Antonio Stocco
email: stocco@unistra.fr

Benjamin Chollet

Xiaolu Wang

Christophe Blanc

Maurizio Nobili

Rotational diffusion of partially wetted colloids at fluid interfaces

Keywords: Rotational diffusion, interfacial diffusion, colloid, air-water interface, viscous drag, line pinning, partial wetting Graphical

Hypothesis

Rotational Brownian diffusions of colloidal particles at a fluid interface play important roles in particle self-assembly and in surface microrheology. Recent experiments on translational Brownian motion of spherical particles at the air-water interface show a significant slowing down of the translational diffusion with respect to the hydrodynamic predictions [Boniello et al. Nat. Mat. 14 (2015) 908-11]. For the rotational diffusions of partially wetted colloids, slowing down of the particle dynamics can be also expected.

Experiments

Here, the rotational dynamics of Janus colloids at the air-water interface have been experimentally investigated using optical microscopy. Bright field and fluorescent microscopies have been used to measure the in-plane and out-of-plane particle rotational diffusions exploiting the Janus geometry of the colloids we fabricated. Findings Our results show a severe slowing down of the rotational diffusion Dr, connected to the contact line motion and wetting-dewetting dynamics occurring on particle regions located at opposite liquid wedges. A slowing down of the particle rotational diffusion about an axis parallel to the interfacial normal Dr,|| was also observed. Contact line fluctuations due to partial wetting dynamics lead to a rotational line friction that we have modelled in order to describe our results.

Introduction

A solid particle straddling an interface should not be simply seen as a geometrical object partially immersed in a liquid but rather as an intriguing partial wetting configuration. For colloidal microparticles, the fluid interface deformation due to gravity or other external fields is usually weak and the solid particle immersion is set by an equilibrium contact angle in analogy with the partial wetting of a sessile drop on a solid substrate [START_REF] Stocco | A comparison between liquid drops and solid particles in partial wetting[END_REF]. This configuration, however, should not be considered static since both the colloidal particle and the contact line are subjected to thermal agitation, which results in the particle Brownian motion and in the displacement of contact line back and forth around some equilibrium position [START_REF] Boniello | Brownian diffusion of a partially wetted colloid[END_REF].

Particles straddling a fluid or a soft interface are encountered in many research fields ranging from Pickering emulsions, self-assembly, flotation, encapsulation, drug delivery, microrheology and microfluidics [START_REF] Vignati | Pickering Emulsions: Interfacial Tension, Colloidal Layer Morphology, and Trapped-Particle Motion[END_REF][4] [START_REF] Agudo-Canalejo | Critical particle sizes for the engulfment of nanoparticles by membranes and vesicles with bilayer asymmetry[END_REF][START_REF] Agudo-Canalejo | Uniform and Janus-like nanoparticles in contact with vesicles: Energy landscapes and curvature-induced forces[END_REF][7] [START_REF] Hassan | Droplet Liquid/Liquid Interfaces Generated in a Microfluidic Device for Assembling Janus Inorganic Nanohybrids[END_REF]. Translational and rotational motions of particles partially immersed at a fluid interface differ strongly from the motions in the bulk [START_REF] Brenner | A Micromechanical Derivation of Fick ' s Law for Interfacial Diffusion of Surfactant Molecules[END_REF][START_REF] Brenner | Conservation and Constitutive Equations for Adsorbed Species Undergoing Surface Diffusion and Convection at a Fluid-Fluid Interface[END_REF]. The fluid interface indeed interacts with the particle motion via hydrodynamic and capillary interactions. As a consequence, the interfacial hydrodynamics becomes rather complex and models are still lacking even for the rotational motion of simple particles. For example, to the best of our knowledge, only the geometry of an half immersed sphere has been modelled but no general expression of the rotational frictions as a function of the particle immersion has been reported [START_REF] O'neill | Slip at the surface of a translating-rotating sphere bisected by a free surface bounding a semi-infinite viscous fluid: Removal of the contact-line singularity[END_REF]. For the translational motion, hydrodynamic models [START_REF] O'neill | Slip at the surface of a translating-rotating sphere bisected by a free surface bounding a semi-infinite viscous fluid: Removal of the contact-line singularity[END_REF] [START_REF] Danov | Viscous drag of a solid sphere straddling a spherical or flat surface[END_REF][START_REF] Fischer | The viscous drag of spheres and filaments moving in membranes or monolayers[END_REF][START_REF] Aaron | Drag and diffusion coefficients of a spherical particle attached to a fluid interface[END_REF], which account for viscous dissipations, particle immersion and finite slip lengths, have been developed. Experiments, however, show large deviations from these models [START_REF] Wu | Dynamics of charged microparticles at oil-water interfaces[END_REF][16] [START_REF] Wang | Probing diffusion of single nanoparticles at water-oil interfaces[END_REF]. Recently, the roles of partial wetting dynamics and contact line pinning (neglected in the previous hydrodynamic models) have been pointed out to explain both the slow particle motion across the interface and the particle translational diffusion parallel to the interface [START_REF] Kaz | Physical ageing of the contact line on colloidal particles at liquid interfaces[END_REF][START_REF] Rahmani | Colloidal particle adsorption at liquid interfaces: Capillary driven dynamics and thermally activated kinetics[END_REF][20] [START_REF] Boniello | Brownian diffusion of a partially wetted colloid[END_REF].

Concerning the rotational motion, for a spherical particle (of radius R) fully immersed in a liquid (with a viscosity ), a unique bulk rotational diffusion coefficient can be defined as Dr,b = kBT/𝜁 𝑟,𝑏 where 𝜁 𝑟,𝑏 is the bulk viscous rotational friction: 𝜁 𝑟,𝑏 = 8R 3 in no slip conditions (and 𝜁 𝑟,𝑏 = 0 in full slip conditions). For a spherical particle half immersed in a liquid, the rotational diffusion is not unique and it will differ if the spherical particle rotates about an axis perpendicular or parallel to the interface normal. Hydrodynamics models predict that in the no slip conditions the rotational diffusion coefficients of an half immersed sphere at a gas-liquid interface should be null for Dr, (𝜁 𝑟,⊥ = ∞) and twice the bulk value for Dr,|| (𝜁 𝑟,∥ = 4R 3 ), where Dr, and Dr,|| are the perpendicular and the parallel rotational diffusion, defined considering the interface normal and the particle axis of rotation, respectively [START_REF] O'neill | Slip at the surface of a translating-rotating sphere bisected by a free surface bounding a semi-infinite viscous fluid: Removal of the contact-line singularity[END_REF]. Removal of the contact-line singularity and the effect of a finite slip length b on the particle rotational diffusions (or frictions) were modelled by O'Neill et al. [START_REF] O'neill | Slip at the surface of a translating-rotating sphere bisected by a free surface bounding a semi-infinite viscous fluid: Removal of the contact-line singularity[END_REF]. This model predicts large variations of the rotational diffusions with the particle size. However, for colloidal particles, one finds that for typical values of b and micrometric particle size, predicted Dr, (and Dr,||) differ only slightly from the bulk rotational diffusion Dr,b being the interfacial diffusions of the same order of magnitude of the bulk Stokes rotational diffusion.

