06, respectively, Table 1). At medium and high loading, Zn remains sorbed at DC/TC sites dominantly in tetrahedral coordination, with the proportion of octahedral Zn increasing from $17-20% to 27-33% at medium and high loading, respectively, in agreement with EX-AFS data modeling that indicates an increase from 14 to 26%. The amount of interlayer Mn does not follow a regular pattern, decreasing first at intermediate loading then increasing again at high loading. With increasing Zn, the CSD dimension decreases steadily from $5.5 to $4.5 nm in the layer plane and remains constant perpendicular to this plane ($1 nm).

Textural evolution

Under the TEM, aggregated crystals have a mean diameter of $10 nm with a few visible euhedral hexagons (Fig. 6a andb). Observation of isolated crystals at higher resolution confirms a mean diameter of 5-10 nm (Fig. 6c), consistent with the CSD sizes of 5-6 nm in the a-b plane (Table 2), and shows that the layers are frequently curled (Fig. 6d), leading to a loss of periodicity in the a-b plane. Crystal aggregation did not allow confirmation of the 0.8-1.1 nm reduction of CSD size with Zn loading (Table 2). Along the c * axis, crystals appear to be composed of $3-4 layers (Fig 6d), compared to mean CSD sizes of $1.5 layers (Table 2).

DISCUSSION

Relation between CSD size and physical particle size

Turbostratic phyllomanganates have CSD sizes in the nanometer range, both in and perpendicular to the layer plane [START_REF] Jurgensen | The structure of the manganese oxide on the sheath of the bacterium Leptothrix discophora: an XAFS study[END_REF][START_REF] Villalobos | Structural model for the biogenic Mn oxide produced by Pseudomonas putida[END_REF][START_REF] Grangeon | Crystal structure of Ni-sorbed synthetic vernadite: a powder Xray diffraction study[END_REF][START_REF] Grangeon | Structure of nanocristalline phyllomanganates produced by freshwater fungi[END_REF][START_REF] Lanson | Formation of Zn-Ca phyllomanganate nanoparticles in grass roots[END_REF][START_REF] Bargar | Structural characterization of terrestrial microbial Mn oxides from Pinal Creek, AZ[END_REF]. There is no evidence yet that these domain sizes are close in value to the actual particle sizes. Aggregation of crystallites, with slight rotations or translations between them, commonly leads to CSD sizes in the a-b plane smaller than particle sizes [START_REF] Drits | X-ray Diffraction by Disordered Lamellar Structures: Theory and Applications to Microdivided Silicates and Carbons[END_REF]. Determining whether CSD sizes are good estimates of particle sizes is however crucial to the quantification and modeling of vernadite reactivity. A key issue is the importance of border 2 and3. sites which becomes paramount when the lateral dimension of the phyllomanganate layer is extremely small, as in the present case [START_REF] Webb | Structural characterization of biogenic Mn oxides produced in seawater by the marine Bacillus sp. strain SG-1[END_REF].

The agreement between TEM (5-10 nm) and XRD (5-6 nm) is quite good in the a-b plane. The lower XRD figure comes in part from the structural strain induced by the curling of the layers. Along the c * direction, the agreement between TEM ($3-4 layers) and XRD ($1.5 layers) is, however, less good. The difference may be explained by a variation of the radius of curvature of the bent layers, which modifies locally the layer-to-layer distance, leading to a loss in the coherence of the diffracted X-rays. This basal distance also depends on the layer charge and its compensation by interlayer species, which have no reason to be homogenous within a given manganese layer and hence across the interlayer space.

Zinc coordination

Atomic coordinates of the layer and interlayer species in Zn-sorbed d-MnO 2 are consistent with those reported previously for natural and synthetic phyllomanganates (see for example [START_REF] Drits | Structure of synthetic monoclinic Na-rich birnessite and hexagonal birnessite; I, Results from X-ray diffraction and selectedarea electron diffraction[END_REF][START_REF] Manceau | Structural mechanism of Co 2+ oxidation by the phyllomanganate buserite[END_REF]Manceau et al., , 2002a;;Lanson et al., 2002b[START_REF] Lanson | Formation of Zn-Ca phyllomanganate nanoparticles in grass roots[END_REF][START_REF] Villalobos | Structural model for the biogenic Mn oxide produced by Pseudomonas putida[END_REF][START_REF] Gaillot | Structure of the synthetic K-rich phyllomanganate birnessite obtained by high-temperature decomposition of KMnO 4 : Substructures of K-rich birnessite from 1000 °C experiment[END_REF][START_REF] Grangeon | Crystal structure of Ni-sorbed synthetic vernadite: a powder Xray diffraction study[END_REF]. Although Zn is always sorbed at DC/TC sites, its coordination varies with the Zn/Mn ratio: it is exclusively tetrahedral at Zn/ Mn <$0.05 and increasingly octahedral at higher surface loading, consistent with previous reports (Manceau et al., 2002a;[START_REF] Toner | Zinc sorption to biogenic hexagonal-birnessite particles within a hydrated bacterial biofilm[END_REF][START_REF] Boonfueng | Zn sorption mechanisms onto sheathed Leptothrix discophoraand the impact of the nanoparticulate biogenic Mn oxide coating[END_REF]. At similar loading, VI Zn is about two times more abundant in Znsorbed birnessite, the 3D-ordered variety of vernadite having thicker and larger crystals (Fig. 7; Manceau et al., 2002a;Lanson et al., 2002b). Geometry optimization based on density functional theory showed that VI Zn is stabilized by electrostatic interactions between water molecules bonded to two neighboring Zn(O,H 2 O) 6 octahedra in the interlayer, each attached to a distinct layer (Kwon et al., 2009b), in agreement with structural studies [START_REF] Drits | Structure of heavy-metal sorbed birnessite: Part 2. Results from electron diffraction[END_REF]Manceau et al., 2002a;Lanson et al., 2002b). These interactions should be weaker in the interlayer of two incoherently stacked and laterally small layers, as it is the case for d-MnO 2 . More generally, the higher abundance of defects in phyllomanganate nanoparticles likely favors IV Zn, because this complex compensates the charge deficits from the unsaturated surface oxygens at Mn vacancies more effectively than does VI Zn (Manceau et al., 2002a;Kwon et al., 2009b).

