Ignacio Martín-Fabiani

Andrea Fortini

Jennifer Lesage De La Haye

Ming Liang Koh

Spen- Cer E Taylor

Elodie Bourgeat-Lami

Muriel Lansalot

Franck D ' Agosto

Richard P Sear

Joseph L Keddie

pH-Switchable Stratification of Colloidal Coatings: Surfaces "On Demand"

Keywords: stimuli-responsive, polymerization-induced self-assembly (PISA), functional coatings, stratification, Brownian dynamics simulations

Stratified coatings are used to provide properties at a surface, such as hardness or refractive index, which are different from underlying layers. Although time-savings are offered by self-assembly approaches, there have been no methods yet reported to offer stratification on demand. Here, we demonstrate a strategy to create self-assembled stratified coatings, which can be switched to homogenous structures when required. We use blends of large and small colloidal polymer particle dispersions in water that self-assemble during drying because of an osmotic pressure gradient that leads to a downward velocity of larger particles. Our confocal fluorescent microscopy images reveal a distinct surface layer created by the small particles. When the pH of the initial dispersion is raised, the hydrophilic shells of the small particles swell substantially, and the stratification is switched off. Brownian dynamics simulations explain the suppression of stratification when the small particles are swollen as a result of reduced particle mobility, a drop in the pressure gradient, and less time available before particle jamming. Our strategy paves the way for applications in antireflection films and protective coatings in which the required surface composition can be achieved on demand, simply by adjusting the pH prior to deposition.

Introduction. Stratified coatings, consisting of two or more layers on top of each other, are used in a wide range of applications, including energy storage, [START_REF] Xu | Three-dimensional micro/nanoscale architectures: fabrication and applications[END_REF] optics, 2 biomedicine, [START_REF] Zervantonakis | Controlled Drug Release and Chemotherapy Response in a Novel Acoustofluidic 3D Tumor Platform[END_REF] and photovoltaics. [START_REF] Xu | A Bifunctional Interlayer Material for Modifying Both the Anode and Cathode in Highly Efficient Polymer Solar Cells[END_REF] The development of fast, inexpensive, and up-scalable fabrication methods for stratified systems is a key challenge in materials science. [START_REF] Hammond | Form and function in multilayer assembly: New applications at the nanoscale[END_REF][START_REF] Richardson | Multilayer assembly. Technology-driven layer-by-layer assembly of nanofilms[END_REF] Here, we introduce a method to obtain self-assembled stratified coatings, along with a simple means to form homogeneous coatings, when desired, using the same starting materials.

The casting of polymer blends from a common solvent provides one of the simplest fabrication methods. Stratified coatings can evolve from the growth of wetting layers at the surface, driven by differences in surface free energies between the two phases. [START_REF] Steiner | Complete wetting from polymer mixtures[END_REF] A three-layer lamellar structure has been reported in solvent-cast polymer binary blends. [START_REF] Geoghegan | Lamellar structure in a thin polymer blend film[END_REF] During spin-casting from solvent, stratified layers develop as a transient stage sometimes followed by lateral phase separation. 9, 10 A limitation when forming stratified coatings by solvent casting is that the final com-position depth profile can only be adjusted by changing the polymer's surface energy, molecular weights, or chain architecture.

Colloidal self-assembly methods, using particles suspended in a solvent as the building blocks, rather than single molecules, have been proposed as single-step alternatives for producing stratified coatings, via the control of colloidal particle diffusion, [START_REF] Nikiforow | Self-Stratification During Film Formation from Latex Blends Driven by Differences in Collective Diffusivity[END_REF][START_REF] Trueman | Auto-stratification in drying colloidal dispersions: A diffusive model[END_REF] sedimentation, [START_REF] Cardinal | Drying regime maps for particulate coatings[END_REF] particle interaction potentials, [START_REF] Atmuri | Autostratification in Drying Colloidal Dispersions: Effect of Particle Interactions[END_REF] or surface free energy. [START_REF] Misra | Fluoromethacrylate-Containing Colloidal Dispersions: Phospholipid-Assisted Synthesis, Particle Morphology, and Temperature-Responsive Stratification[END_REF] We recently discovered a mechanism of self-stratification in blends of colloids of two different sizes, where the small particles segregate into a layer on top of the larger particles. [START_REF] Fortini | Dynamic Stratification in Drying Films of Colloidal Mixtures[END_REF] When drying a blend of colloidal particles in a liquid, the top interface of the liquid falls as a result of evaporation, and an osmotic pressure gradient develops across the thickness of the layer. This pressure gradient pushes larger particles away from the air-liquid interface faster than it pushes smaller particles, creating stratification. Although examples of stratification by particle size can be found in the literature, [START_REF] Nunes | Efficient strategy for hard nano-sphere usage: Boosting the performance of waterborne coatings[END_REF] no suitable physical model existed at that time to explain the effect.

To fulfill the aspirations of materials scientists for designer materials, there is a demand that the stratification of a coating is responsive, such that it can be switched on and off as needed, or varied between set limits. There is currently a gap in existing technologies to offer a combination of stratification and switchability to yield surface properties "on demand". For instance, in applications as a protective coating, the surface might need a higher hardness [START_REF] Nunes | Efficient strategy for hard nano-sphere usage: Boosting the performance of waterborne coatings[END_REF] to impart scratch-resistance. In antireflection coatings, a lower refractive index at the surface will reduce the optical reflectivity. [START_REF] Chhajed | Nanostructured multilayer graded-index antireflection coating for Si solar cells with broadband and omnidirectional characteristics[END_REF] Gradients in composition suppress reflection losses significantly, in a broad bandwidth and under diffuse illumination. [START_REF] Yu | Photon management for photovoltaics[END_REF] A means to adjust stratification without altering the starting composition or the deposition method would offer a huge efficiency gain over conventional fabrication technology. [START_REF] Richardson | Multilayer assembly. Technology-driven layer-by-layer assembly of nanofilms[END_REF][START_REF] Goldstein | Growth by molecular-beam epitaxy and characterization of INAs/GaAs strained-layer superlattices[END_REF][START_REF] Choy | Chemical vapour deposition of coatings[END_REF][START_REF] Jensen | X-ray reflectivity characterization of ZnO/Al2O3 multilayers prepared by atomic layer deposition[END_REF] Our vision in the design of a switchable, stratified coating is to draw upon insights from our earlier work [START_REF] Gurney | Switching Off the Tackiness of a Nanocomposite Adhesive in 30 s via Infrared Sintering[END_REF] to bring together two different materials technologies: colloidal stratification and pH-responsive particles. Here, we show how the stratification of binary particle blends can be switched off (or on) simply by raising (or lowering) the pH of the initial dispersion. Using stimuli-responsive polymer colloids that increase in size when the pH is raised, the driving force for segregation during drying is reduced enough to suppress stratification. Thus, without changing the composition of the materials, the properties of the surface layer and bulk film are manipulated on demand. We envision that our design will allow end-users to define the properties of the final coating via a pH adjustment before deposition. To this end, we present a proof of concept of a new class of coating that offers a function beyond the ordinary.