From an applied point of view, rotational diffusion of a colloid at the fluid interface is a key factor for both the design of particle hybrids and for the control of the active motion of self-propelled particles. In wet routes, particle hybrids are sometimes fabricated exploiting the partial wetting of colloids at a fluid interface [START_REF] Fujimoto | Preparation of Unsymmetrical Microspheres at the Interfaces[END_REF] [START_REF] Gu | Heterodimers of nanoparticles: Formation at a liquid-liquid interface and particle-specific surface modification by functional molecules[END_REF][START_REF] Liu | Janus colloids formed by biphasic grafting at a pickering emulsion interface[END_REF]. Adsorption or chemical reactions can be carried only on one partial wetted surface of the particle. Janus or more complex geometry particles have been formed in this way. 18 However to obtain non-symmetric structures, it is crucial that the rotational particle motion is slow enough so that adsorption or chemical reactions occur only on well defined regions of the particle's surface [START_REF] Fujimoto | Preparation of Unsymmetrical Microspheres at the Interfaces[END_REF]. Still at the single particle level, experiments on the translational and rotational dynamics at fluid interfaces remain very challenging, in particular for particle sizes approaching the nanoscale. Numerical studies have mainly focused on nanoparticles, showing that the continuum description of the free interfacial energy valid for micron-size particles breaks down for truly nanometric particles [START_REF] Cheung | Interaction of Nanoparticles with Ideal Liquid-Liquid Interfaces[END_REF][START_REF] Cheung | Stability of Janus nanoparticles at fluid interfaces[END_REF].

Rotational Brownian diffusion is also a key parameter that sets the persistence of active motion of self-propelled colloids [START_REF] Howse | Self-Motile Colloidal Particles: From Directed Propulsion to Random Walk[END_REF]. Janus spherical silica particles half coated with a thin platinum layer are such particles, self-propelling in presence of hydrogen peroxide [START_REF] Wang | Wetting and orientation of catalytic Janus colloids at the surface of water[END_REF]. Recently, we have studied their behaviour at the air/water interface. They possess two hydrophilic faces with similar wetting properties and are only partially wetted when trapped at the interface. We have revealed an enhancement of their two dimensional active motions compared to the bulk [START_REF] Wang | Enhanced active motion of Janus colloids at the water surface[END_REF] [START_REF] Wang | Janus Colloids Actively Rotating on the Surface of Water[END_REF]. In this paper, we report new experimental results on their rotational Brownian motion extending our first observations on the slowing down of the perpendicular and parallel rotational diffusion coefficients, Dr, and Dr,|| [START_REF] Wang | Wetting and orientation of catalytic Janus colloids at the surface of water[END_REF][START_REF] Wang | Janus Colloids Actively Rotating on the Surface of Water[END_REF]. A model for the rotational friction is also developed in order to describe our experimental findings.

Materials and Methods

Colloidal particles

Two particle systems have been investigated: (i) fluorescent platinum-melamine resin (Pt-MF) Janus colloids, and (ii) non-fluorescent platinum-silica (Pt-SiO2) Janus colloids. The first ones were fabricated starting from melamine resin MF particles R = 1.15 ± 0.3 µm (Microparticles GmbH, Germany). Pt-SiO2 were fabricated starting from silica particles R = 1.06 ± 0.3 µm (Microparticles GmbH, Germany). Particle size measurements by scanning electron microscopy agree with the nominal size and polydispersity provided by the supplier. Both Pt-MF and Pt-SiO2 Janus colloids were fabricated by physical vapour deposition [START_REF] Love | Fabrication and Wetting Properties of Metallic Half-Shells with Submicron Diameters[END_REF]. Details on the fabrication protocol can be found in [START_REF] Wang | Wetting and orientation of catalytic Janus colloids at the surface of water[END_REF][START_REF] Wang | Enhanced active motion of Janus colloids at the water surface[END_REF][START_REF] Wang | Janus Colloids Actively Rotating on the Surface of Water[END_REF]. Two metal thin layers were deposited on top of colloid monolayers in order to have a stable and homogeneous coating on the particles. On the bare colloids, first 10 nm of titanium and then 20 nm platinum were deposited, see Fig. 1.

Sample preparation

Dilute colloidal dispersion of Janus particles were sprayed by airbrush deposition on water, which was filled inside a cylindrical container of 10 mm in diameter [START_REF] Boniello | Brownian diffusion of a partially wetted colloid[END_REF][START_REF] Wang | Enhanced active motion of Janus colloids at the water surface[END_REF]. Area fraction of Janus particles at the interface is very low, << 0.1%. After particle deposition the container was also close in order to reduce water evaporation. All measurements are performed at room temperature (T = 22 °C).

Particle tracking, image analysis and particle contact angle

Bright field and fluorescence optical microscopies were used for particle tracking and imaging. Up-right and inverted optical microscopes mounted on anti-vibration tables were used. In typical experiments, images of isolated Janus particles were recorded at a rate of 30 frames per second using objective of different magnifications (×32, ×50, ×63 and ×100). The partial coating of platinum on the colloid modifies the light transmission through the particles or the fluorescence of the particle. It is then possible to evaluate Pt region under adequate illumination. Using IDL (Interactive Data Language) routines, we treated the raw image sequences and detected the Pt-cap of Janus particles by applying a grayscale threshold. The out-of-plane orientation  of the particle with respect to the interface was evaluated by measuring the absolute value of the visible Pt cap area. The in-plane orientation  of the particle was instead evaluated by measuring the orientation of the lever arm L connecting the center of the whole particle and the center of the Pt-cap. Tracking of the particle center was done by an IDL routine or by using an image correlation-based approach (''Stat Tracker St. Andrews'') implemented in Labview (National Instruments).

A "Gel trapping" technique was used to measure the particle contact angle [START_REF] Paunov | Novel Method for Determining the Three-Phase Contact Angle of Colloid Particles Adsorbed at Air -Water and Oil -Water Interfaces[END_REF]. Details on the protocol used can be found in [START_REF] Boniello | Brownian diffusion of a partially wetted colloid[END_REF]. Briefly, Janus particles were deposited on a gelled water (Phytagel (Sigma-Aldrich) solution, 2% wt. in water) surface at room temperature. Then, the temperature was raised briefly to 90°C in order to let the particles finding the stable contact angles at the air-water interface. Back at room temperature, Janus particles are transfer in a film (Norland Optical Adhesive 81 (NOA81)) which was photopolymerized by UV light. In this way, the polymerized film contained the Janus particles trapped at a complementary position with respect to the air-water interface Scanning Electron Microscopy (SEM) on a FEI Quanta 200 FEG microscope in a tilted configuration was used to evaluate the particle contact angle.

Fig. 1(A) and (B) show SEM pictures corresponding to (gel-trapped) Janus colloidal particles. Pt-MF Janus colloids show contact angles = 65°±6° and Pt-SiO2 Janus colloids show  = 64 ± 2° at the air-water interface. It is important to note that bare particles have smooth surfaces with negligible roughness (< 1 nm). Janus colloids instead show surface roughness of about 10 nm, which is comparable with the Pt coated layer thickness. We also noted that the morphology of the coated Pt layer is more homogenous for silica than MF colloids, probably due a better adhesion of titanium and platinum on silica than MF.

Results: Rotational diffusion of Janus colloids at the gas-liquid interface

To measure the rotational diffusion of spherical particles, we used Janus particles with two distinguishable faces. If the Janus boundary crosses the fluid interface, particle orientation angles  and  can be evaluated and rotational diffusions can be measured, see Fig.

2 [START_REF] Wang | Wetting and orientation of catalytic Janus colloids at the surface of water[END_REF][START_REF] Wang | Janus Colloids Actively Rotating on the Surface of Water[END_REF].

An example of fluorescent microscopy experiments on Pt-MF Janus colloids at the air-water interface are shown in Fig. 2(A). In these experiments, the Pt cap strongly diminishes the particle fluorescent signal and particle images appear as the crescent moon phases. Hence, the fluorescent region of particle corresponds to the silica area of the colloid, which is not covered by Pt. Subtracting the latter region to the circular area of the entire particle, the Pt cap region can be obtained and its area and orientation fluctuations can be monitored in time, Fig. 2

(B) and (C).