Modification of vernadite structure and reactivity with metal sorption

The density of vacant sites on synthetic vernadite is considered usually to be invariant at constant pH with the metal loading in the interlayer (e.g. [START_REF] Tonkin | Modeling sorption of divalent metal cations on hydrous manganese oxide using the diffuse double layer model[END_REF][START_REF] Villalobos | Mechanisms of Pb(II) sorption on a biogenic manganese oxide[END_REF][START_REF] Zhao | Relationship between Pb 2+ adsorption and average Mn oxidation state in synthetic birnessite[END_REF]Zhu et al., 2010b). Results from this study show that the crystal size, density of layer vacancies, and redox properties (i.e., layer Mn 3+ /Mn 4+ ratio) of vernadite, hence its sorption capacity and surface reactivity, evolve dynamically with Zn sorption over vacancy sites (Fig. 8). The density of sorption sites increases both as a result of a reduction of the CSD dimension in the a-b plane and an increase of the number of layer vacancies, this number being anti-correlated, within uncertainties, to layer Mn 3+ (Table 1). These profound transformations of the sorbent structure and chemistry are likely irreversible.

Mechanistically, Zn replaces interlayer Na + and Mn 3+ when entering the structure, as reported previously for Pb [START_REF] Zhao | Relationship between Pb 2+ adsorption and average Mn oxidation state in synthetic birnessite[END_REF]. In addition, it expels layer Mn 3+ , thus creating new layer vacancies and catalyzing the sorption process. This second effect is detected by XRD at high loading of sorbed Zn, but may occur also at low loading, where the XRD technique is insensitive to small changes in layer site occupancies. Layer Mn 3+ may be released to solution or instead may disproportionately release Mn 2+ to solution [START_REF] Silvester | Structure of synthetic monoclinic Na-rich birnessite and hexagonal birnessite; II. Results from chemical studies and EXAFS spectroscopy[END_REF]. The driving force for the decrease of layer Mn 3+ could be the 3d 10 electronic configuration of Zn that favors regular coordinations (octahedral or tetrahedral), that cannot be achieved when surface oxygens around a vacancy site are bonded to a Mn 3+ octahedron distorted by the Jahn-Teller effect (Manceau et al., 2002a). At highest loading, DC/TC Mn increased though, perhaps because of retention of Mn 3+ in the interlayer or re-adsorption of excess aqueous Mn produced by the dissolution of the nanoparticles at their edges, as suggested by the strong reduction of the CSD size (Table 2). With an initial CSD diameter of 54-58 A ˚in the a-b plane, this $15-20% reduction increases by $0.03 the number of border sites available for Zn sorption [START_REF] Webb | Structural characterization of biogenic Mn oxides produced in seawater by the marine Bacillus sp. strain SG-1[END_REF], this effect remaining minor compared to layer vacancy creation. The reduction of the CSD size and the increasing number of layer vacancies with Zn loading do not have the same dependence on pH. At pH 5 and 7, the density of layer vacancies remained equal to 0.14-0.17 per octahedral site at low and medium surface coverage and increased to 0.21-0.24 at high surface coverage (Table 3). In contrast, the CSD size decreased from low to medium surface coverage and remained stable from medium to high surface coverage at pH 5, whereas it continuously decreased at pH 7 (Table 2).

Concluding remarks

The observed modification of the phyllomanganate layer structure by surface complexation of a metal over vacancy sites from the MnO 2 layer is reported for the first time in this paper. According to the current paradigm, hydrolyzable cations had to penetrate into layer vacancies to change the layer composition and structure. This process reduces the layer charge by two valence units when Ni 2+ or Cu 2+ are incorporated into a Mn 4+ vacancy (Manceau et al., 2007a;[START_REF] Peacock | Crystal-chemistry of Ni in marine ferromanganese crusts and nodules[END_REF][START_REF] Sherman | Surface complexation of Cu on birnessite (d-MnO 2 ): controls on Cu in the deep ocean[END_REF]. However, it may also increase, not necessarily decrease, the sorbent reactivity by reductive dissolution of the manganese layer through the oxidation of Co 2+ to Co 3+ or Cr 3+ to Cr 6+ with electron transfer to Mn 3+ / Mn 4+ and the subsequent release into solution of Mn 2+ [START_REF] Manceau | X-ray absorption spectroscopic study of the sorption of Cr(III) at the oxide/water interface. I Molecular mechanism of Cr(III) oxidation on Mn oxides[END_REF][START_REF] Silvester | The mechanism of chromium(III) oxidation by Na-buserite[END_REF][START_REF] Manceau | Structural mechanism of Co 2+ oxidation by the phyllomanganate buserite[END_REF]. The new type of metal-vernadite interaction described here is an additional source of complexity for the meaningful interpretation and modeling of chemistry data on vernadite, and by extension the phyllomanganate-water interface [START_REF] Appelo | A consistent model for surface complexation on birnessite (d-MnO 2 ) and its application to a column experiment[END_REF][START_REF] Tonkin | Modeling sorption of divalent metal cations on hydrous manganese oxide using the diffuse double layer model[END_REF]. MB4 is from a marine nodule (Marcus et al., 2004a), 3SP and 6KR are from quartz-coatings (Manceau et al., 2007a), Festuca was produced by the graminaceous Festuca rubra [START_REF] Lanson | Formation of Zn-Ca phyllomanganate nanoparticles in grass roots[END_REF], biomin1 and biomin3 by the bacterial strain Pseudomonas [START_REF] Toner | Zinc sorption to biogenic hexagonal-birnessite particles within a hydrated bacterial biofilm[END_REF], Zn-dMnO 2 [START_REF] Toner | Zinc sorption to biogenic hexagonal-birnessite particles within a hydrated bacterial biofilm[END_REF] and Zn-HMO [START_REF] Boonfueng | Zn sorption mechanisms onto sheathed Leptothrix discophora and the impact of the nanoparticulate biogenic Mn oxide coating[END_REF] are synthetic samples. Birnessite data are from Lanson et al. (2002b) and Manceau et al. (2002a). Birnessite is a 3D-ordered phyllomanganate and vernadite a turbostratic phyllomanganate.

Fig. 1 .