In our previous work, we observed that stratification in binary colloidal blends becomes less efficient either when the initial solids content is increased or when the size ratio of the particles is reduced. [START_REF] Fortini | Dynamic Stratification in Drying Films of Colloidal Mixtures[END_REF]24 To exploit this behavior, we employ switchable or responsive polymers, which are ideal platforms because of their ability to respond to a variety of external stimuli, e.g. temperature, light or pH, with conformational and/or chemical changes. [START_REF] Stuart | Emerging applications of stimuli-responsive polymer materials[END_REF] This versatility makes them a key part of advances in drug delivery, [START_REF] Organic Coatingszhang | Near Infrared-Guided Smart Nanocarriers for MicroRNA-Controlled Release of Doxorubicin/siRNA with Intracellular ATP as Fuel[END_REF] sensors, [START_REF] Kim | Thermoresponsive Polymer and Fluorescent Dye Hybrids for Tunable Multicolor Emission[END_REF] and nano-and microactuation. [START_REF] Epstein | Colloidal Particles that Rapidly Change Shape via Elastic Instabilities[END_REF] Via emulsion polymerization, [START_REF] Asua | Emulsion polymerization: From fundamental mechanisms to process developments[END_REF][START_REF] De Bruyn | Characterization of electrosterically stabilized polystyrene latex; implications for radical entry kinetics[END_REF] polymer particles can be synthesized with a dense polymer core on which hydrophilic polymer chains, referred to as hairy layers, are anchored to create a shell. [START_REF] Charleux | Preparation of Hybrid Latex Particles and Core-Shell Particles Through the Use of Controlled Radical Polymerization Techniques in Aqueous Media[END_REF] Raising the pH can be used to increase the hydrophilicity of the hairy layer, and hence to increase the effective size of the particles. [START_REF] Xie | Fluorescence Correlation Spectroscopy Monitors the Hydrophobic Collapse of pH-Responsive Hairy Nanoparticles at the Individual Particle Level[END_REF] In this work, we use the recently-developed method of polymerization-induced self-assembly (PISA) to synthesise particles with pH-responsive hairy layers as a means to adjust the particle size. [START_REF] Charleux | Polymerization-Induced Self-Assembly: From Soluble Macromolecules to Block Copolymer Nano-Objects in One Step[END_REF][START_REF] Canning | A Critical Appraisal of RAFT-Mediated Polymerization-Induced Self-Assembly[END_REF][START_REF] Lansalot | Polymerization-Induced Self-Assembly: the Contribution of Controlled Radical Polymerization to the Formation of Self-Stabilized Polymer Particles of Various Morphologies[END_REF] PISA combines emulsion polymerization and reversible deactivation radical polymerization (RDRP) concepts to produce surfactant-free latexes. The process requires the synthesis by RDRP of hydrophilic polymer chains followed by their chain extension with a hydrophobic monomer in water leading to the formation of amphiphilic block copolymers. The hydrophilic segment covalently anchored at the particle surface will ensure the stabilization.

Results. PISA was employed to synthesize copolymer particles composed of styrene and acrylate derivatives and stabilized by poly(methacrylic acid) (PMAA). These particles are pH-responsive, as the PMAA chains on their surfaces will be protonated at low pH. Protonation reduces the charge and thus causes chain collapse at a pH below the pKa. When the pH is raised, these chains are deprotonated and extend as their affinity with water increases, as shown in Figure 1. The particle hydrodynamic diameter, as measured by dynamic light scattering (DLS), increases with increasing pH, as is shown in Figure 2a. At pH 9.5, the effective diameter of the small particles is almost double that at pH 4. Another clear sign of the increase in particle size can be seen from the pH dependence of the viscosity of a dispersion of these particles (at a fixed concentration of 20 wt% solids). As shown in Figure 2b, there is a remarkable increase in viscosity above pH 5.

Figure 1. Effects of pH on hairy-layer PISA particles: Scheme depicting the extension of PMAA chains at the particle surface when the pH of the initial dispersion is raised.

The viscosity dependence on the particle volume fraction (adjusted through the pH) is presented in Figure 2c.

Here, an effective volume fraction of particles,  eff , was calculated using the number density of the particles and the diameters obtained from DLS for a particular pH. (At 20 wt%, the number density is 2.4 ×10 21 /m 3 for the small particles and 6.0 ×10 18 /m 3 for the large particles.) A general trend for the viscosity to increase with increasing  eff is observed, with the exception of the viscosity at the highest  eff , where a decrease is observed.

For comparison, the prediction of the Krieger-Dougherty model 36 for the viscosity of hard colloidal spheres is shown in Figure 2c. There is poor agreement. However, because the diffuse shell of the particles is made of swollen PMAA chains, the particles cannot be treated as hard spheres at high densities. Instead, the hairy layer shells can interact with and interpenetrate neighboring shells, which causes the dispersion viscosity to be large but finite. The observed trend differs from that seen with hard particles jamming, which causes the viscosity to diverge towards infinity. Thus, the rapidly increasing but non-diverging viscosity seen in Figure 2c is as is expected for swollen, soft spherical particles. As the viscosity increases, the particle mobility, which is essential for stratification, decreases.

The pH-responsive particles, with a size at low pH of approximately 50 nm, were labeled with fluorescein for confocal microscopy experiments. In stratification experiments, they were blended with larger particles (385 nm), synthesized via a conventional emulsion polymerization process using surfactant as a stabilizer and labeled with a red fluorescent dye (Rhodamine B). These large red particles show no significant changes in size (Figure S1) or viscosity (Figures 2b andS3) with increasing pH. In the blends, the number ratio of large:small particles was fixed at N L :N S = 1:800 (equivalent to 70 wt% small particles), and the initial solids contents of the dispersions were fixed at ca. 10 wt%. It is important to clarify that both large and small particles are charge-stabilized over the entire pH range studied here. With a negative surface charge, which increases with increasing pH (Figure S2), they are subject to charge repulsion that imparts colloidal stability.

The structures of dried films were non-invasively probed using confocal laser scanning microscopy with two excitation wavelengths. These measurements allow the reconstruction of a 3D image of the distributions of the two kinds of particles. As is shown in Figure 3a-b (left column), for an initial dispersion pH of 3 and 4, a layer of green (small) particles is clearly seen at the top of the coating, whereas below the surface layer, red (large) particles predominate. The integrated intensity profiles (right column), which are proportional to the particle concentration, show peaks in the green channel intensity near the top surface, and thus provides unequivocal evidence for stratification. (The method of data reduction is explained in the Supporting Information.) The thickness of the upper layer is about 2 µm, which is equivalent to ca. 40 diameters of the small particles.

When the pH of the initial dispersion is raised to 7 and beyond (Figures 3c-d), there is no evidence for stratification within the dried films. In fact, the intensities of both the red and green channels are seen to follow each other almost exactly, as is shown in the integrated intensity 1D profiles (right column). There is a broadening of the step in the intensity at the film surface because of the combined effects of imperfect sample levelling and fluctuations in thickness. To verify this transition in stratification, the top surface of the final films was characterized by means of atomic force microscopy (AFM) as can be seen in Figures 4a-d. At low pH, the top surface of the film is covered with small particles and just a few large ones can be visualized (Fig- ures 4a-b). This is consistent with a picture of a stratified coating where small particles accumulate at the top, with the large ones below. However, for pH 7 and above, numerous large particles can be seen at the top surface (Fig- ures 4c-d). The AFM images indicate a transition from a stratified to a non-stratified coating at pH around 7. (Although the small particles swell in alkaline water, they will collapse upon drying and film formation.)

To shed light on the effect of reduced particle mobility on stratification, we carried out Langevin dynamics simulations [START_REF] Plimpton | Fast Parallel Algorithms for Short-Range Molecular Dynamics[END_REF] of drying films with a binary mixture of large and small spherical particles. The mixtures all had number ratios of large to small particles of N L :N S = 1:800 to match the experiments. Screened charged particles were assumed. The model is described in the Supporting Information and in detail elsewhere. [START_REF] Fortini | Dynamic Stratification in Drying Films of Colloidal Mixtures[END_REF] Briefly, we started with a size ratio between the large and small particles of D L :D S = 7:1, which corresponds to the effective size ratio in experiments at low pH. We then increased D S , keeping the D L and the number densities of the particles the same, to model the swelling of the small particles with increasing pH.