Bright field microscopy experiments of Pt-SiO2 Janus colloids were already described in our previous articles [START_REF] Wang | Wetting and orientation of catalytic Janus colloids at the surface of water[END_REF][START_REF] Wang | Janus Colloids Actively Rotating on the Surface of Water[END_REF][START_REF] Wang | Enhanced active motion of Janus colloids at the water surface[END_REF], where the darker side of the particle corresponds to the Pt cap possessing a complex refractive index of 0.48 + 4.87i (at 532 nm wavelength, whereas the silica refractive index is 1.46 + 0i) [START_REF] Wang | Wetting and orientation of catalytic Janus colloids at the surface of water[END_REF][START_REF] Wang | Janus Colloids Actively Rotating on the Surface of Water[END_REF][START_REF] Wang | Enhanced active motion of Janus colloids at the water surface[END_REF]. By analysing the images taken during the tracking of the Brownian motion of Pt-SiO2 Janus colloids at the air-water interface, we were able to evaluate the changes of the absolute area of the platinum cap. We then evaluated the orientation angle  (see Fig. 2(B)) from the visible Pt absolute area, APt, knowing that APt = 1/2(1cos)R 2 , and calculated the mean square angular displacement MSAD(). In Fig. 3, we plotted MSAD() as a function of the lag time for three specific datasets corresponding to three different particles for which  varies of  during 30 s. We fitted the MSAD data by:

MSAD() = MSAD0 + 2Dr,t, (1)
where the parameter MSAD0 accounts for the noise introduced by the image treatment. From the fits in Fig. 3, we find that rotational diffusion times r,=1/Dr, = 87 s (triangle), 152 s (circle), and 547 s (square) are larger by one order of magnitude or more than the hydrodynamic prediction for particles half immersed in water with finite slip lengths b, r, = 𝜁 𝑟,⊥ /kBT = 8. 4 s if b = 1 nm (r,= 11 s if b = 0.1 nm) [START_REF] O'neill | Slip at the surface of a translating-rotating sphere bisected by a free surface bounding a semi-infinite viscous fluid: Removal of the contact-line singularity[END_REF]. Note that the rotational diffusion time in the bulk is r,b=1/Dr,b = 6.3 s, which is of the same order of magnitude of the rotational times calculated with a finite slip length.

In order to discuss these results, we assume the hydrodynamic prediction of 𝜁 𝑟,⊥ for b = 1 nm for half immersed particles [START_REF] O'neill | Slip at the surface of a translating-rotating sphere bisected by a free surface bounding a semi-infinite viscous fluid: Removal of the contact-line singularity[END_REF], and associate an Arrhenius form to the rotational diffusion Dr,:

𝐷 𝑟,⊥ = 𝑘𝑇 𝜁 𝑟,⊥ exp (- |Δ𝐸 𝛽 | 𝑘 𝐵 𝑇 ), ( 2
)
where E is the activation energy that is required for the out-of-plane change of orientation. Averaging on all MSAD data, we found E = 3.6 ± 0.9 kBT. Now we turn our attention to the in-plane rotational diffusion, see Fig. 2(C). By tracking the motion of fluorescent MF particles partially covered by platinum, we were able to distinguish the fluorescent cap of the colloid from the platinum cap that strongly reduces the particle fluorescence (see Fig. 2(A)). Thus, we calculate the angle  between the projected Janus axis and the lab frame.  was evaluated from the orientation of the lever arm L with respect to the laboratory x-y axis in the interfacial plane, see Fig. 2(C). MSAD() was calculated for different L/R datasets. In Fig. 4(A), MSAD() data show several slopes in different lag time intervals. We fitted the data in the short time limit, for t < 0.2 s, by:

MSAD() = MSAD0 + 2Dr,||t. (3)
From the fits, we plotted the coefficient Dr,|| as a function of L/R in Fig. 4(B). Dr,|| for Pt-MF Janus colloids is surprisingly low. In no-slip conditions, given the particle contact  65°, the diffusion coefficient Dr,|| = kBT /𝜁 𝑟,|| is expected to be in a range between the bulk value of kBT/(8R 3 ) and the half immersed particle value of kBT/(4R 3 ). Moreover, Dr,|| should be higher than the latter prediction for positive slip lengths [START_REF] O'neill | Slip at the surface of a translating-rotating sphere bisected by a free surface bounding a semi-infinite viscous fluid: Removal of the contact-line singularity[END_REF]. Except for one measurement, Dr,|| is however lower than the prediction and it is even lower than the bulk value. In the long lag time limit, most of MSAD data show low slopes or even plateaus, which points to confined dynamics probably due to long range capillary interactions, see inset Fig. 4(A) [START_REF] Wittmeier | Rotational Analysis of Spherical, Optically Anisotropic Janus Particles by Dynamic Microscopy[END_REF][START_REF] Xu | Subdiffusion of a Sticky Particle on a Surface[END_REF][START_REF] Castro-Villarreal | A Brownian dynamics algorithm for colloids in curved manifolds[END_REF].

Just for the sake of comparison with Dr,, Dr,|| can be also written in an Arrhenius form:

𝐷 𝑟,∥ = 𝑘𝑇 𝜁 𝑟,∥ exp(- |Δ𝐸 𝜑 | 𝑘 𝐵 𝑇 ), ( 4
)
where E is the activation energy that is required for a change of orientation . For a half immersed particle,  = 90°, 𝜁 𝑟,||  4R 3 (if b = 0.1 or 1 nm as before) [START_REF] O'neill | Slip at the surface of a translating-rotating sphere bisected by a free surface bounding a semi-infinite viscous fluid: Removal of the contact-line singularity[END_REF]. Given the Janus particle contact angle   65°, we assume here that 𝜁 𝑟,|| = 1.45 (8R 3 ) in analogy with the contact angle correction in the model of Fischer et al. for the translational motion [START_REF] Fischer | The viscous drag of spheres and filaments moving in membranes or monolayers[END_REF]. Accounting for all MSAD data, we find E = 1.8 ± 0.9 kBT. Hence, the slowing down of Dr,|| is much less severe than the one of Dr, as Eis smaller than E.

Discussion: Line friction

As pointed out in Boniello et al. for the slowing down of the translational diffusion of bare particles at the air-water interface, our experimental results cannot be described by current hydrodynamic models that assume a flat and static fluid interface [START_REF] Boniello | Brownian diffusion of a partially wetted colloid[END_REF]. We suggested that thermally activated deformations at the contact line lead to fluctuating random forces on the particle. We described these fluctuating forces for the translational motion and associated an extra viscous friction on the particle, which leads to a measured translational diffusion slowing down. Here we extend this analysis for the rotational diffusion.

We start summarizing the force calculations for the translational diffusion as reported in Boniello et al. [START_REF] Boniello | Brownian diffusion of a partially wetted colloid[END_REF]. A fluctuating force F and a torque M acting on the particle can result from an interface deformation due to a contact line displacement, see Fig. 5(A). Considering a short contact line segment l and time t at an angular position 𝛷 𝑖 with respect to an arbitrary axis w in the interface plane, a contact line displacement  induces a force F and also a torque M on the particle (Fig. 5). Focussing on the force, one can write the component along w by 𝐹 𝐿,𝑖 (𝑡, 𝑙) = 𝐹 𝐿 0 (𝑡, 𝑙)cos𝛷 𝑖 , where 𝐹 𝐿 0 (𝑡, 𝑙) = 𝛾𝑙(1 -cos𝜒), where  is the deformation angle between the horizontal plane and a plane defined by the tangents to the fluid interface at the contact line, see Fig. 5(A) and (B). Several fluctuations may occur along the contact line. Assuming that these fluctuations are not correlated over a finite distance l=, the number n of possible independent fluctuations is:

n = 2Rsin/ (5)
Hence, the total random force is 𝐹 𝐿 (𝑡) = ∑ 𝐹 𝐿,𝑖 (𝑡, 𝜆) 𝑛 𝑖=1

. One may associate a characteristic time L to the dynamics of 𝐹 𝐿 (𝑡). For t >L, the mean of this random force should be zero, i.e. < 𝐹 𝐿 (𝑡) > = 0. However, the mean squared of 𝐹 𝐿 (𝑡) is different from zero and equal to:

< 𝐹 𝐿 (𝑡) 2 >= 𝑛 < 𝐹 𝐿,𝑖 (𝑡, 𝜆) 2 >= 𝑛 < [𝛾𝜆(1 -cos𝜒)] 2 >= 1 2 𝑛[𝛾𝜆(1 -cos𝜒)] 2 (6)
Hence, this random force due to contact line fluctuations will affect the Brownian motion of the particle.