 1 Fig. 1. Possible inner-sphere cation complexes at the d-MnO 2 surface. Octahedral and tetrahedral coordinations are represented as closed polyhedra (left) and sorption sites as ball-and-sticks (right). DC, TC, TE and E refer to double-corner sharing, triplecorner sharing, triple-edge sharing interlayer sites and octahedral layer sites, respectively.

Fig. 2 .

 2 Fig.2. Zn-K-edge EXAFS spectra of Zn5dBi13, Zn5dBi61 and Zn5dBi156 (solid lines) with their best simulations overlaid (dashed lines). The spectra of the VI Zn (chalcophanite) and IV Zn ( IV Znsorbed vernadite) references are shown on top. Fitting residuals are shown at the bottom. Zn5dBi03 was too diluted to measure a good quality spectrum.

Fig. 3 .

 3 Fig.3. Zn-K-edge EXAFS spectra of Zn5dBi61 (solid line) and Zn7dBi53 (dashed line), with difference at the bottom.

Fig. 4 .

 4 Fig. 4. XRD patterns of Zn-sorbed d-MnO 2 . (a) pH 5, (b) pH 7. The high-angle regions on the right side of the grey bars were scaled by a factor 5. In each series, the sample with the lowest Zn/Mn ratio is shown as a light grey line to emphasize the evolution of the XRD traces with Zn content (arrows).

Fig. 5 .

 5 Fig. 5. Simulations of the XRD patterns for Zn-sorbed d-MnO 2 . (a) 11, 20, 02, 31, and 22, 40 scattering bands. (b) 0 0 l basal reflections. Black crosses are experimental data, solid overplots are calculated profiles, and solid blacklines at the bottom are difference plots. Parameters used for the simulations are listed in Tables2 and 3.

Fig. 6 .

 6 Fig. 6. Electron micrographs of Zn-sorbed d-MnO 2 . (a) Overview of Zn5dBi156. (b) View of a hexagonal shaped Zn5dBi03 crystal. (c) Detailed view of Zn5dBi156 crystals. (d) Lattice fringe images of Zn5dBi03 crystals with the electron beam parallel to the layers.

Fig. 7 .

 7 Fig. 7. Fraction of VI Zn to total Zn sorbed on phyllomanganate as a function of Zn loading. Solid circles: this study; solid triangles: previous studies on vernadite; solid diamonds: previous studies on birnessite. MB4 is from a marine nodule(Marcus et al., 2004a), 3SP and 6KR are from quartz-coatings(Manceau et al., 2007a), Festuca was produced by the graminaceous Festuca rubra[START_REF] Lanson | Formation of Zn-Ca phyllomanganate nanoparticles in grass roots[END_REF], biomin1 and biomin3 by the bacterial strain Pseudomonas[START_REF] Toner | Zinc sorption to biogenic hexagonal-birnessite particles within a hydrated bacterial biofilm[END_REF], Zn-dMnO 2[START_REF] Toner | Zinc sorption to biogenic hexagonal-birnessite particles within a hydrated bacterial biofilm[END_REF] and Zn-HMO[START_REF] Boonfueng | Zn sorption mechanisms onto sheathed Leptothrix discophora and the impact of the nanoparticulate biogenic Mn oxide coating[END_REF] are synthetic samples. Birnessite data are fromLanson et al. (2002b) andManceau et al. (2002a). Birnessite is a 3D-ordered phyllomanganate and vernadite a turbostratic phyllomanganate.

Fig. 8 .

 8 Fig. 8. Evolution of coherent scattering domain sizes in the a-b plane (triangles) and layer vacancies (circles) as a function of Zn/ Mn ratio for Zn-sorbed d-MnO 2 prepared at pH 5 (open symbols) and 7 (solid symbols).

Table 1

 1 Chemical composition of Zn-sorbed d-MnO 2 expressed as atomic ratios. coherent scattering domains (CSDs) in the a-b plane were determined first from the simulation of the high-angle region (30-80 °2h) dominated by hk diffraction bands, hkl reflections being unresolved owing to sample turbostratism. The hk bands at 2.42 A ˚, 1.41 A ˚and 1.22 A ˚were indexed as 11, 20, 31, 02 and 22, 40 with a C-centered unit cell. The a and b parameters were calculated from the position of the 31, 02 band

	Sample	Zn/Mn	Na/Mn	Mn ox. degree a	Layer Mn 3+,b
	Zn5dBi03	0.0032 ± 0.0013	0.2417 ± 0.0024	3.76 ± 0.01	0.13 ± 0.01
	Zn5dBi13	0.0132 ± 0.0043	0.2563 ± 0.0068	3.79 ± 0.01	N.D. c
	Zn5dBi61	0.0613 ± 0.0024	0.2207 ± 0.0040	3.79 ± 0.01	0.12 ± 0.01
	Zn5dBi153	0.1531 ± 0.0012	0.0784 ± 0.0012	3.85 ± 0.01	0.03 ± 0.01
	Zn7dBi03	0.0030 ± 0.0018	0.3153 ± 0.0025	3.83 ± 0.02	0.06 ± 0.01
	Zn7dBi11	0.0108 ± 0.0043	0.3375 ± 0.0087	3.83 ± 0.01	N.D. c
	Zn7dBi53	0.0531 ± 0.0020	0.2841 ± 0.0039	3.83 ± 0.01	0.06 ± 0.01
	Zn7dBi156	0.1555 ± 0.0021	0.1624 ± 0.0021	3.88 ± 0.01	0.00 ± 0.02

a Standard errors calculated from triplicates

[START_REF] Webster | Statistics to support soil research and their presentation[END_REF]

). b Layer Mn 3+ calculated from the average oxidation degree and the amount of interlayer Mn deduced from XRD. c Not determined because the XRD patterns are similar to Zn5dBi03/Zn7dBi03. of

Table 2

 2 Crystal data. The CSD size in the a-b plane is expressed as the mean diameter of disk-shaped domains.

	Sample	a (A ˚)	b (A ˚)	d (0 0 1) (A ˚)	Average CSD size (nm)		R wp (%) b	GoF (%) b
					In the a-b plane a	Along the c * axis
	Zn5dBi03	4.919	2.840	7.2	5.4	1.1	5.25-6.99	9.24-5.05
	Zn5dBi61	4.922	2.842	7.2	4.7	1.1	3.53-5.97	4.25-3.89
	Zn5dBi153	4.915	2.838	7.2	4.6	1.1	2.92-4.56	3.07-2.53
	Zn7dBi03	4.929	2.846	7.2	5.8	1.1	4.37-6.82	6.41-5.22
	Zn7dBi53	4.922	2.842	7.2	5.2	1.1	3.84-5.99	5.05-4.03
	Zn7dBi153	4.915	2.838	7.2	4.7	1.2	3.52-4.63	4.66-2.82

a b Calculated over the low-and high-angle regions, respectively.