The initial volume fraction occupied by the particles in the simulation increased from 0.1 to 0.55, with increasing D S . When the small particles are 54 nm in diameter (Figure 5a), they accumulate in a top layer, and the system is stratified. But when D S increases, the stratification disappears (Figure 5b). Indeed, Figure 6a shows that the width of the layer of small particles falls towards zero when their diameter is above approximately 80 nm, which is very close to the diameter where stratification is lost in the experiments (Figures 2a and3c). We note that halving the initial number densities of the particles did not cause the stratification effect to return, just as it did not in the experiments (Figure S7).

In earlier work, [START_REF] Fortini | Dynamic Stratification in Drying Films of Colloidal Mixtures[END_REF] we found that stratification occurred because the larger particles moved down faster than the small particles during drying. We estimated that the excess velocity of the large particles over that of the small particles scales approximately as the product of the square of the size ratio and the pressure gradient; it scales inversely with the suspension viscosity. (See Equation S3.) As the pH increases in our experiments, the size of small particle increases. Our simulations show that as D S increases with the number of particles constant, the segregation mechanism is hindered by four effects. Three of these effects reduce the relative downward velocities of the large and small particles. It is this relative motion that drives the segregation. Firstly, the size ratio decreases from 7:1 to approximately half that value, and the relative motion tends to zero as the size ratio tends toward unity.

Secondly, the initial  eff increases, which leads to an increased suspension viscosity. Thirdly, the pressure gradients decrease, as shown in Figure S8, reducing the velocity difference between the particles. Fourthly, the time available before jamming of the particles decreases. Hence, with a larger D S , the particles jam before they have finished stratifying. This effect is represented in the map in Fig. 6b, which identifies the region (shaded green) where particles are not jammed and can stratify. A drying film follows vertical time trajectories in this figure.

Conclusions.

To summarize, we have demonstrated a bimodal colloidal system that allows self-stratification during drying to be switched off using pH as the trigger. Coatings are stratified when cast from dispersion with a pH below 7, but the effect is lost at higher pHs. Our stimuli-responsive polymer colloids increase in size when the pH is raised. We carried out simulations that showed that when the particle size increases above 80 nm, the stratification is suppressed, which agrees remarkably well with the experiments. These simulations allowed us to determine the mechanism that controls stratification and to explain the observed switchability.

Achieving such control over the stratification process allows not only the independent programming of the properties of the top surface, but also the possibility of switching the surface properties without changing the starting materials. Our design potentially provides a means to change -whenever desired -the hardness and optical reflectivity of a coating during deposition.

Our concept has significant potential for a wide range of applications, especially smart paints and inks. The stratification control could also be used to tailor the tack strength of pressure-sensitive adhesives. [START_REF] Gurney | Switching Off the Tackiness of a Nanocomposite Adhesive in 30 s via Infrared Sintering[END_REF] Although our focus here is on switchable stratification, our insights into the effects of particle size and concentration on the stratification of binary particle blends can be exploited to achieve homogeneous coatings.

Materials and Methods

Particle synthesis and characterization. The large Rhodamine B (RhB)-labeled latex particles (solids content of 20.6 wt%) were produced by emulsion copolymerization of methyl methacrylate and n-butyl acrylate (40 : 60 g/g) using sodium persulfate (0.5 wt% relative to monomers) as initiator and a combination of non-ionic and anionic surfactants (99 : 1 g/g), Synperonic NP30 and sodium dodecyl sulfate, respectively. The polymerization was conducted in a batch process at 70 °C under a nitrogen atmosphere in a 300 mL glass reactor fitted with a condenser and a nitrogen gas inlet. Degassing of an aqueous solution of initiator was first carried out for 30 min. In the meantime, RhB (0.2 wt% based on monomers) was dissolved in a water solution containing the surfactants (3 g L -1 ). This solution was degassed, mixed with the monomers, and introduced in the reactor with vigorous stirring before increasing the temperature to start the polymerization. At the end of the reaction, the latex suspension was centrifuged, and fluorescence spectroscopy performed on the supernatant solution showed an extremely weak signal indicating that almost no RhB was present in the aqueous phase. [START_REF] Soleilhac | Temperature Response of Rhodamine B-Doped Latex Particles. From Solution to Single Particles[END_REF] The hydrodynamic particle diameter was measured on dilute dispersions by DLS using a Malvern Zetasizer Nano ZS with a 633 nm wavelength laser and a scattering angle of 173°. These particles had a z-average diameter, D L = 385 nm with a dispersity of 0.013 (PDI value). The copolymer's midpoint glass transition temperature was 11 °C, according to differential scanning calorimetry (Q1000, TA Instruments, New Castle, DE, USA) at 10 °C/min. Film formation could occur at a typical room temperature.

The small fluorescent particles were composed of amphiphilic block copolymers obtained by polymeriza-tion-induced self-assembly (PISA). [START_REF] Canning | A Critical Appraisal of RAFT-Mediated Polymerization-Induced Self-Assembly[END_REF][START_REF] Lansalot | Polymerization-Induced Self-Assembly: the Contribution of Controlled Radical Polymerization to the Formation of Self-Stabilized Polymer Particles of Various Morphologies[END_REF] Controlled radical polymerization (namely, reversible additionfragmentation chain transfer (RAFT) polymerization) of methacrylic acid (MAA) in water was performed to obtain, firstly, a PMAA macroRAFT agent (about 4000 g mol -1 ), [START_REF] Chaduc | RAFT Polymerization of Methacrylic Acid in Water[END_REF] which was then chain-extended with a mixture of n-butyl acrylate, styrene and fluorescein o-acrylate (54.9/44.7/0.4 wt%) in a H 2 O/EtOH mixture (90/10 v/v). 4,4'-Azobis(4-cyanopentanoic acid) (ACPA) was used as an initiator with [ACPA] H2O/EtOH = 2.2 mmol L -1 and [PMAA]/[ACPA] = 4.9. After the synthesis, the stable polymer dispersion was degassed under argon to remove traces of n-butyl acrylate. It was also dialyzed against water over 69 h, thus allowing the removal of ethanol in the final dispersion. The final solids content was 20.9 wt%. DLS found D S = 54 nm with a PDI value of 0.065 at an initial pH of 4. At this pH, which is below PMAA's pK a value of 5.5, the PMAA chains at the particle surface are only weakly ionized and likely adopt a hypercoiled conformation. [START_REF] Ruiz-Perez | Conformation of poly(methacrylic acid) chains in dilute aqueous solution[END_REF] The copolymer's midpoint glass transition temperature was 16 °C, according to differential scanning calorimetry at 10 °C/min.

Blend preparation and drying. After blending the two dispersions to achieve the desired number ratio, deionized water was added to adjust the final solids content to the range from 9 to 13 wt%. By adding small amounts of ammonia (35 %) or 1M HCl solution the pH of the blend was adjusted to pH values between 3 and 9.5. The pH of the colloidal mixture was estimated using pH indicator paper, because of the small sample volume. Films of these blends were cast on glass substrates (18 × 18 mm 2 ), previously cleaned with acetone and a UV ozone treatment (Bioforce Nanosciences, model UV.TC.EU.003). Film formation took place under ambient conditions (typically a temperature of 20 °C and a relative humidity of 40%). Average drying times were 1-2 h. Structure characterization. Height and phase images of the top surface of the films were acquired by atomic force microscopy (AFM), using an NT-MDT Ntegra Prima microscope with intermittent contact. Images were analyzed using NOVA software. A Zeiss LSM510 confocal microscope (on an Axiovert 200M microscope) was used to obtain stacks of plane images at varying depths within the sample. The green and red fluorochromes were excited using an argon laser (488 nm) and a HeNe laser (543 nm), respectively. Two-dimensional images (83 × 83 µm 2 ) were acquired in 0.5 µm increments when moving from the substrate at the bottom toward the top of the dry film. A second acquisition was made close to the top surface to characterize the upper layer with greater precision, acquiring images with increments in spacing of 0.1 µm. Results were analysed using the image processing package Fiji (a version of Image J). A second-order polynomial equation was fit to the detected intensity as a function of depth from the surface and then used to define a baseline, to correct for the depth-dependence of the detected intensity. The corrected intensity was normalized by divid-ing by the maximum intensity in the profile. An example can be seen in the Supporting Information.