Under some assumptions, one can define a line friction coefficient 𝜁 𝑡,𝐿 associated with the fluctuations of the contact line: Note that in Eq. 7 we impose that < 𝐹 𝐿 (0)𝐹 𝐿 (𝑡) > vanishes if t >L. The total friction experienced by the particle is the sum of 𝜁 𝑡,𝐿 and 𝜁 𝑡,𝐻 , where 𝜁 𝑡,𝐻 is the hydrodynamic friction, which depends only on the particle immersion and the viscosity [START_REF] Danov | Viscous drag of a solid sphere straddling a spherical or flat surface[END_REF][13] [START_REF] Pozrikidis | Particle motion near and inside an interface[END_REF]. Eqs. 5, 6 and 7 allow us to write 𝜁 𝑡,𝐿 as:

𝜁 𝑡,𝐿 = 1 2𝑘 𝐵 𝑇 ∫ < 𝐹 𝐿 (0)𝐹 𝐿 (𝑡) > 𝑑𝑡 ≈ +∞ -∞ 1 2𝑘 𝐵 𝑇 < 𝐹 𝐿 (0)
𝜁 𝑡,𝐿 ≈ 1 4𝑘 𝐵 𝑇 𝑛[𝛾𝜆(1 -cos𝜒)] 2 𝜏 𝐿 = π𝑅sin𝛼 2𝑘 𝐵 𝑇 𝜆[𝛾(1 -cos𝜒)] 2 𝜏 𝐿 . ( 8
)
The remaining unknowns in eq. 8 are L and . The characteristic time L of the interface fluctuations is given by the molecular kinetic theory of partial wetting [START_REF] Blake | The physics of moving wetting lines[END_REF]:

𝜏 𝐿 ≅ 𝜂𝑣 𝑚 𝑘 𝐵 𝑇 exp 𝐸 𝑎 𝑘 𝐵 𝑇 = 𝜂𝑣 𝑚 𝑘 𝐵 𝑇 exp 𝜆 2 𝛾(1+cos𝛼) 𝑘 𝐵 𝑇 ( 9
)
where vm is the molecular volume of the liquid (vm = 2.99 10 29 m 3 for water) and 𝐸 𝑎 is the activation energy needed for the line displacement, which can be written as the adhesion energy 𝐸 𝑎 = 𝜆 2 𝛾(1 + cos𝛼) [START_REF] Blake | The physics of moving wetting lines[END_REF].

Finally, the deformation angle  of the interface (Fig. 5(A)) can be found for n >>1 [START_REF] Lehle | Ellipsoidal particles at fluid interfaces[END_REF].

tan  4sin/ . (10)
Now, we focus our attention on the rotational dynamics. Following the same approach as for the translational friction, the rotational line friction related to Dr, (Fig. 2(B)) can be written as [START_REF] Boniello | Brownian diffusion of a partially wetted colloid[END_REF]:

𝜁 𝑟⊥,𝐿 ≈ 1 2𝑘 𝐵 𝑇 〈𝑀 𝐿,⊥ (0) 2 〉𝜏 𝐿 , (11)
where 𝑀 𝐿,⊥ is the total torque (see Fig. 5(A)) due to contact line fluctuation, 〈𝑀 𝐿,⊥ (𝑡) 2 〉 = 𝑛〈𝑀 𝐿⊥,𝑖 (𝑡) 2 〉, and n is given by eq. 5.

A difference between the translational and rotational friction calculations can now be pointed out. If the fluctuation of the contact line corresponds to an advancing line motion (positive vertical displacement, see Fig. 5), corresponding to the wetting of a particle region ×the torque on the particle becomes 𝑀 𝐿⊥ 0 (𝑡) = 𝐹 1 𝑅cos𝛼 -𝐹 2 𝑅sin𝛼, where 𝐹 1 = 𝛾𝜆(1 -cos𝜒) and 𝐹 2 = 𝛾𝜆sin𝜒. While if the contact line fluctuation leads to a dewetting of a particle region ×(negative vertical displacement), 𝑀 𝐿⊥ 0 (𝑡) = 𝐹 1 𝑅cos𝛼 + 𝐹 2 𝑅sin𝛼. Hence,

< 𝑀 𝐿⊥ (𝑡) 2 >= 𝑛 < 𝑀 𝐿⊥,𝑖 (𝑡) 2 >= 1 2 𝑛[(𝐹 1 𝑅cos𝛼) 2 + (𝐹 2 𝑅sin𝛼) 2 ] (12)
The rotational line friction 𝜁 𝑟⊥,𝐿 can be now written as:

𝜁 𝑟⊥,𝐿 ≈ 1 2𝑘 𝐵 𝑇 𝜋𝑅 3 sin𝛼𝛾 2 𝜆[(1 -cos𝜒) 2 cos 2 𝛼 + (sin𝜒sin𝛼) 2 ]𝜏 𝐿 . ( 13
)
where equations 9 and 10 give 𝜒 and 𝜏 𝐿 .

In Fig. 6, we show that for = 0.4 nm at intermediate particle contact angles 𝜁 𝑟⊥,𝐿 (equation 13) becomes comparable to the bulk rotational friction, 8R 3 . For  as for Pt-MF Janus colloids, and = 0.6 nm, 𝜁 𝑟⊥,𝐿 is three orders of magnitude higher than the bulk value. Hence  between 0.4 nm and 0.6 nm could explain our experimental findings showing a severe slowing down of the rotational diffusion Dr, (Fig. 2(B)). These values also agree with the value of  evaluated from the translational friction [START_REF] Boniello | Brownian diffusion of a partially wetted colloid[END_REF]. Note that the energy E in the Arrhenius expression of Dr, is related to the adhesion energy in the molecular kinetic theory of partial wetting, which is the energy needed to displace the contact line on the particle surface over a distance . Given that the Janus particle surface is not perfectly smooth due to the platinum coating and intrinsic nanometric roughness, this energy is strictly connected to the strength of line pinning [START_REF] Ramos | Pinning-depinning of the contact line on nanorough surfaces[END_REF] [START_REF] Boniello | Brownian diffusion of a partially wetted colloid[END_REF]. An analogy can be also made between the activation energy 𝐸 𝑎 = 𝜆 2 𝛾(1 + cos𝛼) in eq. 9 and the activation energy described for the rotation of nanoparticles with defects in molecular dynamics (MD) simulations [START_REF] Razavi | Nanoparticles at liquid interfaces : Rotational dynamics and angular locking[END_REF]. In MD simulations for very small nanoparticles with a cylindrical symmetry, the life-time of the nanoparticle metastable orientations depends strongly on the presence of a satellite surface defect, which could lead to life-times from 5 to 10 4 times higher than in absence of the surface defect. Here, surface defects also affect  that should be considered as an averaged value since the particle is composed of two faces (Pt and silica). Hence, a slowing down of the rotational diffusion Dr, can be interpreted in terms of thermal hopping of the contact line as for colloidal particles adsorbing at the oil-water interface [START_REF] Boniello | Brownian diffusion of a partially wetted colloid[END_REF] [START_REF] Kaz | Physical ageing of the contact line on colloidal particles at liquid interfaces[END_REF].

Finally, we can discuss the in-plane rotational diffusion Dr,|| results shown in Fig. 4. A slowing down of Dr,|| points to the existence of a line friction for the rotational diffusion about an axis parallel to the interfacial normal. However, the model built before for the translational motion and for the rotation about an axis perpendicular to the interfacial normal (Dr,) assumed that contact line fluctuations lead to forces directed to the vertical axis passing through the center of a perfectly spherical particle (see Fig.