Table 3

 3 Atomic coordinates and site occupancies of Zn-sorbed vernadite.

	Atom	x a	yz	Occ b	Occ	Occ	Occ	Occ
				Zn5dBi03	Zn5dBi61	Zn5dBi153	Zn7dBi03	Zn7dBi53

ACKNOWLEDGMENTS

Nicolas Geoffroy is thanked for assistance with XRD data collection, and Jon Chorover and three anonymous reviewers for their constructive comments and suggestions on the manuscript. This work was supported by the Universite ´Joseph Fourier through its Po ˆle TUNES, and by the INSU-CNRS "actions the ´matiques". The ALS is supported by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences Division of the U.S. Department of Energy under Contract DE-AC03-76SF00098 at the Lawrence Berkeley National Laboratory.

Note: Symmetry operations: (x, y, z), (Àx, Ày, Àz), (x +½,y +½,z), (Àx+½, Ày +½,Àz). The C2/m space group can be used to represent the structure model. However, care has to be taken to not generate equivalent positions from adjacent layers because d-MnO 2 has no 3D periodicity. a Atomic coordinates x, y, z are expressed as fractions of the a, b and d 001 parameters, respectively. b Occupancies are given per half unit cell (i.e., per octahedral layer site), and as the sum of the (x, y, z) and (Àx, Ày, Àz) equivalent sites. c Atomic sites (E, TC, TE) and coordinations (IV, VI) are schematized in Fig. 1. The Debye-Waller thermal factors (B) were fixed to 0.5 A ˚2

for Mn1, 1.0 A ˚2 for O1, 2.0 A ˚2 for O6 and K + , and 1.5 A ˚2 for the other species. d DC and TC sites are undistinguishable by XRD in such disordered structures owing to their similar atomic coordinates [START_REF] Grangeon | Crystal structure of Ni-sorbed synthetic vernadite: a powder Xray diffraction study[END_REF].

APPENDIX A. SUPPLEMENTARY DATA

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.gca.2012.02.019.


Gabriel Guenoun
email: gabriel.guenoun@ens-paris-saclay.fr

Jean-Yvon Faou

Gilles Régnier

Nicolas Schmitt

Stéphane Roux

Lmt

Test Method Thermal cycling of cold-pressed PTFE compacts: Reversible and irreversible behavior

Keywords:

Cold uniaxial pressed PTFE compacts were subjected to thermal cycles of increasing maximum temperature below melting temperature, and thermal expansion was followed in both the compaction and transverse directions. The measurements reveal that thermal expansion consists of two distinct contributions: i) an irreversible part that is controlled only by the maximum temperature experienced by the sample, and ii) a reversible, or thermo-elastic, part that is observed while cycling below the maximum temperature. Moreover, both of these thermal strains exhibit marked anisotropy, resulting from the cold oedometric compaction of the sample. A quantitative analysis of these eigenstrains is proposed, following a formal analogy with elasto-plasticity. Finally, it is shown that such behavior is specific to cold-pressed compacts as sintered samples exhibit isotropic and purely reversible thermo-elastic behavior.

Introduction

Well-known for its remarkable properties, Polytetrafluoroethylene (PTFE) is employed in various engineering applications. The main assets of this material are its extremely low coefficient of friction, high thermal stability, good electrical insulation, resistance to corrosion, hydrophobicity and biocompatibility [START_REF] Biswas | Friction and wear of PTFE-a review[END_REF][START_REF] Cox | Thermal degradation of fluorine-containing polymers. Part I. Degradation in vacuum[END_REF][START_REF] Zhang | Superhydrophobic PTFE surfaces by extension[END_REF]. This unique semi-crystalline polymer owes its attributes to the presence of fluorine atoms all around the carbon chain. Fluorine is responsible for the chemical inertness of the polymer and for the low friction as the polymer chains do not bond to each other [START_REF] Golub | Reactions of atomic oxygen (O(3P)) with various polymer films[END_REF][START_REF] Giannetti | Semi-crystalline fluorinated polymers[END_REF]. PTFE polymerizes in extended chain configuration leading to very high crystallinity (more than 90%) whereas melt-crystallized PTFE is much less crystalline (around 50%) due to chain entanglements [START_REF] Melillo | Extended-chain crystals: VIII. Morphology of polytetrafluoroethylene[END_REF]. Several phase transitions exist in PTFE at atmospheric pressure. At room temperature two first-order crystalline phase transitions occurs, namely Triclinic phase II -Hexagonal phase IV at 19 °C and Hexagonal phase IV -Pseudo-hexagonal phase I at 30 °C [START_REF] Brown | The role of crystalline phase on fracture and microstructure evolution of polytetrafluoroethylene (PTFE)[END_REF]. Two second-order transitions occur in PTFE. The -transition around -100°C seems to correspond to the glass transition of mobile amorphous fraction (MAF), and the -transition around 130 °C to the glass transition of rigid amorphous fraction (RAF) [START_REF] Dlubek | Glass transition and free volume in the mobile (MAF) and rigid (RAF) amorphous fractions of semicrystalline PTFE: a positron lifetime and PVT study[END_REF][START_REF] Calleja | Where is the glass transition temperature of poly(tetrafluoroethylene)? A new approach by dynamic rheometry and mechanical tests[END_REF]. This polymer is processed from powder with very specific methods such as billet pressing and sintering, ram extrusion and film casting.

The choice of the manufacturing process and of type of PTFE powder is made according to the application [START_REF] Ebnesajjad | Non-melt Processible Fluoropolymers: the Definitive User's Guide and Data Book Plastics Design Library[END_REF]. There are two types of polymerization of TFE available, leading to different pure PTFE resins: emulsion polymerized PTFE and suspension polymerized PTFE. From the former, PTFE dispersion and fine powder are obtained. From the latter, granular PTFE is obtained. The granular PTFE can be separated into two categories: low flow and free flow resins depending on the size of the grains (fine and large respectively). All of these powders can be mixed with fillers.