Dispersion viscosity measurements. The viscosities of the large and small particle dispersions containing 20 wt% solids were determined over the pH range from 2.5 to 9.5. Small amounts of concentrated aqueous ammonia (35 %) or 1M HCl solutions were used to adjust the original pH, in order to minimize changes to the particle concentration. Viscosity measurements were made on 0.8 mL of each dispersion at ambient temperature (24  2 C) using a low-shear rheometer (Contraves A.G., Zürich, Switzerland) with concentric cylinder measuring geometry over a range of shear rates.

Figure 2 .

 2 Figure 2. Effects of pH on hairy-layer PISA particles. (a) Particle diameters measured by dynamic light scattering as a function of pH. (b) Viscosity at a shear rate of 2.4 s -1 as a function of the dispersion pH. The number density of particles is constant across the series (corresponding to 20 wt%). For comparison, the dependence of the viscosity of large (385 nm) emulsion polymer particles at 20 wt% is plotted (red triangles). (c) Viscosity of dispersions of pH-responsive particles (as in b) replotted as a function of their effective volume fraction,  eff , as the pH is raised while the number density of particles is fixed. The theoretical curve for hard spheres drawn using the Krieger-Dougherty model 36 is shown as the solid line for comparison.

Figure 3 .

 3 Figure 3. Confocal laser scanning microscopy of dried films formed from a binary mixture of large particles and small pH-responsive particles, with number ratio of N L :N S = 1:800 and an initial solids content of 10 wt%. Large particles are labeled with a red fluorescent dye, and small pH-responsive particles are labeled with a green dye. The left column shows three-dimensional confocal reconstructions of the dried films, obtained from for four different pH values of the initial dispersion: (a) pH 3, (b) pH 4, (c) pH 7 and (d) pH 9.5. The right column shows the integrated intensities of red (red triangles) and green (green squares) channels close to the top surface, as a function of the vertical distance, z. The surface is represented at z = 0 as the center of the broadened step in intensity. A correction was made for the depth dependence of the detected fluorescence intensity.

Figure 4 .

 4 Figure 4. Atomic Force Microscopy (AFM) of dried films formed from a binary mixture of large particles and small pH-responsive particles, with number ratio of N L :N S = 1:800 and an initial solids content of 10 wt%. Height images (5 x 5 µm 2) obtained from for four different pH values of the initial dispersion: (a) pH 3, (b) pH 4, (c) pH 7 and (d) pH 9.5.

Figure 5 .

 5 Figure 5. (a), (b) Simulation snapshots at the end of drying runs, showing the top 30% of the simulation box. Large and small particles are red and green, respectively. For clarity in the visualization, we present the small particles as having a diameter 1/70 of the large particle

Figure 6 .

 6 Figure 6. (a) Width of the stratified top layer of small particles, as a function of their diameter. (b) The sketch shows the dynamic region where segregation is possible (green shaded area) and where jamming occurs (white area). Ds is normalized by the initial size without swelling, ; the time is normalized by the simulation time unit, t 0 . The full curve denotes the elapsed normalized time until an average volume fraction of 60% is reached. Evaporation corresponds to moving vertically in the plane. The vertical arrow indicates an example drying path. The solid arrow shows the part of the dynamic path where segregation is possible. Further details of the simulations are given in the Supporting Information.

Funding Sources

European Union Seventh Framework Programme BARRIER-PLUS project (FP7-SME-2012-2, No. 304758).

ACKNOWLEDGMENT

This work was funded by the European Union Seventh Framework Programme BARRIER-PLUS project (FP7-SME-2012-2, No. 304758). We thank Dr Rachel E. Butler at the University of Surrey Bioimaging and Flow Cytometry Core Facility for assistance with confocal microscopy experiments and Violeta Doukova (University of Surrey) for general laboratory support.

ASSOCIATED CONTENT

Supporting Information. Hydrodynamic diameters of large particles by DLS; zeta potential measurements of large and small particles; shear rheology; visible absorption spectra of fluorescent particles; 3D confocal reconstructions of films at pH 3.5 and 8; analysis of confocal laser scanning images; information on Langevin dynamics simulations. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author

* E-mail: J.Keddie@Surrey.ac.uk Present Addresses †Department of Materials, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK.

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.


Fabrice Brunel
email: fabrice.brunel@univ-lyon1.fr

Guilhem Billuart

Pierre-Yves Dugas

Muriel Lansalot

Elodie Bourgeat-Lami

Vincent Monteil
email: vincent.monteil@univ-lyon1.fr

Crystallization of Nano-domains in Polyethylene Latexes

Semi-crystalline polyethylene (PE) nanoparticles were obtained by free radical emulsion polymerization under mild conditions of pressure and temperature. At high surfactant concentration, the obtained anisotropic nanoparticles exhibit a strong degree of supercooling. This paper explores the relationship between the morphology of such particles and their high degree of supercooling. The shape anisotropy of the semi-crystalline PE particles already observed by transmission electron microscopy was confirmed by dynamic light scattering with the autocorrelation function containing both translational and rotational diffusion coefficients as well as by in situ synchrotron small-angle and wide-angle X-ray scattering (SAXS/WAXS). Temperature-resolved synchrotron scattering was used to further characterize the evolution of particles morphology and crystallinity during cooling. Paying special attention to the role of the surfactant we propose a novel mechanism which contributes to a better understanding of the crystallization of PE nanoparticle. The observed supercooling might be the result of the Coulomb repulsion between the surfactant head groups present at the particle surface, which hinders the particle contraction upon crystallization. The high surface charge density prevents the reduction of the particle surface, thus forcing a morphological transition from sphere to oblate ellipsoid during crystallization. This mechanism would act as potential barrier to the crystallization, resulting in supercooling.