5(B))

. Hence in this case, the force acting on the segment  has no component tangent to the contact line perimeter. Consequently, no fluctuating torque related to Dr,|| should exist, and a rotational line friction connected to a rotation about an axis parallel to the interfacial normal is not expected. However, a breaking of the particle spherical symmetry could occur for Janus colloids given the non-negligible thickness and the non-regular shape of the Pt coating. In this case, Janus colloids can be regarded as low aspect ratio ellipsoids for which a rotational line friction was modelled and a slowing down of the rotational diffusion has been experimentally observed [START_REF] Boniello | Brownian diffusion of a partially wetted colloid[END_REF]. Additionally, one could also consider a generic scenario for which the contact line fluctuations yield both to a radial and an azimuthal force component, 𝐹 𝛷 , able to generate a fluctuating torque parallel to the interface normal, see Fig. 5(C) .

Following the same approach as before, a rotational line friction related to Dr,|| can be written as [START_REF] Boniello | Brownian diffusion of a partially wetted colloid[END_REF]:

𝜁 𝑟∥,𝐿 ≈ 1 2𝑘 𝐵 𝑇 〈𝑀 𝐿,∥ (0) 2 〉𝜏 𝐿 , (14)
where 𝑀 𝐿,∥ is the total torque due to contact line fluctuations and 〈𝑀 𝐿,∥ (𝑡) 2 〉 = 𝑛〈𝑀 𝐿∥,𝑖 (𝑡) 2 〉, n is given by eq. 5 and:

< 𝑀 𝐿,∥ (𝑡) 2 >= 𝑛 < 𝑀 𝐿∥,𝑖 (𝑡) 2 >= 1 2 𝑛[𝐹 𝛷 𝑅sin𝛼] 2 (15)
where 𝐹 𝛷 = 𝛾𝜆 cos Ξ, where Ξ is an angle which defines the azimuthal force component 𝐹 𝛷 generating a torque parallel to the interface normal, see Fig. 5(B) and (C). Hence, a rotational friction 𝜁 𝑟∥,𝐿 can be written:

𝜁 𝑟∥,𝐿 = 1 2𝑘 𝐵 𝑇 𝜋𝑅 3 sin 3 𝛼𝛾 2 𝜆 cos 2 Ξ𝜏 𝐿 = sin 3 𝛼 2 𝑣 𝑚 𝜆𝛾 2 cos 2 Ξ (𝑘 𝐵 𝑇) 2 exp 𝜆 2 𝛾(1+cos𝛼) 𝑘 𝐵 𝑇 𝜋𝜂𝑅 3 . ( 16
)
Note that for Ξ =  (in the ideal case shown in Fig. 5(B)) there is no rotational line friction 𝜁 𝑟∥,𝐿 . Since Ξ cannot be calculated or estimated without making several assumptions, in Fig. 7 we plotted the ratio of 𝜁 𝑟∥,𝐿 and the bulk rotational friction as a function of the contact line displacement  for and for three given values of 90° Ξ = 0.1°, 1° and 10°. These calculations can be compared with experimental values of Dr,|| ,which are about five times slower than the hydrodynamic prediction.

In the range of  between 0.4 nm and 0.7 nm, the calculated 𝜁 𝑟,|| (eq. 16) agree with the experimental results. However as pointed out before, the value of Ξ cannot be accessed.

Before concluding this section, it is worth noting that particle surface heterogeneity (roughness or defects) would lead not to a single value of contact line displacement but to a range of  values (and deformation angle Ξ values). For Janus colloids, surface roughness and defects due to the coating fabrication were observed and their distributions seem also non-homogeneous (see Fig. 1). Hence, a distribution of  (and Ξ) values due to particle surface heterogeneity can be also related to a large distribution of results observed for the rotational diffusions of Janus particles.

Conclusion

Rotational diffusion of partially immersed particles at a fluid interface has been experimentally investigated focussing on Janus spherical colloids at the air-water interface. The Janus geometry has been exploited to distinguish the two faces of the particle in optical microscopy. Given that two particle's faces have similar wetting properties [START_REF] Wang | Wetting and orientation of catalytic Janus colloids at the surface of water[END_REF], no strong line pinning on the Janus boundaries has been observed. In this regard, similar results can be expected for non-Janus particles. In agreement with the slowing down of the translational diffusion previously reported for bare spherical and ellipsoidal particles [START_REF] Boniello | Brownian diffusion of a partially wetted colloid[END_REF], we have observed a slowing down of the rotational diffusion both for the perpendicular and parallel rotations, Dr, and Dr,|| (Fig. 3 and4). Hydrodynamic models, which assume a flat and calm fluid interface, fail to explain our experiments [START_REF] O'neill | Slip at the surface of a translating-rotating sphere bisected by a free surface bounding a semi-infinite viscous fluid: Removal of the contact-line singularity[END_REF]. In order to describe our results, instead, we have extended a model built for the translational diffusion [START_REF] Boniello | Brownian diffusion of a partially wetted colloid[END_REF] of bare spherical colloids to the rotational diffusion. In the model, contact line fluctuations and weak line pinning on the surface defects of the particles result in contact line displacement , which impacts dramatically the rotational diffusion (Fig. 6 and7).

The severe slowing down of Dr, is in agreement with the experiments reported by Kaz et al. [START_REF] Kaz | Physical ageing of the contact line on colloidal particles at liquid interfaces[END_REF] on the slow vertical motion of single colloids breaching a fluid interface. The slowing down in both cases is related to the relative motion of the contact line on the solid particle, and connected to wetting or dewetting processes occurring on the particle surface. The slowing down of Dr,|| reveals that contact line fluctuations may also lead to force components tangential to the contact line and result in a rotational line friction 𝜁 𝑟,|| .

In general, nanoscale roughness and heterogeneity present on the particle's surface have a very strong impact on the interfacial frictions. This result can be rationalised considering that single nanometric defects possess a defect energy of few kBT, and, in absence of any external field, the diffusion dynamics is driven by thermal agitation (kBT) only. A large distributions of the rotational frictions were observed, which reflect the dramatic dependence of the rotational frictions to  variations (Fig. 6 and7).

The results presented here have clear impacts on the understanding and control of assembly occurring at the fluid interface and in the field of surface microrheology. Dr, is in fact a key parameter for the fabrication of Janus particles via adsorption or chemical reactions of partially wetted bare colloids in one fluid phase [START_REF] Hassan | Droplet Liquid/Liquid Interfaces Generated in a Microfluidic Device for Assembling Janus Inorganic Nanohybrids[END_REF]. Dr,|| and the associated rotational line friction 𝜁 𝑟,|| plays also a pivotal role in the modelling of passive surface microrheology, because it represents a large contribution to the dissipation measured [START_REF] Dhar | Active interfacial shear microrheology of aging protein films[END_REF] [START_REF] Maestro | Surface rheology: macro-and microrheology of poly(tert-butyl acrylate) monolayers[END_REF].

Perspectives of this work include the role of line pinning strength (weak or strong line pinning) on the contact line frictions, and on how rotational line frictions change in the presence of external fields or persistent velocities as in active microrheology or macrorheology.

Figure 1

 1 Figure 1 Particles trapped in a polymer layer at the complementary contact angle position with respect to the airwater interface. (A) SEM images of two Pt-MF Janus particles, with a contact angle at the air-water interface of   65°. (B) SEM images of two gel trapped Pt-SiO2 Janus particles, with a contact angle at the air-water interface of   64°. Dashed lines indicate the Janus boundaries. Scale bars correspond to 2 µm.