PTFE powder pressing, sintering and skiving is used to create films to make bearing components. Low flow (also called fine cut) resin is pressed into a die to form a cylinder called a "billet" [START_REF] Frédy | Modelling of the mechanical behaviour of two pure PTFE powders during their compaction at room temperature[END_REF]. The preform is then sintered to reduce and homogenize porosity created during compaction and to blur the powder grain interfaces thanks to chain entanglements, and thereby enhance the final mechanical properties. During the thermal treatment large strains occur due to the melting and recrystallization of the polymer [START_REF] Canto | Experimental identification of the deformation mechanisms during sintering of cold compacted polytetrafluoroethylene powders[END_REF]. Thermal gradients coupled to these strains lead to strain incompatibilities, and hence stress concentration that could damage the billet [START_REF] Andena | Simulation of PTFE sintering: thermal stresses and deformation behavior[END_REF].

During the sintering cycle, the PTFE experiences significant strains. A convenient concept to characterize the thermo-mechanical behavior is that of eigenstrains, namely the strain that would be measured in the polymer if microstructure and temperature were always spatially uniform (and hence devoid of any kinematic incompatibility). The overall eigenstrain of PTFE is due to several physical mechanisms such as thermal expansion dependent on the crystallinity content, melting, crystallization [START_REF] Bassett | On crystallization phenomena in polytetrafluoroethylene[END_REF], gas diffusion and porosity closure [START_REF] Canto | Experimental identification of the deformation mechanisms during sintering of cold compacted polytetrafluoroethylene powders[END_REF]. This eigenstrain is observed to be anisotropic as induced by the uniaxial compaction that forms a transverse isotropic material. This paper aims to study the overall eigenstrain of a PTFE compact through arbitrary thermal histories without melting, and to unravel the role of different mechanisms.

In section 2, dilatometry measurements during thermal cycles reveal an unexpected evolution of the eigenstrain, formally similar to elastoplasticity, that can be decomposed into reversible and irreversible parts. A descriptive model is then developed in section 3 to express this strain as a function of the maximum experienced temperature. The tensorial aspect of the reversible and irreversible parts of the eigenstrain is studied and reveals the anisotropy induced by the initial cold pressing. This observation translates into a swelling of the material as a result of internal stress relaxation, suggesting the creation of micro-or mesoporosity.

Experimental

In order to better understand the strain induced by thermal treatment, uniaxially compacted PTFE samples were subjected to different heating/cooling histories, and followed through dilatometry. To avoid the very large dimensional changes that go together with melting, unless explicitly mentioned, the maximum temperature was kept below that of the melting transition.

Material

A fine cut granular PTFE resin was chosen. This type of resin is currently used for molding and is suitable for compounding with fillers because of the small particle size which is in the range of 20-100 μm [START_REF] Ebnesajjad | Non-melt Processible Fluoropolymers: the Definitive User's Guide and Data Book Plastics Design Library[END_REF]. The initial crystallinity content is above 90%.

Thermal characterization

A calorigram of compacted PTFE is shown Fig. 1. This experiment was performed on a differential scanning calorimeter (DSC) Q10 from TA instruments with a 5 mg sample heated up at 20 °C/min. The calorigram shows that the melting temperature of this resin is close to 340 °C. It highlights an inflexion close to 250 °C revealing a diffuse phase transition below the melting peak that could correspond to the melting of smaller crystals.

Sample preparation

The different specimens were prepared at the same time with PTFE resin from the same batch. PTFE powder is recommended to be conditioned at 21-25 °C at atmospheric pressure for better compaction [START_REF] Ebnesajjad | Non-melt Processible Fluoropolymers: the Definitive User's Guide and Data Book Plastics Design Library[END_REF]. These precautions ensure very reliable and reproducible experiments.

The powder was uniaxially compacted at 50 MPa in a die using a universal testing machine to form cubes of 8 mm long edges (Fig. 2a). The PTFE cubes were removed from the die and kept at room temperature for at least 2 days to allow entrapped air to diffuse out before being tested.

Microstructural analysis

On the SEM image of the PTFE powder in Fig. 3, PTFE particles in the range of 20-100 μm can be observed. Those particles appear as fluffy flakes with a complex sub-microstructure (Fig. 3b). The individual size of those elements is in the range of 100-500 nm. Therefore, two types of porosities can exist in the material after compaction, one macro-porosity to be linked with the particles size itself and a microporosity at a submicrometric scale.

The compaction pressure controls the level of final macro-porosity as shown in Fig. 4 indicating the density of the PTFE sample as a function of the compaction pressure. For a compaction pressure of 50 MPa, the level of macro-porosity can be neglected as the density is not increasing at higher pressures. Moreover, no porosity was observed using X-ray computed microtomography with 1 μm resolution.

Another impact of the compaction is the induced orientation texture. As the PTFE is uniaxially compacted in a mold, the crystals are reoriented in the transverse directions (perpendicular to the compaction direction). A Herman's orientation factor for the chains orientation of -0.1 was determined in the compaction direction via X-Ray diffraction [START_REF] Ward | Structure and Properties of Oriented Polymers[END_REF].

Dilatometric measurements

A thermomechanical analyzer TMA/SDTA 840 from Mettler Toledo was used to perform the dilatometry tests. The PTFE cubic specimen was placed inside an oven and a prescribed temperature history was applied. The thermal cycle was chosen to be slow enough to ensure good temperature homogeneity inside the sample. The temperature difference was limited to 2 °C between the core and the edge of the sample for a heating rate of 1.5 °C/min (result obtained by thermal simulation). The force applied by the probe on the sample was maintained at 0.01 N. Assuming a homogeneous state (from quasi-static temperature variations) the true (or logarithmic) strain ii in direction i is estimated from the displacement u i and initial size L i , as

+ u L log 1 ii i i (1)
all along the thermal cycle (no implicit summation on index i). Note that this is the mean strain from the initial state considered as a reference, and the current state. Resorting to true strains allows us to change reference if so desired by mere subtraction of the strain of the newly chosen reference state. Because of the homogeneity assumption and the assumption that the applied force is null, the measured strains are actually "eigenstrains" for constitutive law formulation of the thermo-mechanical behavior.