Introduction

Polyethylene (PE), the top manufactured polymer, is synthesized from either very sensitive and hazardous organometallic catalysts (i.e. Ziegler-Natta catalysis) [START_REF] Ziegler | Das Mülheimer Normaldruck-Polyäthylen-Verfahren[END_REF][START_REF] Natta | The Kinetics of the Stereospecific Polymerization of α-Olefins[END_REF][START_REF] Mark | Encyclopedia of polymer science and engineering[END_REF][START_REF] Mülhaupt | Catalytic polymerization and post polymerization catalysis fifty years after the discovery of Ziegler's catalysts[END_REF][START_REF] Stürzel | From Multisite Polymerization Catalysis to Sustainable Materials and All-Polyolefin Composites[END_REF] or by an energy intensive process (200-300 • C, 2000 bar) using free-radical polymerization (FRP). [START_REF] Taylor | The Thermal Decomposition of Metal Alkyls in Hydrogenethylen mixtures[END_REF][START_REF] Flory | The Mechanism of Vinyl Polymerizations[END_REF][START_REF] Aggarwal | Polyethylene: Preparation, Structure, and Properties[END_REF][START_REF] Mark | Encyclopedia of polymer science and engineering[END_REF] In the latter case a branched, low-density polyethylene (LDPE) is produced, which exhibits low crystallinities and melting temperatures. Suspensions of LDPE particles in water are used as wax dispersions in cement, bitumens and in the papermaking industry. Such dispersions are obtained by mixing melted polymer with water at high temperature followed by a high-pressure homogenization step in order to reduce the polymer particle size down to ≈ 2 µm. [START_REF] Stanley | Production of aqueous dispersions of ethylene polymer[END_REF][START_REF] Shimandle | Method for producing wax microspheres[END_REF][START_REF] Hunter | Aqueous polyethylene dispersions produced by subjecting molten polymer in water to ahigh rate of shear[END_REF][START_REF] Moncla | Aqueous dispersion, its production method, and its use[END_REF] This process is however energy consuming. We have recently developed the direct synthesis of PE nanoparticles by FRP in water under mild conditions of pressure and temperature (T ≈ 70 • C and P ≈ 50 bar), which could advantageously replace the above mentioned processes. [START_REF] Grau | Aqueous dispersions of nonspherical polyethylene nanoparticles from free-radical polymerization under mild conditions[END_REF][START_REF] Billuart | Free Radical Emulsion Polymerization of Ethylene[END_REF] Indeed, ethylene polymerization in aqueous medium has been achieved by using a water-soluble initiator, either cationic or anionic. The PE particles were assumed to be stabilized by charged initiator fragments located at the polymer chain ends. Improved stabilization was obtained through the addition of a surfactant bearing the same charge as the initiator. In both cases, increasing the surfactant concentration led to higher yield of smaller particles with a high polydispersity, as determined by dynamic light scattering. [START_REF] Billuart | Free Radical Emulsion Polymerization of Ethylene[END_REF] The high polydispersity of the PE nanoparticles, obtained in the presence of surfactant, was attributed to non-spherical, disk-like particle morphologies whereas surfactant-free systems always led to spherical particles. Another difference between PE latexes obtained with or without surfactant was the degree of supercooling. PE latex obtained with surfactant exhibits a much lower crystallization temperature compared to the surfactant-free latex. Supercooling is usually attributed to the occurrence of homogeneous nucleation. In a bulk material, the presence of heterogeneities lowers the activation barrier to nucleation (i.e. heterogeneous nucleation).

When the number of micro-domains is several orders of magnitude higher than the number of heterogeneities, heterogeneous nucleation can completely disappear. In this case, highly confined isolated nano-domains can undergo homogeneous nucleation. Such nucleation requires a much higher activation barrier thus lowering the crystallization temperature (i.e. increased supercooling). The enhanced supercooling of confined PE chains has been evidenced in various systems such as: droplet dispersions, [START_REF] Massa | Crystal nucleation of polymers confined to droplets: Memory effects[END_REF][START_REF] Arnal | Evaluation of the fractionated crystallization of dispersed polyolefins in a polystyrene matrix[END_REF][START_REF] Michell | Confinement effects on polymer crystallization: From droplets to alumina nanopores[END_REF] immiscible polymer blends, [START_REF] Guo | Phase behavior and crystallization in blends of a low molecular weight polyethylene-block-poly(ethylene oxide) diblock copolymer and poly(hydroxyether of bisphenol A)[END_REF][START_REF] Takeshita | Formation of phase structure and crystallization behavior in blends containing polystyrenepolyethylene block copolymers[END_REF] block copolymers, [START_REF] Michell | The Crystallization of Confined Polymers and Block Copolymers Infiltrated Within Alumina Nanotube Templates[END_REF][START_REF] Xu | Study of crystallization and melting behavior of polypropylene-block-polyethylenes copolymers fractionated from polypropylene and polyethylene mixtures[END_REF][START_REF] Lorenzo | Confinement effects on the crystallization and SSA thermal fractionation of the PE block within PE-b-PS diblock copolymers[END_REF][START_REF] Lorenzo | Nucleation and isothermal crystallization of the polyethylene block within diblock copolymers containing polystyrene and poly(ethylene-alt-propylene)[END_REF][START_REF] Yu | Control of the confined and unconfined crystallization in glassy-crystalline poly(vinylcyclohexane)-b-poly(ethylene)-bpoly-(vinylcyclohexane) triblock copolymer in solution[END_REF] and thin films. [START_REF] Bernal-Lara | Structure and thermal stability of polyethylene nanolayers[END_REF][START_REF] Bernal-Lara | Morphology studies of multilayered HDPE/PS systems[END_REF] Crystallization kinetics are often described using the Avrami equation: [START_REF] Avrami | Kinetics of Phase Change. I -General theory[END_REF][START_REF] Avrami | Kinetics of Phase Change. II -Transformation-Time Relations for Random Distribution of Nuclei[END_REF][START_REF] Avrami | Kinetics of Phase Change. III -Granulation, Phase Change, and Microstructure Kinetics of Phase Change[END_REF]

v c = exp(-kt n )
Where k is the overall crystallization rate constant, n the Avrami exponent ranging from 1 to 4 and related to the dimensionality of nucleation and growth and v c is the relative volumetric transformed fraction. The Avrami exponent can be considered, as a first approximation, to be composed of two terms, 31 n = n n + n gd , where n gd is the fraction of the exponent related to the growth dimensionality ranging from 1 to 3 for one-dimensional to three-dimensional growth, while the nucleation term (n n ) can have values from 0 to 1 by considering that nucleation can be instantaneous (n n = 0) or sporadic (n n = 1). Müller et al. compiled the Avrami exponent values obtained for several systems and observed a decrease of the Avrami exponent with increasing degree of confinement. [START_REF] Müller | Crystallization in Nano-Confined Polymeric Systems[END_REF] Some authors have reported Avrami indices around 1 or lower, which should rule out the possibility of an homogeneous nucleation because n = 1 could only be obtained when the nucleation is instantaneous and the growth is one-dimensional. According to classical nucleation theory, a rapid (instantaneous) nucleation rate implies a low energy barrier and thus heterogeneous nucleation. However, considering that growth is very fast and confined in all three dimensions of space, the crystallization kinetics is completely dominated by the nucleation process (i.e. n gd = 0). The low value of the Avrami exponent obtained under strong confinement could therefore be consistent with an homogeneous nucleation. However, discriminating between growth and nucleation in the Avrami equation is not straightforward and the intensity of the supercooling at high degree of confinement remains the best proof of the occurrence of homogeneous nucleation.

Recently, extremely large supercooling of PE single lamellae has been achieved. [START_REF] Weber | Single lamella nanoparticles of polyethylene[END_REF][START_REF] Trzaskowski | Anisotropic nanoparticles of precise microstructure polyolefins[END_REF] The authors observed that the crystallization temperature evolved as a function of the crystal thickness. The relationship between the crystallization temperature and the crystal thickness was given by Strobl and implies the existence of an intermediate phase (mesomorphic phase) along the crystallization pathway. Evidence of a mesomorphic hexagonal phase of PE has been reported for short alkane chains (n < 20) under pressure [START_REF] Gan | n-Alkane Homogeneous Nucleation: Crossover to Polymer Behavior[END_REF][START_REF] Sirota | Polymer crystallization: Metastable mesophases and morphology[END_REF] and with constrained ultra-drawn PE fibers. [START_REF] Strobl | Crystallization and melting of bulk polymers: New observations, conclusions and a thermodynamic scheme[END_REF][START_REF] Yasuniwa | Hexagonal Phase of Polyethylene fibers under high pressure[END_REF] This is also supported by molecular dynamics simulations of supercooled PE melt, which reveal a stiffening of the chains prior to nucleation as well as an hexagonal arrangement of the chains in the critical nuclei. [START_REF] Yamamoto | Molecular dynamics simulations of polymer crystallization in highly supercooled melt: Primary nucleation and cold crystallization[END_REF][START_REF] Yamamoto | Molecular dynamics of polymer crystallization revisited: Crystallization from the melt and the glass in longer polyethylene[END_REF][START_REF] Anwar | Crystallization of polyethylene: A molecular dynamics simulation study of the nucleation and growth mechanisms[END_REF] These simulations suggested that growth proceeds via alignment of segments close to the growth front, followed by lamella thickening through sliding of the segments from the amorphous regions into the crystalline regions. The lamella thickness can be related to the stability of the mesomorphic layer, i.e. the energy required during this lamellar thickening growth mechanism. A lower crystallization temperature could reduce the chain mobility and thus hinder the lamella thickening mechanism detailed above. However, a question remains: is the supercooling observed during the crystallization of confined polymer the result of a true homogeneous nucleation? There seems to be a vast consensus in the case of poly(ethylene oxide) (PEO) but, for PE, some authors believe that homogeneous nucleation has never been achieved so far. [START_REF] Michell | Confinement effects on polymer crystallization: From droplets to alumina nanopores[END_REF] In this paper, we used synchrotron-SAXS and WAXS to investigate the supercooling of PE confined in nanoparticles obtained by free-radical emulsion polymerization. Cationic and anionic PE latexes were obtained using different initiating systems. In each case, PE latexes were prepared with and without the use of an ionic surfactant bearing the same charge as the initiator. In situ SAXS and WAXS measurements allowed us to confirm that the observed supercooling is associated with the rapid crystallization of thin PE lamellae (thickness < 10 nm). The nucleation mechanism is discussed in the light of recent literature on PE crystallization. Special attention is given to the role of the surfactant which is often overlooked. Indeed the presence of surfactant is not only necessary in order to reduce the size of the nanoparticles, but it could also directly influence the nucleation during supercooling.