Figure 2 (Figure 3

 23 Figure2(A) Fluorescent microscopy images of a Pt-MF Janus colloid at the air-water interface taken at different time t. The bright region of the particle corresponds to the silica face of the Janus colloid. (B) Side view sketch of a Janus particle at the gas-liquid interface.  is the angle defined by the normal to the interface (𝑧) and the Janus axis (𝑗) and Dr, is the associated rotational diffusion. (C) Top view sketch of a Janus particle at the gas-liquid interface. L is the lever arm that connects the center of the whole particle and the center of the visible Pt cap.  is the angle defined by x-axis (in the laboratory frame) and the projected direction of L in the x-y interfacial plane.

Figure 4

 4 Figure 4 (A) Mean squared angular displacement (MSAD) of the in-plane orientation angle  as a function of the lag time of fluorescent Pt-MF Janus colloids at the air-water interface for different L/R. Solid lines represent best fits of MSAD() = MSAD0+2Dr,||t for t < 0.2. (B) Interfacial rotational diffusion Dr,||t as a function of L/R.

Figure 5 (

 5 Figure 5 (A) Side view sketch of an interface fluctuation at the contact line. On the left side of the particle, interfacial tensions are in equilibrium and  is the equilibrium contact angle defined by Young's equation. On the right side, an interface fluctuation displaces the contact line on the particle over a distance  and drives the interfacial tensions out of equilibrium.  is the angle between the tangent to the fluid interface at the particle and the horizontal. The imbalance between  and cos leads to a force 𝐹 𝐿 0 on the particle. (B) Top view of a line deformation, over a segment , at the angular position 𝛷 𝑖 . (C) Sketch of a contact line displacement × on the particle surface for = 90° and ≠ 90°.

Figure 6

 6 Figure 6 Rotational line friction 𝜁 𝑟⊥,𝐿 divided by the bulk Stokes rotational friction as a function of the particle contact angle for different values of the contact line displacement .

Figure 7

 7 Figure 7 Rotational line friction 𝜁 𝑟||,𝐿 divided by the bulk Stokes rotational friction as a function of the contact line displacement for different values of the angle  (see Fig. 5(B) and (C)).

Acknowledgements

We acknowledge financial supports from the ANR SURFANICOL ANR-14-CE07-0039-01. We also thank F. Fernandez and the MEA Platform of University of Montpellier for SEM characterizations.


ABSTRACT: Aqueous interfaces are ubiquitous in Nature and play a fundamental role in environmental, biological processes, or modern nanotechnologies. These interfaces are negatively charged and despite several decades of research, the rationale behind this phenomenon is still under debate. Two main controversial schools of thought argue on this issue; the first relies on the adsorption of hydroxide anions on hydrophobic surfaces, whereas the second one supports a self-rearrangement of water molecules at the interface bearing hydronium ions. Here, we report on two series of independent experimental studies (nanoprecipitation and interfacial tension measurements) that demonstrate that in the pH 5-10 range, the negative interfacial charge of the colloids mostly stems from bicarbonate ions; whereas, at lower and higher pH, protons and hydroxide ions contribute, with bicarbonate ions, to the interfacial charging. This new interpretation complies with previous studies and opens new prospective to this striking physical chemical issue.

Table of Contents Graphic

The origin of the negative charge arising on surfaces in contact with water is a relevant question that did not get a definitive answer so far (For two very recent, complete reviews on the field, see [START_REF] Agmon | Protons and Hydroxide Ions in Aqueous Systems[END_REF][START_REF] Bjorneholm | Water at Interfaces[END_REF] ). For about 100 years, it has been established that air bubbles [START_REF] Currie | Adsorption at a water surface[END_REF] and oil or polymers dispersions [START_REF] Zimmermann | Hydroxide and hydronium ion adsorption -A survey[END_REF] display a negative potential in water. Initially evidenced by (micro)electrophoresis, this phenomenon was further investigated by acid-base titration experiments on oil/water interfaces over a large pH range (from 3-4 to 11-12). [START_REF] Beattie | The Pristine Oil/Water Interface: Surfactant-Free Hydroxide-Charged Emulsion[END_REF] More recently, Colussi et al. nebulized acid or basic vapors at water/air surface to promote the reaction of the generated ions with interfacial ones and probe the pH of water at the interface with air. The authors detected an isoelectric point around 4, the surface becoming negatively charged above this pH value. [START_REF] Enami | Proton Availability at the Air/Water Interface[END_REF][START_REF] Mishra | Brønsted basicity of the air-water interface[END_REF] Hence, there is currently a general consensus on the fact that the surface of neutral water is negatively charged. [START_REF] Chaplin | Theory vs Experiment: What is the Surface Charge of Water?[END_REF] On the other hand, in spite of the high level of interest expressed by the scientific community in solving this open question, there is currently no clear understanding of the nature and the extent of ions present at hydrophobic interfaces. A first explanation put forward for such a behavior is that hydroxide ions preferentially adsorb at the interface. [START_REF] Marinova | Charging of Oil-Water Interfaces Due to Spontaneous Adsorption of Hydroxyl Ions[END_REF] Some theoretical models proposed by Gray-Weale and Beattie [START_REF] Greay-Weale | An explanation for the charge on water's surface[END_REF][START_REF] Liu | The Surface Relaxation of Water[END_REF] and others, [START_REF] Zang | Physisorption of Hydroxide Ions from Aqueous Solution to a Hydrophobic Surface[END_REF][START_REF] Bai | Surface Propensities of the Self-Ions of Water[END_REF] suggest the autolysis of water molecules close to the interface, releasing excess hydroxide ions keen to reach the interface. This natural splitting of water molecules close to interfaces would occur under a large pH range, independently of the natural content of hydroxides in solution. The concurrent school of thought relies on molecular simulation, [START_REF] Buch | Water surface is acidic[END_REF][START_REF] Mundy | Hydroxide anion at the air-water interface[END_REF][START_REF] Duignan | Hydronium and hydroxide at the air-water interface with a continuum solvent model[END_REF] sum frequency spectroscopy analyses, [START_REF] Vacha | The Orientation and Charge of Water at the Hydrophobic Oil Droplet-Water Interface[END_REF][START_REF] Samson | Sum frequency spectroscopy of the hydrophobic nanodroplet/water interface: Absence of hydroxyl ion and dangling OH bond signatures[END_REF] and surface tension of concentrated salt solutions, [START_REF] Santos | Ions at the Water-oil Interface: Interfacial Tension of Electrolyte Solutions[END_REF][START_REF] Levin | Ions at hydrophobic interfaces[END_REF] to infer that water/air surfaces and hydrophobic/water interfaces are primarily covered by protons. In their views, water molecules then self-arrange to accommodate these physisorbed hydronium ions at the interface, which then displays a virtual negative charge. Consistent with this assumption, it was recently shown by electrophoresis that water droplets floating in different oils (silicone, paraffin) bear a positive charge, whatever the original pH of the drops. [START_REF] Schoeler | Charge of water droplets in non-polar oils[END_REF] Both schools thus propose convincing arguments to support their view and debate vigorously on potential inconsistencies between experimental and simulation data for each proposed model. [START_REF]A complete volume of Faraday Discussions[END_REF] As a consequence, it is at present difficult to side with one movement of thought.

Besides, it is worth noting that direct observation, identification and quantification of adsorbed ions is hardly feasible (for instance by SFG [START_REF] De Agular | The Interfacial Tension of Nanoscopic Oil Droplets in Water Is Hardly Affected by SDS Surfactant[END_REF][START_REF] Jena | Surface Impurities Are Not Responsible For the Charge on the Oil/Water Interface: A Comment[END_REF] ), owing to the very low content of ions to be found at the interface (vide infra). It remains nevertheless that these two proposed approaches seem somehow oversimplified in the fact that they consider exclusively one type of ions at the time to account for the interfacial charge. Quite originally, the team of Ruckenstein proposed to reconcile observed surface tensions with zeta potentials at air/water interfaces by taking into account 'all ions' introduced in water for measurement: namely, Na + , Cl -, H 3 O + and OH -(the pH is generally adjusted by using HCl or NaOH solutions). [START_REF] Manciu | Ions near the air/water interface: I. Compatibility of zeta potential and surface tension experiments[END_REF][START_REF] Manciu | Ions near the air/water interface. II: Is the water/air interface acidic or basic? Predictions of a simple model[END_REF][START_REF] Manciu | On the surface tension and Zeta potential of electrolyte solutions[END_REF] Doing so, and using up to 5 adjusting parameters, adsorption of OH -at the interface was validated, but in far less quantity than what zeta potential measurements suggest, which is not satisfactory.