The dilatometry test was performed on different samples, some to test the compaction direction (CD) and others for the transverse direction (TD) as the samples are transversely isotropic due to the uniaxial compaction (Fig. 2b).

From this transverse isotropy symmetry, the strain tensor is expected to be fully characterized by the TD and CD strain components. Choosing the third axis along the CD, the strain tensor assumes the following form

= 0 0 0 0 0 0 TD TD CD (2)
In this study, successive thermal cycles with an increasing maximal temperature were chosen to investigate the strain behavior of compacted PTFE powder under thermal treatment below melting temperature. The thermal path consisted of three successive cycles reaching, respectively, 175 °C, 250 °C and 300 °C (Fig. 5a). The heating and cooling rates were 1.5 °C/min and the holding time at maximal temperature was 30 min. The PTFE specimen was held for 5 min at 25 °C before each new cycle. A final cycle ended the thermal path to complete the sintering of the sample, with the same heating and cooling rates with a longer plateau of 100 min above the melting temperature at 370 °C. In this paper, = T T 0 , refers to the temperature variation counted from the reference temperature T 0 which was chosen to be 25 °C.

Results and discussion

Reversible and irreversible eigenstrain decomposition

Fig. 5b shows the true strain curves for CD and TD as function of time.

The major strain variations are observed during the last thermal cycle at the end of the test and correspond respectively to melting and crystallization of PTFE compact as crystalline phase is denser than amorphous phase. The strain due to crystallization stretches on a longer temperature range than melting. The melting mechanism is essentially controlled by the crystallite size distribution of the PTFE resin [START_REF] Hoffman | The rate of crystallization of linear polymers with chain folding[END_REF]. In contrast, the crystallization is ruled by different mechanisms that depend on the cooling rate. The crystallization mechanism is a complex and not fully understood topic due to the presence of secondary crystallization [START_REF] Ozawa | Nonisothermal crystallization of poly(tetrafluoroethylene)[END_REF][START_REF] Seo | Nonisothermal crystallization kinetics of polytetrafluoroethylene[END_REF]. Because of this, the present study does not address melting and crystallization mechanisms, but rather focuses on the earlier stages prior to melting which, although simpler, reveal unexpected manifestations of stress relaxation already observed by Canto et al. [START_REF] Canto | Experimental identification of the deformation mechanisms during sintering of cold compacted polytetrafluoroethylene powders[END_REF]. Nevertheless, the last cycle that goes above melting temperature is shown in some of the following figures in order to see the very strong effect of sintering.

The CD and TD strains versus time are shown in Fig. 5b with the reference chosen at the initial state at temperature T 0 . A first observation is that the CD and TD directions show very different strains, even in the first three cycles. This means that the cold uniaxial compaction process induces pronounced anisotropy [START_REF] Andena | Simulation of PTFE sintering: thermal stresses and deformation behavior[END_REF][START_REF] Frédy | Modeling of the Mechanical Behavior of Polytetrafluoroethylene (PTFE) Compounds during Their Compaction at Room Temperature[END_REF][START_REF] Li | Measurement of anisotropic behavior of dry cohesive and cohesionless powders using a cubical triaxial tester[END_REF][START_REF] Galen | Strength anisotropy in cold compacted ductile and brittle powders[END_REF]. After successive cycles, the sample tends to dilate in the compaction direction (CD), and to contract in the transverse direction (TD), and the apparent coefficient of thermal expansion appears to differ in these two directions, again a manifestation of compaction-induced anisotropy.

When plotted as a function of temperature rather than time, as done in Fig. 6, it is observed again that sintering has a very major impact on the dilatometric behavior and, as mentioned above, the present study focuses on the pre-melting behavior, as shown in Fig. 6b andd. In this first subsection, any of the principal eigenstrain, CD or TD, is considered independently without index.

These figures first show that, even in the absence of phase transformation, the thermo-mechanical behavior is not a reversible thermal dilation, in as much as the thermal eigenstrain is not given by a single function of the temperature variation . However, when the temperature variation is decreased from any previously experienced peak value , then a one-to-one relationship between eigenstrain and is observed, as can be seen for all branches B A i i in Fig. 6b or 6d. These curves seem, however, to depend on but in a rather simple way: mere translations along the strain axis allow all reversible branches to superimpose exactly. This observation suggests that two parameters are needed to characterize the thermo-mechanical eigenstrains: 1) the current (relative) temperature, , along a reversible path and 2) the maximum previously experienced relative temperature,

= t t ( ) max[ ( )] t t (3)
that controls the overall translation of the thermal response. Moreover, an additive decomposition of the overall thermal eigenstrain into two contributions can be made:

= + t t [ ( )] ( ( )) ( ( )) rev irr ( 4
)
where rev is the thermal expansion that only depends on the instantaneous relative temperature, , and irr is an irreversible eigen- strain that only depends on the maximum of the previously encountered relative temperature. Note that the notation t [ ( )] refers to a functional dependence over the entire (past) temperature history, whereas t ( ( )) refers to a function dependence on the scalar instantaneous variation of temperature occurring at time t.

This additive strain decomposition is formally reminiscent of the one encountered in (rate-independent) elasto-plasticity, but where relative temperature plays the role of stress. Introducing the functions defining the reversible and irreversible eigenstrains for i {CD, TD}:

= = f ( ) ( ) ( ) ( ) i i i i rev irr (5)
It is easy to have access these functions experimentally by noting the following property: In the thermal cycles, one can select those instants of time noted + t where = + + t t ( ) ( ). For those, the eigenstrain obeys

= = + + + + + + + + t t t t f t g t ( ( )) ( ( )) ( ( )) ( ( )) ( ( )) ( ( )) i i i i i i envel rev irr (6)
This relation is the "envelope" curve (path

O A A A 1 2
3 ) of Fig. 6b or 6d and drawn in purple. Conversely, the longest descending temperature ramp (A B 3 3 ), corresponds to instants of time noted t for which is frozen to the temperature reached at point A 3 , 3 , and hence

= = + + t t t f t g ( ( )) ( ( )) ( ( )) ( ) ( ( )) ( ) i i i i i i desc rev irr 3 3 (7)
Thus, the reversible eigenstrain function is obtained (for < 3 ) as

= f ( ) ( ) (0) i i i desc desc (8)
while the irreversible part is

= g f ( ) ( ) ( ) i i i envel (9)
An illustration of the evaluation of these eigenstrains in the TD and CD directions is given in Fig. 7a andb.