Benefiting from these high degree of supercooling, potential application of these PE latexes as phase change material for thermal energy storage could be targeted. These PE dispersions would also represent an interesting model to study degradation of marine litter accumulated in the center of oceanic gyres (e.g. Great Pacific Garbage Patch).

Methods

Ethylene Polymerization. Surfactant-free anionic and cationic PE nanoparticles (named A 0 and C 0 , respectively) were synthesized by emulsion polymerization. The synthesis of anionic PE nanoparticles using ammonium persulfate (APS) as initiator was previously described by Billuart et al. [START_REF] Billuart | Free Radical Emulsion Polymerization of Ethylene[END_REF] Cationic PE nanoparticles were obtained using 2,2'-azobis(2methylpropionamidine) dihydrochloride (AIBA) as initiator. [START_REF] Grau | Aqueous dispersions of nonspherical polyethylene nanoparticles from free-radical polymerization under mild conditions[END_REF] For both systems, PE nanoparticles were also obtained with the use of a surfactant: sodium dodecyl sulfate (SDS) or cetyltrimethylammonium bromide (CTAB) for anionic and cationic latexes, respectively. These samples were named A S and C S (the subscript "S" corresponding to the presence of surfactant and the subscript "0" to the surfactant-free particles). A brief summary of the process as well as the synthesis conditions is given in supplementary material (Figure S1).

The general characteristics of the obtained PE particles are given in Table 1.

Table 1: General characteristics of the studied PE nanoparticles. we used a two-decay exponential and Perrin friction factors to account for the translational and rotational diffusion coefficients (see the Supplementary Information pages S3 to S6 for more detail on the calculation). The ζ-potential was derived from electrophoretic mobility measurements using the Smoluchowski's equation. [START_REF] Smoluchowski | Contribution to the theory of electro-osmosis and related phenomena[END_REF] Small and Wide-Angle X-ray Scattering (SAXS and WAXS). SAXS measurements were carried out at the BM02 beamline of the European Synchrotron Radiation Facilities (ESRF, Grenoble, France). Experiments were carried out at an energy of 25.5 keV with a sample to detector distance of 164 or 16 cm for SAXS and WAXS, respectively, using a 1242

Initiator (%wt.) Surfactant (%wt.) PE (%wt.) Solids Content (%) T c ( • C) a Z b ave (nm)
× 1152 CCD camera. The recorded images were first corrected from dark current and flat field and normalized with respect to the intensity of the incident beam. The azimutal integration of the corrected images gave the radial integration (scattering curves). Finally the obtained scattering curves were calibrated (q-axis) using silver behenate and corrected for sample transmission and background subtraction. In order to study morphological changes during crystallization, the samples were heated up to 100 • C to erase previous thermal history and allowed to cool down to 40 • C while SAXS or WAXS intensities were recorded.

SAXS measurements were analysed using SASfit 0.93.3 software. The form-factor equations used to fit the curves are given below for the different situation.

All melted particles were fitted using the form factor of a sphere:

I sphere (q, r, ∆η) = 4 3 πr 3 ∆η3 sin qr -qr cos qr qr 3 2
With r the radius of the sphere and ∆η the scattering length density difference between the PE particle and the water (i.e. ∆η = η PE -η water ).

When crystallization arose (T < T c ) for samples A 0 and C 0 , a broad correlation peak (Teubner and Stray model [START_REF] Teubner | Origin of the scattering peak in microemulsions[END_REF] ) was added to fit the high q-range:

I(q) = 8π∆η/ξ a 2 -2bq 2 + q 4 a 2 = (k 2 + 1/ξ 2 ) 2 b 2 = k 2 -1/ξ 2
Where ξ is the correlation length (length beyond which correlations die out), d = 2π/k is the d-spacing (characteristic of the domain size or periodicity) and ∆η is the scattering length For A S and C S , at T < T c , the form factor of an ellipsoidal core-shell was used:

density contrast (∆η = η PE crystallite -η amorphous PE ). b a t D = 2b + 2t τ = 2b (a) (b) l = 2a
I ECSh = 1 0 (η core -η shell )V c 3j 1 (x c ) x c + (η shell -η solvent )V t 3j 1 (x t ) x t 2 j 1 (x) = sin(x) -x cos(x) x 2 x c = q a 2 µ 2 + b 2 (1 -µ 2 ) x t = q (a + t) 2 µ 2 + (b + t) 2 (1 -µ 2 ) V c = 4 3 πab 2 V t = 4 3 π(a + t)(b + t) 2
Where a is the semi-principal axe of the elliptical core, b the equatorial semi-axis of the elliptical core and t the thickness of the shell (cf. Figure 1a). V c and V t are the volume of the core and the total volume of the core plus the shell, respectively, while η core , η shell and η solvent are the scattering length densities of the core (crystalline PE), the shell (amorphous PE) and the solvent (water), respectively. The scattering length densities were calculated using sasfit SLD Calculator giving: η PE crystallite = 9.716 × 10 -10 cm -2 , η amorphous PE = 8.255 × 10 -10 cm -2

and η water = 9.344 × 10 -10 cm -2 . The diffraction peaks and the amorphous halo were fitted using a Gaussian function which allowed us to calculate a crystallinity index (i c ):

i c (%) = A peak A peak A halo × 100
Where A peak and A halo are the area of the crystalline peaks and the amorphous halo, respectively.

The characteristic domain size (τ in Figure 1b) is obtained from the Scherrer equation:

τ = Kλ β cos θ
Where K is a dimensionless shape factor of about 0.9 under the assumption of a Gaussian line shape, λ is the X-ray wavelength, β is the line broadening at half the maximum intensity, after subtracting the instrumental line broadening in radians (determined using silver behenate sample) and θ is the Bragg angle also in radians.