Another important fact when dealing with aqueous dispersions is the carbonation of water. [START_REF] Ninham | Building bridges between the physical and biological sciences[END_REF] Indeed, even under inert conditions, it is impossible to avoid the uptake of carbon dioxide by water (into its H 2 CO 3 form), and its transformation into bicarbonate (HCO 3 -) anions, and at high pH into carbonate ones (CO 3 2-) (basically >10). [START_REF] Stirling | H 2 CO 3 Forms via HCO3in Water[END_REF] All these species, in addition to the ions quoted above, should theoretically be considered as potential participants to the overall charge of the hydrophobic interface. Theories about a potential role of such ions on the negative charge of hydrophobic surfaces are not new per se: bicarbonate adsorption was suggested back in 1991 by Medrzycka, but the author stated "that further experiments are necessary for explaining the observed phenomena [negative zeta potential of hexadecane droplets in water]". [START_REF] Medrzycka | The effect of particle concentration on zeta potential in extremely dilute solutions[END_REF] Recently, Jungwirth and Vacha also put some hints on the presence of carbonic acid in water, [START_REF] Buch | Water surface is acidic[END_REF][START_REF] Mundy | Hydroxide anion at the air-water interface[END_REF][START_REF] Duignan | Hydronium and hydroxide at the air-water interface with a continuum solvent model[END_REF] but did not take it into account in their simulation parameters. Authors defending the OH -adsorption theory [START_REF] Marinova | Charging of Oil-Water Interfaces Due to Spontaneous Adsorption of Hydroxyl Ions[END_REF] have also evoked water carbonation and discarded this hypothesis on the basis of nonconclusive experiments. [START_REF]The authors performed microelectrophoresis of xylene emulsions prepared in 10 -3 M Na 2 CO 3 aqueous solutions, with those obtained in similar pH (9.8) and ionic strength[END_REF] Other authors proposed to boil water before use to remove CO 2 ; 32 a protocol that does not avoid instantaneous re-carbonation of water through fast reaction with aqueous OH -. 33 From this basis, we revisit here the open question about the origin of hydrophobic surface charging and propose a unified theory that points out the key role of bicarbonate anions, and their preferential interfacial adsorption, on a large range of pH. In the following, after a thorough evaluation of the content and properties of the ions in presence in water as a function of pH, two series of experiments are displayed to unravel the respective influence of these different ions.

The first one deals with interfacial tension (IFT) measurements of hexadecane (HD) in (pHvaried) water, so as to track the kinetics of adsorption of (any) ions at the oil interface. The other set of studies deals with the nanoprecipitation of HD or standard polymers at different pHs, where the size of the resulting colloids is directly related to the rapid adsorption of species at their interface during the nanoparticles growth. Then, by processing these data, and comparing them with available literature, we propose a general interpretation relying on the respective quantities of the different ions and, most importantly, on the conditions of measurements (see e.g. direct and reverse interfacial tension measurements). Note that all products used here have been characterized in details and when needed, purified accordingly, to remove any impurity that would lead to the misinterpretation of our results. [START_REF] Roger | Why Are Hydrophobic/Water Interfaces Negatively Charged?[END_REF] Figure 1 shows the content of all species present in a pH-stabilized aqueous dispersion in a closed system. [START_REF] Lower | Chem1 reference text[END_REF] Several major facts can be said from this carbonation textbook figure. First, there is a constant equilibrium between all species, i.e. dissolved CO 2 gas, H 2 CO 3 , HCO 3 -, and

CO 3 2-
, according to the pH. In a close system, pKas given for CO 2 /HCO 3 -and HCO 3 -/H 2 CO 3 ions pairs are 6.3 and 10.3, respectively. H + and CO 2 curves cross each other at 5, a value that corresponds to the pH of distilled water. The intersection between H 2 CO 3 and HCO 3 -curves is found at pKa=3.5, [START_REF] Loerting | Aqueous Carbonic Acid (H 2 CO 3 )[END_REF] according to the ratio between gaseous CO 2 soluble in water, and liquid H 2 CO 3 , of around 100. pH-neutral counter-ions, i.e. Na + and Cl -, are present approximatively at similar concentrations as OH -and H 3 O + , respectively, whereas bicarbonate anions are found in much larger quantities in a large pH window. In the study that follows, we have prepared aqueous solutions using either HCl or NaOH and measured their pH and conductance prior to use. Knowing the CO 2 concentration at targeted pH, we can recalculate HCO 3 -content using the Henderson-Hasselbalch (see section S1 for details). Figure 1 shows the numerous solutions that we prepared in this study.

Another important parameter to take into account deals with ions' propensity to adsorb at apolar interfaces, which principally depends on their polarizability and hydrophilicity. Some Cl -, [START_REF] Collins | Charge density-dependent strength of hydration and biological structure[END_REF] close to zero, reflecting intermediate behavior in contrast with the other cited ions. The ions affinity towards hydrophobic interfaces can also be evaluated by measuring the surface tension of highly concentrated corresponding water solutions. Typically, H + prefers interfaces more than OH -does. [START_REF] Buch | Water surface is acidic[END_REF] Studies on flotation of bicarbonate and carbonate concentrated brine solutions showed that bicarbonate ions specifically adsorb at the air/water interface, whereas carbonate ions hardly do; [START_REF] Ozdemir | Adsorption of carbonate and bicarbonate salts at the air-brine interface[END_REF][START_REF] Du | Molecular features of the air/carbonate solution interface[END_REF] such result was confirmed by sum frequency spectroscopy. [START_REF] Hua | Phase-Sensitive Sum Frequency Revealing Accommodation of Bicarbonate Ions, and Charge Separation of Sodium and Carbonate Ions within the Air/Water Interface[END_REF] These results

coefficients
clearly underline that bicarbonate anions, which are excessively present in a fair pH range (6-10), are among the best candidates for interacting with surfaces. Whereas the surface tension between air and water has been extensively studied, [START_REF] Beattie | pH and the surface tension of water[END_REF] there is very little information on (direct or reverse) interfacial experiments between oil and water. [START_REF] Santos | Ions at the Water-oil Interface: Interfacial Tension of Electrolyte Solutions[END_REF][START_REF] Levin | Ions at hydrophobic interfaces[END_REF] Commercial oil HD 99% (used in this study) typically contains variable amounts of heptadecane and fatty acids (section S2 and S1) :

(

) 1
where IFT 0 is the bare interfacial tension. IFT data were also plotted as a function of t and fitted simply by:

(2)

(3)