The irreversible part of the eigenstrain g i is very close to 0 up to about 60 °C, just as if the PTFE sample had already experienced such a maximum temperature in its past. In some way, the function g encodes a memory of the sample. it may be that the effect of temperature can also be obtained with time through similar, but now thermally activated, irreversible microscopic events. This temperaturetime analogy has, however, not been studied herein.

Both CD and TD directions obey the same formalism, thereby reducing the full history dependent behavior to four (reversible and irreversible parts, CD and TD directions) scalar functions. However, they show very different quantitative contributions. This sheds some light on the subtle question of anisotropy.

The quantification of anisotropy can be done from the direction of the path followed by eigenstrains in strain space. The symmetry of the problem reduces the tensorial nature of the strain tensor to only two components CD and TD.

From 200 °C and above, some new features that were not visible at lower temperatures begin to appear. First, the reversible part is very close to linear up to 200 °C, and markedly non-linear (yet still reversible) above. Second, a more and more pronounced gap appears at temperature reversal points of the cycles (Fig. 6), suggesting the progressive relevance of viscous effects that could be neglected at lower temperatures [START_REF] Araki | Stress relaxation of polytetrafluoroethylene in the vicinity of its glass transition temperature at about 130°C[END_REF]. Third, the irreversible part of the eigenstrain seem to reveal higher and higher densification, which may be due to a different phenomenon than in the low temperature regime where a net expansion is observed. One may speculate that the collapse of nanocavities may take place and contribute to the irreversible mechanism at such high temperatures. The melting of smaller crystals suggested by the calorigram shown in Fig. 1 around 250 °C may help close nanocavities. The plots of the irreversible and thermo-elastic (reversible) eigenstrains in CD and TD against each other are shown in Fig. 8. In such plots, an isochoric (isovolumic) transformation is a straight line of slope -2 because of the transversely isotropic character of the specimen.

In Fig. 8a, the irreversible eigenstrain contribution corresponds at low temperature to a fixed direction in strain space, so that the ratio of volumetric to deviatoric strain is constant and positive (meaning an irreversible swelling). Because no phase transformation is expected in this range of temperature, such an effect could correspond to the opening of nanopores. The scale of those pores is termed nano to signify submicrometric, as they are not seen in x-ray computed microtomography. It would be interesting to use small angle x-ray scattering to investigate this point. At about 200 °C, a contraction character begins to set in and, as mentioned above, it could correspond to the closing of nano-cavities.

The thermo-elastic eigenstrain contribution shown in Fig. 8b is remarkably linear and reveals anisotropic dilation. Unlike the irreversible eigenstrain, this behavior remains linear at higher temperatures (at 250 °C and above). This indicates that the origin of the anisotropy is different for the reversible and irreversible contributions. For the reversible eigenstrain, which can be associated to the thermal expansion, the anisotropy may be induced by the crystalline texture caused by the compaction. A possible origin of the irreversible eigenstrain anisotropy is discussed in the next subsection.

Proposed mechanisms for irreversible eigenstrains

In order to distinguish the respective contribution of two categories of porosities (macro and micro) mentioned in subsection 2.4, varying the compaction pressure provided some insight. At the highest compaction pressure considered in this study, 50 MPa, no macro-pores are observed to remain in the compacted sample. In contrast, we supposed that for lower pressures, (pressures down to 10 MPa were tested) some macroporosity is left after compaction as the density is not saturated (Fig. 4). However, it is observed to be stable when the temperature is varied, up to temperature close to fusion, where surface tension leads to closure of the pores. For lower temperatures, macro-pores when they exist seem not to play any significant role. Besides, for these different compaction pressure, the dilatometry experiment revealed a similar irreversible expansion behavior. Therefore, the latter characteristic is believed to be due to the densification that takes place at the nanoscale. This is consistent also with the observation that no porosity became visible at the 1 μm scale resolution from tomography of samples compacted at 50 MPa, after the thermal cycles of the dilatometry experiment. The irreversible expansion due to the thermal cycle did only generate submicrometric pores.

From the above observations, it is deduced that the mechanism for the irreversible expansion of the sample:

-has to find its origin in the initial cold mechanical compaction -has to result from the deformation of the constitutive particles -has to involve a stored mechanical energy that will allow to compete with the surface tension cost of creating a pore -has to correspond to a metastable state becoming unstable under a temperature rise.

These points led us to propose a mechanistic scenario whereby the closing a micro-pores goes together with an internal stress field (where the potential elastic energy is stored). Porosity (at least supermicrometric) disappears during compaction under a macroscopic oedometric strain, as sketched in Fig. 9a. Elementary particles are thus deformed plastically, so that they come together and stick from interparticle adhesion (Fig. 9b), that opposes residual stress due to the deformation of particles. The oedometric compression induces polarization of these internal stresses, as shown in (b). As temperature increases, such contacts may snap open, with a local kinematics that is illustrated in Fig. 9c. Even if locally rather complex rearrangement of grains may exist, the net effect of a local contact opening can be inferred from the classical "Eshelby" problem, where an inclusion embedded in an elastic matrix undergoes a plastic strain [START_REF] Nemat-Nasser | Micromechanics: Overall Properties of Heterogeneous Materials[END_REF]. Actually, all complications coming from the local details of such events can be accounted for by a multipolar expansion of type terms vanishing with distance to the inclusion center r as r with d where = d 3 is the space dimension. The dominant contribution is the only one that survives at the macroscopic scale and is precisely the usual "Eshelby" solutions, that contains three elementary purely deviatoric components polarized along x, y or z and one isotropic term (dilation of the inclusion). A finite density of such inclusions will produce, at a macroscopic scale, a strain reflecting the symmetry of the locally locked residual stress. In our case, it is expected that the macroscopic strain released by these local contact break-ups is simply opposed to the oedometric compaction, in agreement with the observed irreversible thermal eigenstrain.