Results and Discussion

At 100 • C, in the surfactant-free systems (i.e. samples A 0 and C 0 ), the scattering intensities of the melted particles clearly show wavelets characteristic of a spherical form factor (Figure 3a andc). These curves were fitted using a spherical form factor with a log-normal distribution (red curves in Figure 3a andc), giving a mean particle radius of around 38 and 35 nm, for A 0 and C 0 , respectively, and in both cases, a standard deviation, σ, of 0.05. After cooling down to 40 • C (Figure 3b andd) the particle size decreased and a broad correlation peak appeared at higher q-range indicating the presence of crystalline domains within the particles (see supplementary information Figure S4). We have plotted in Figure 4a the evolution of the particle radius with the temperature (i.e. during the cooling process). The size slowly decreased from 100 to 60 • C where the particles suddenly shrink to smaller sizes. The evolution of the particle radius is consistent with the increase of the crystallinity index measured by WAXS (see Figure 5). During cooling from 100 to 40 • C, the diffraction peaks characteristic of orthorhombic PE appeared around 80 • C and increased in intensity more or less steadily until about 60 • C where a corresponding increase of crystallinity index is observed. At room temperature, large spherical nanoparticles were obtained (R ≈ 35 nm) as previously evidenced by TEM and DLS (Table 2). [START_REF] Grau | Aqueous dispersions of nonspherical polyethylene nanoparticles from free-radical polymerization under mild conditions[END_REF][START_REF] Billuart | Free Radical Emulsion Polymerization of Ethylene[END_REF] In the presence of surfactant (i.e. samples A S and C S ), the picture is quite different. At 100 • C, the scattering intensities of the melted particles (A S and C S ) were also fitted using a spherical form factor (Figure 6a andc) giving much smaller particle radius of around 10.5 nm. The evolution of the particle radius during cooling is reported in Figure 4b. The initial melted nanoparticles shrink down until a temperature of 65 • C while remaining completely amorphous (i c = 0 in Figure 5). This is the logical consequence of the negative thermal expansion (i.e. "thermal contraction"). Between 65 and 55 • C, the particle radius remained q (nm -1 ) 0.8 0.6 0.4 0.2 1 q (nm -1 ) 0.8 0.6 0.4 0.2 1 q (nm -1 ) 0.8 0.6 0.4 0.2 more or less constant (Figure 4b) while crystallization was still not observed (i.e. the supercooling occurred). Around 55 • C and 50 • C, for cationic (C S ) and anionic (A S ) particles, respectively, the crystallisation occurred suddenly (sharp bump in Figure 5). From the evolution of the crystallinity index, the Avrami exponent values could be calculated. One should note that, in the present work, the Avrami's exponents are derived from non-isothermal experiments, while such kinetic investigations are usually carried out isothermally. Indeed, the JMAK model assumes isokinetic conditions, i.e. nucleation and growth rates being time independent. However, in the present case, crystallization occurred very rapidly (∆T < 2 • C) and therefore we can assume that the isokinetic criteria is satisfied. The Avrami exponent values were found to be 1.1 and 0.7 for A S and C S , respectively. These results compare well with typical values obtained with other systems made of highly isolated PE micro-domains.

In such confined systems, one can reasonably assume that the growth is limited in all three dimensions (i.e. point-like crystallization: n gd = 0), hence the crystallization kinetics is completely dominated by nucleation. Indeed, considering the enthalpy of fusion of PE (∆H) of 293 J g -1 (2.94×10 8 J m -3 ) and the surface energy of PE crystal (σ) of 0.7 J m -2 , 36,45 the critical radius of the nuclei is about 5 nm (r * = 2σ ∆H ) which is of the same order of magnitude as the crystallite dimension (Table 2). In this case, the crystallization kinetics is considered to be dominated solely by the nucleation rate and thus the Avrami exponent is equal to the nucleation term (n = n n ≈ 1), which suggests a sporadic (or homogeneous) nucleation.

Below T c , when a broad correlation peak was added to the spherical form factor, the obtained radius increased up to 12 nm which is physically unrealistic. Alternatively, the increase in particle dimension observed here was likely the result of a change in the particle morphology. Indeed, previous observation of both samples A s and C s by TEM showed a non-spherical morphology. [START_REF] Grau | Aqueous dispersions of nonspherical polyethylene nanoparticles from free-radical polymerization under mild conditions[END_REF][START_REF] Billuart | Free Radical Emulsion Polymerization of Ethylene[END_REF] DLS measurements indicates a small average particle diameter (Z ave ≈ 25 nm) but very high poly values (poly ≈ 0.3 -0.4) compared to the surfactant free-system (poly ≈ 0.01 -0.03). A closer examination of the DLS auto-correlation function revealed the presence of a two-exponential decay, characteristic of two time-correlations (see Supplementary Information, Figure S2). This second time-correlation remained at high dilution and after filtration (0.22 µm) independently of the scattering angles (90

R (nm)
• or 173 • ),
thus the presence of large or aggregated particles can be ruled out. The shape of the autocorrelation function could be the result of the non-spherical shape of the particles. For anisotropic particles, both translational and rotational motion must be considered because the light scattering depends on particle orientation. [START_REF] Eimer | Rotational and Translational Diffusion of Short Rodlike Molecules in Solution -Oligonucleotides[END_REF][START_REF] Aragón | Theory of dynamic light scattering from polydisperse systems[END_REF][48] The Perrin friction factors were used to calculate the characteristic dimensions of the ellipsoidal particles using the rotational and translational diffusion coefficients determined from a double decay exponential fit of the autocorrelation function (cf. Figure S3, Supplementary Information). [START_REF] Perrin | Mouvement Brownien d'un ellipsoide (II). Rotation libre et dépolarisation des fluorescences. Translation et diffusion de molécules ellipsoidales[END_REF][START_REF] Koenig | Brownian motion of an ellipsoid. A correction to Perrin's results[END_REF][START_REF] Matsuoka | Rotational diffusion of ellipsoidal latex particles in dispersion as studied by depolarized dynamic light scattering[END_REF][START_REF] Hoffmann | 3D Brownian Diffusion of Submicron-sized Particle Clusters[END_REF] The results of these calculations are given in Table 2 and show good agreement with previous TEM observations.

These results also compared well with SAXS-scattering intensities fitted using the form factor of a core/shell ellipsoid. Note that the size of the core obtained by SAXS also agreed with the dimensions of the crystallites measured by WAXS using the Scherrer equation (see Table S7 and S8 in the Supplementary Information).

Table 2: Summary of the PE particle dimensions at room temperature measured by synchrotron-SAXS and WAXS (Scherrer equation) and by DLS using either the cumulant method for spherical particles (D = Z ave ) or the translational and rotational diffusion coefficients for ellipsoidal particles (see Supplementary Information Table S2). 1), ϵ= 2b+2t 2a+2t the eccentricity of the ellipse (ϵ = 1 for a sphere) and τ the size of the crystalline domains (τ = 2b, see Figure 1). q (nm -1 ) 0.8 0.6 0.4 0.2 1 q (nm -1 ) 0.8 0.6 0.4 0.2 1 q (nm -1 ) 0.8 0.6 0.4 0.2 With T ∞ mc the temperature of a virtual transition between the mesomorphic and the crystalline phases. σ ac and σ am denote respective surface free energies between the amorphous phase and either the crystalline or the mesomorphic phases, ∆H mc the heat of transition from the mesomorphic to the crystalline phase and l the lamella thickness. The exact value of each constant from this extended-Gibbs-Thomson equation are still unknown but interestingly one could note that the crystallization line plotted by Weber et al. used the data obtained from rapid quenching of melted PE. In our case, the presence of a surfactant-covered surface could act as an "electrostatic quenching". The same would probably apply to Weber's nanocrystals obtained using the same anionic surfactant (SDS). The evolution of the particle radius during supercooling provides crucial evidence of the proposed "electrostatic quenching" mechanism. The nanoparticles obtained in the presence of surfactant showed very limited reduction in diameter, especially between 65 and 55 • C (Figure 4b). In this temperature range, where the supercooling occurs, the dimensions of the particles remain more or less constant. In other words, the thermal energy removed from the nanoparticles is not compensated by the contraction of the polymer chains. This is equivalent to a significant drop of the internal pressure of the particles, i.e. a temperature decrease at constant volume. This de-pressurization of the nanoparticles artificially maintains the PE at a constant density instead of decreasing with the temperature, thus effectively hindering the crystallization. Such shrinkage hindrance can be the result of strong Coulombic repulsions between surfactant charged groups present at the particle surface. The thermal energy removed from the particles being stored as Coulomb repulsion on the particle surface, this prevents the shrinkage and crystallization of the particles during supercooling. The surface could hold this energy up to a point where the Coulombic repulsion becomes too strong so that the system reaches the Rayleigh instability limit. [START_REF] Rayleigh | On the equilibrium of liquid conducting masses charged with electricity[END_REF] The Rayleigh critical radius (r limit , see Table S11 in the supplementary Information) that can be reached by PE particles was estimated from their surface charge (Q) and the cohesion energy of PE in water (γ = 30 J m -2 ).