It is important to note that this elementary stress field involves a tension at the scale of the micro-pore (nm range) that has to be counterbalanced by a compression at a further distance. However the latter stress field decreases very fast with the distance r to the initial pore (Eshelby outer field decaying as r 3 ). This is to be contrasted with a structural internal stress field (such as a skin compression balanced by a bulk traction as produced e.g. by thermal tempering or shot-peeing). As a result, it is not possible to reveal these internal stresses by cutting or drilling because the net effect of introducing a free surface has to balance out at the scale of the micro-pores. Hence ideally no more than a nano-roughness should be expected. Nevertheless, when a spatially uniform distribution of such locked-in internal stresses is freed a uniform macroscopic strain is expected, consistently with the observed irreversible dilation.

At high temperature, the elastic properties of the material are expected to soften, (possibly involving viscous relaxation) and surface tension of nanocavities may proceed with a similar mechanism.

Sintered PTFE

In order to highlight the specificities of the green compact, a similar dilatometry experiment was performed on a compacted PTFE sample first sintered with a thermal cycle above melting temperature and 100 min hold time at 370 °C. Then, a similar temperature cycling (as shown in Fig. 2a) was applied to the sintered specimen. The strains in CD and TD corresponding to the three thermal cycles are shown in Fig. 10 as a function of the temperature. Those strains reveal no irreversibility during the successive cycles. This suggests that most residual stresses have been relaxed after the melting of PTFE, and no residual stress susceptible to be relaxed by thermal activation has been regenerated during the recrystallization. The sintering of PTFE leads to the loss of granular structure as the particles interfaces are merged during melting and recrystallization. This could also explain that no residual stress can be trapped in the same way as for the compacted nascent powder.

Also, the behavior appears to be isotropic [START_REF] Canto | Experimental identification of the deformation mechanisms during sintering of cold compacted polytetrafluoroethylene powders[END_REF], the expansion comes mainly from the amorphous phase which is more likely to be isotropic, and the recrystallized PTFE is much more amorphous (around 50%) than nascent PTFE (more than 90% crystalline). It is then also important to note that the thermal expansion is very different from sintered PTFE and green compact of PTFE due to this difference of crystallinity content, so that these results cannot be used to compare with the reversible part of the unsintered sample. The thermal expansion stops being linear with temperature above 130 °C, which may be due to the glass transition of RAF. This transition may impact sintered PTFE more than nascent PTFE as the amorphous fraction is much more important after sintering [START_REF] Araki | Thermal expansion coefficient of polytetrafluoroethylene in the vicinity of its glass transition at about 400°K[END_REF]. Around 250 °C, the curvature of the strain may be explained by other phenomena such as melting of smaller crystals coming from secondary crystallization.

Conclusions

Compacted nascent PTFE powder presents a peculiar behavior under thermal cycling. In addition to a reversible thermo-elastic contribution, an irreversible contribution has been shown. The latter may be progressively erased by previous thermal treatment at higher and higher temperatures. Such behavior is formally reminiscent of an elasto-plastic behavior, with an additive decomposition of strains between the reversible and irreversible parts. Moreover, both of these strains reveal anisotropic behavior that is due to the preceding cold compaction process of nascent PTFE powder. Remarkably, after sintering, the irreversible part disappears, and the anisotropy (that still exists in the microstructure) has no manifestation in the thermal cycles studied.

It is speculated that the irreversible part of the thermal eigenstrain is due to local stress relaxation mechanisms, occurring at a submicrometer scale. Above 250 °C, some other mechanisms appear that modify the strain behavior of PTFE, such as possible porosity closure.

To refine those observations and deepen the understanding of this phenomenon, it would be interesting to study the residual stress relaxation of PTFE with different multiaxial compactions such as hydrostatic or biaxial compaction. This should have an effect on the anisotropy of the relaxation strain by modifying the residual stress formation. Further investigations will be performed on the strain behavior to study melting and crystallization of PTFE and the variation of thermal expansion during a complete sintering cycle.

Fig. 1 .

 1 Fig. 1. DSC melting peak of compacted PTFE powder. A zoom is shown at lower temperatures where a change is observed around 250 °C.

Fig. 2 .

 2 Fig. 2. (a) PTFE powder uniaxially compacted inside a die to form small PTFE cubes; (b) dimension variations of the cubic sample measured during a given thermal treatment in the compaction direction (CD) and in the transverse direction (TD).

Fig. 3 .

 3 Fig. 3. SEM observation of the PTFE powder used for the experiments. (b) is a zoom of (a). The images are coming from an earlier work [15].

Fig. 4 .

 4 Fig. 4. Density of the PTFE sample as function of the applied pressure during uniaxial compaction.

Fig. 5 .

 5 Fig. 5. Thermal cycle applied to the small PTFE block (a) and related measured true strain in compaction direction (CD) and transverse direction (TD) as function of time (b).

Fig. 6 .

 6 Fig. 6. (a) Measured true strain in TD; (c) Measured true strain in CD; (b) zoom of (a) and (d) zoom of (c) on the three first cycles prior to melting, where the followed path is O-A 1 -B 1 -A 1 -A 2 -B 2 -A 2 -A 3 -B 3 -A 3 . Branches A i -B i appear to be reversible behaviors valid when the temperature remains lower than that of point A i .

Fig. 7 .

 7 Fig. 7. Evaluation of the overall eigenstrain split in the reversible and irreversible contributions for (a) the TD direction and (b) the CD direction.

Fig. 8 .

 8 Fig. 8. Residual stress relaxation in CD as function of the residual stress relaxation in TD for the (a) irreversible and (b) reversible eigenstrains.

Fig. 9 .

 9 Fig. 9. Sketch representing PTFE particles uniaxially compacted (a). The particles deform and trap residual stress. The compacted sample is removed from the mold (b) and is relaxed by applying a thermal treatment (c).

Fig. 10 .

 10 Fig. 10. Measured true strain in CD and TD for a sintered PTFE cube during successive thermal cycles below melting temperature.

Acknowledgements

The authors would like to thank Saint-Gobain for sponsoring this work and especially Monika Brodesser, Ansgar Haeger, Georges Moineau, Xavier Brajer, René Gy and François Creuzet for their implication in the project. The authors would like to thank the ANRT for sponsoring this project as well.

Data availability

The raw data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.polymertesting.2019.01.018.