D (nm) a ϵ a τ a (nm) τ b (nm) D (nm) c ϵ c A 0 72
Q = 64πϵ 0 ϵ r γr 3 limit ⇒ r limit = Q 2 64πϵ 0 ϵ r γ 1/3
where ϵ 0 and ϵ r are respectively the free space permittivity (8.85 × 10 -12 F m -1 ) and the relative permittivity of the solution (79.1 for water at 25 • C). The surface charge was estimated assuming the presence of one initiator molecule per polymer chain and considering that all surfactant molecules are located at the surface of the nanoparticles. The calculated values of the Rayleigh critical radius (10.3 and 8.9 nm for A S and C S , respectively) show good agreement with limiting particle radius during supercooling (Figure 4b) whereas for A 0 and C 0 the particle radius remains above the critical Rayleigh radius (r limit = 24.9 and 11.3 nm for A S and C S , respectively). Below 50 -55 • C, the excess energy from the Coulomb repulsion can trigger the expulsion of a surfactant molecule from the surface. The ejection of one surfactant molecule will cause the surrounding neighbouring ones to follow in a process similar to a Coulomb explosion. These rapid movements of the surfactant molecules propagate along the surface as a shock wave which would strongly deform the particles. These contractions of the particle could set off the rapid crystallization of the PE into a single lamella and therefore cause the particles to collapse into an ellipsoidal shape.

Conclusions

FRP of ethylene in aqueous medium under moderate pressure and temperature conditions yields small anisotropic PE nanoparticles which exhibit a high degree of supercooling. In situ synchrotron-SAXS/WAXS analyses of the crystallization kinetics and particle morphology confirmed many of the recent finding on PE crystallization in confined micro-domains.

Low values of the Avrami exponent (n ≤ 1) are obtained under very strong confinement (nano-domain). In this case, the crystallization kinetics is dominated by the nucleation rate since the growth within such nanoparticles can be considered instantaneous. The enhanced supercooling observed with such small particles (R ≈ 10 nm) scales as the inverse of the crystal thickness. According to Strobl's thermodynamic scheme, such relationship implies the existence of an intermediate phase (mesomorphic phase) along the crystallization pathway.

The thickness of the lamella is the result of the reduced mobility of the PE chains at low crystallization temperature (high supercooling). Finally, we propose a novel mechanism (i.e. "electrostatic quenching") explaining the origin of this enhanced supercooling in accordance with the evolution of the particle morphology. The change of morphology (from spherical to ellipsoidal particles) observed with small PE particles may be caused by the high charge density of the surface provided by the ionic surfactant. During cooling, the particles shrink down to the Rayleigh limit, hence provoking their strong deformation. These contractions could set off the rapid crystallization of the PE into a single lamella and therefore induce the collapsing of the particle into an ellipsoidal shape. The strong supercooling observed with these PE nanoparticles can thus be related to the occurrence of an homogeneous nucleation kinetic. However the high energy barrier responsible for this nucleation mechanism is provided by the Coulomb repulsion of the surfactant heads present at the surface and thus cannot be called true homogeneous nucleation.

Better understanding of PE crystallization is a field of tremendous interest because PE is employed in a multitude of applications due to its low cost and tunable semicrystalline properties. Among these applications, phase change material could be developed by taking

, 15 b

 15 Determined by DLS T c the crystallization temperature. The percentage by mass (%wt.) are relative to the mass of the dry particles (PE + surfactant + initiator). Dynamic Light Scattering (DLS). The intensity average hydrodynamic particle diameter (Z ave ), the poly values and the ζ-potential of the PE latexes were determined at 90 • and 173 • with a Zetasizer NanoZS (Malvern instrument Ltd, Worcestershire, UK) equipped with a 4 mW He/Ne laser beam operating at λ = 633 nm. All measurements were performed at 25.0 ± 0.2 • C. For spherical particles, a simple exponential decay was used to fit the autocorrelation function and the correlation decay rate was expanded in a power series (Cumulants methods) giving particle diameter and poly values. For the anisotropic particles,

Figure 1 :

 1 Figure 1: Representation of the geometrical parameters used for the different models. (a) SAXS ellipsoidal core-shell form factor: a the semi-major axe of the elliptical core and b the semi-minor axis of the elliptical core, t the shell thickness. (b) Characteristic domain size ,τ , measured by WAXS, the long axis diameter, D, determined by DLS and the lamella thickness, l, determined by SAXS (l ≈ 2a).

Figure 2 44 IFigure 2 :

 2442 Figure2shows the two main peaks of the diffraction planes (110) and (200) observed by WAXS and characteristic of orthorhombic polyethylene.[START_REF] Bunn | The crystal structure of long-chain normal paraffin hydrocarbons. The "shape" of the CH 2 group[END_REF]

Figure 3 :

 3 Figure 3: Synchrotron-SAXS analysis of PE latexes C 0 (top) and A 0 (bottom) obtained without surfactant at 100 • C (left) and 40 • C (right), Fitting curves: form factor of polydisperse spheres plus an additional correlation peak (Teubner and Stray model) at 40 • C. Cationic (C 0 ) and anionic (A 0 ) particles were obtained using respectively AIBA or APS as initiator.

Figure 4 :

 4 Figure 4: Evolution of the size of PE nanoparticles during cooling measured by SAXS. PE latexes obtained (a) in the absence of surfactant (A 0 and C 0 ) and (b) in the presence of surfactant (A S and C S ).

Figure 5 :

 5 Figure 5: Evolution of the crystallinity of PE nanoparticles during cooling from 100 • C to 40 • C. The crystallinity index is calculated as the ratio of crystalline peaks over the total area under the curve (i.e. crystalline peaks and amorphous halo).

Figure 6 :

 6 Figure 6: Synchrotron-SAXS analysis of PE latexes C S (top) and A S (bottom), obtained in the presence of surfactant at 100 • C (left) and 40 • C (right). Fitting curves: spherical form factor at 100 • C plus an additional ellipsoidal core/shell form factor at 40 • C. Cationic (C S ) and anionic (A S ) particles were obtained using respectively AIBA/CTAB and APS/SDS as initiator/surfactant systems.

For

  Table of Contents Use Only

  , b and c measured by SAXS, WAXS and DLS respectively D is the longest diameter of the ellipse (D = 2b + 2t in Figure

			1	15	14	82	1
	C 0	66	1	15	15	79	1
	A s	24	0.6	12	12	36	0.56
	C s	24	0.66	16	13	30	0.5

a

Acknowledgement

The authors thank Cyrille Rochas for his help on the ESRF: BM02 -D2AM French CRG Beamline. The authors thank R. Seguela, C. Chassenieux and T. Nicolay for fruitful discussions. ANR (Agence Nationale de la Recherche) and competitiveness clusters AXELERA and PLASTIPOLIS are acknowledged for financial support (project FRaPE; ANR 2011 JS08 008 01).

Conflict of Interest Disclosure

The authors declare no competing financial interest

Supporting Information Available

Supporting information includes:

• Free radical emulsion polymerization process and synthesis conditions

• Dynamic Light Scattering raw data and analysis

• SAXS and WAXS spectra and fitting parameters

• Avrami analysis

• Rayleigh critical radius calculation