Results are compiled in Figures 2d and2e. Since t 0 =0 is very difficult to assign for these experiments, IFT 0 varies slightly, with an average value of 52 mN/m that agrees with literature values for the HD/water system. [START_REF] Goebel | Interfacial Tension of the Water/n-Alkane Interface[END_REF] On the other hand, the slope (α) is not dependent on this initial value and shows a clear trend as a function of pH. The slope is constant from pH 3 to about 8, and starts to decrease slightly above that. We further extrapolated the IFT curves at infinite time (Figure S3-2) to obtain an equilibrium interfacial tension value of about 38 mN/m, independent of the starting pH. Note that the latter interfacial tension is surprisingly low when compared to the values typically observed at the aqueous-air interfaces. In section S3 of the supporting information, we discuss this strong decrease of IFT observed at the alkane-water interface. One can conclude here that in a large range of pH (5 to 10), there is a strong adsorption of ions at the HD/water interface, first in a fast motion and then slowly with time. OH -and H + ions represent a small minority, albeit between 6 and 8, which cannot explain the strong adsorption observed through these indirect interfacial tension measurements. We anticipate that the surface is first progressively covered with bicarbonate anions originally present in water, and then slowly gets saturated with excess bicarbonates generated from the atmospheric CO 2 (we can consider here an open system on long range of time). 45 Another way to qualitatively and quantitatively investigate ion adsorption on interfacial surfaces as a function of pH relies on the nanoprecipitation technique (see reviews in [START_REF] Ganachaud | Nanoparticles and Nanocapsules Created Using the Ouzo Effect: Spontaneous Emulsification as an Alternative to Ultrasonic and High-Shear Devices[END_REF][START_REF] Schubert | Nanoprecipitation and nanoformulation of polymers: from history to powerful possibilities beyond poly(lactic acid[END_REF][START_REF] Lepeltier | Nanoprecipitation and the "Ouzo effect": Application to drug delivery devices[END_REF] ). This solvent shifting process indeed implies the very quick generation of particles or droplets by supersaturation of a solute (polymer or oil, respectively) initially added in a solvent (typically acetone), when the latter migrates towards the antisolvent (water) (Figure 3a). The process generates submicronic colloids in a given frame of the phase diagram, generally in a diluted region. [START_REF] Vitale | Liquid Droplet Dispersions Formed by Homogeneous Liquid-Liquid Nucleation: "The Ouzo Effect[END_REF] In this spontaneous emulsification technique, oil emulsions and polymer dispersions are grown by nucleation/aggregation events at a very fast rate of encounters. [START_REF] Lannibois | Surfactant Limited Aggregation of Hydrophobic Molecules in Water[END_REF] The aggregation phenomenon stops when surfaces repulse each other. Most authors have shown that, even in absence of surfactants, polymer particles having a negative surface charge are generated, as confirmed by zeta potential measurements. [START_REF] Zimmermann | Hydroxide and hydronium ion adsorption -A survey[END_REF] The idea admitted so far was that OH -anions adsorb at interfaces thus stopping coalescence at some point. [START_REF] Wu | Solvent Effect on ζ Potential at an Aqueous/Oil Interface in Surfactant-Free Emulsion[END_REF] In this context, we have undertaken a series of experiments with different solutes, i.e. HD oil, [START_REF] Ma | Impact of Spontaneously Adsorbed Hydroxide Ions on Emulsification via Solvent Shifting[END_REF] and polymers, PMMA and PS. [START_REF] Aubry | Nanoprecipitation of Polymethylmethacrylate by Solvent Shifting:1. Boundaries[END_REF] For the former, we have compared data on an as received hexadecane oil and a purified one. For the latter, polymer polar end-groups clearly influence the nanoprecipitation process; [START_REF] Roger | Uncontaminated Hydrophobic/Water Interfaces Are Uncharged: A Reply[END_REF] we have then used polymer standards prepared by anionic polymerization, for which neutral chain ends, clearly identified by NMR, do not play any role in colloids stabilization (see full NMR characterization in supporting information, section S2). Note that to ensure mid-term colloidal stability required for size characterization by QELS, a slight amount of non-ionic surfactant (here brij 56) was added in the organic phase prior to solvent shifting (see section S4 for experimental conditions). It is worth noting that polymer nanoprecipitation gives particles whose dimensions are independent of the surfactant content and phase location; [START_REF] Ganachaud | Nanoparticles and Nanocapsules Created Using the Ouzo Effect: Spontaneous Emulsification as an Alternative to Ultrasonic and High-Shear Devices[END_REF] whereas, for molecular solutes including oils, adding a surfactant in the organic phase gives much lower droplet sizes than when introduced in water. [START_REF] Lannibois | Surfactant Limited Aggregation of Hydrophobic Molecules in Water[END_REF] We assign this behavior to the fact that, for polymers, the size of the resulting nanoparticles is driven solely by the (very fast) adsorption of ions (compared to surfactant's one) at particles' interface whereas, for HD, the rate of surfactant adsorption at the droplet's surface, directly arising from acetone, is significantly larger than ions' one (Figure 3b).

Results for HD, given in supporting information, nevertheless illustrate the general character of the conclusions drawn from polymer nanoprecipitation experiments (Section S4). Figure 3c shows the variation of particle diameters for the two polymer systems as a function of the pH of the water phase before solvent shifting. One clearly sees a range of lower dispersion size, typically between 6 and about 9.5. Below pH 4.5, and above pH 12, unstable dispersions were obtained so that sizes could not be measured by the Nanosizer. Note that this lack of stability is not due to a too large ionic strength as, at pH 10, the ionic strength has been evaluated at 5×10 -2 M (according to the content of OH -, HCO 3 -, and CO 3 2-in the medium), conditions that our dispersion perfectly stands in presence of the non-ionic surfactant. It is also important to point out the rather constant and small values of d V /d N (where d V is the volume-average particle size and d N is the number-average particle size) for both polymers, independent of particle sizes (Figure 3c). This feature of the resulting polymer dispersions clearly demonstrates that the observed variations of colloid dimensions are not the consequence of undesired particles aggregation. A similar trend is noticed for HD droplets, either starting from the pristine HD 99%

or the purified one, albeit in a narrower size range due to surfactant competitive adsorption (Figure S4). We further plotted the zeta potential of PMMA dispersions (after evaporation of acetone) versus the pH at which the nanoprecipitation was done (Figure 3d). As particle size has a significant impact on zeta potential measurements, data processing is limited here to the pH range (6-10) where colloidal dimensions are constant (see next section). Basically, the zeta potential follows a marked decrease on a large range of pH, and an increase above pH 9. Figure 3e depicts the evolution of PMMA NP diameter vs the content of bicarbonate ions in aqueous dispersions of various pHs. Regardless of the error naturally occurring in these experiments, the plot highlights that the size of PMMA dispersions is minimal with a bicarbonate concentration as low as 10 -5 M, irrespective of the pH. This concentration is so small that it is likely that colloidal stability is not achieved in these systems without the presence of brij surfactant. Interestingly, addition of extra sodium bicarbonate salt in the aqueous solution (prior to solvent shifting) does not promote further decrease of the particle size because of increasing ionic strength (while not drastically changing the pH, see Figure S5). In brief, the range of pH where the size is best controlled by nanoprecipitation is when the bicarbonate concentration is at its maximum (in agreement with the diagram of carbonate species distribution vs pH given in Figure 1), and both H + and OH -are in large depression. Taking advantage of the two sets of experiments presented above, we subsequently aimed at determining average overall ion contents on HD droplet interfaces or on polymer particles. The slope  of the interfacial tension evolution is expressed using the following equation =2RTc(D/π) 1/2 . In a first approximation, assuming an average diffusion coefficient of 10 -9 m 2 /s for every ion (Table S1), we calculated the overall concentration c=[2RT(D/π) 1/2 ] of ions adsorbing onto the interface. Figure 4a shows these c values as a function of pH. The concentration of each species HCO 3 -, H 3 O + , OH -at different pHs was determined from carbonation equilibria data from Figure 1. [START_REF] Petersen | Note that we have also stated as a hypothesis that whatever the nature of the ionic species, its adsorption always leads to[END_REF] Comparing the concentrations of carbonation equilibria with c=[2RT(D/π) 1/2 ] (IFT data), we find a good agreement for a narrow pH range of 6 to 9. At acidic or basic pH, data do not fit with the model of full coverage of any ion, suggesting that H + or OH -ions hardly adsorb at these pHs, respectively.

We also analyzed the zeta potential data for the PMMA particles using the Debye-Hückel theory in the pH range where particle sizes are constant (i.e. between 6 and 10). The electric potential as a function of the distance r from the center of the drop/particle is:

(

) 4
where q is the charge,  is the inverse of the Debye length and R is the particle radius. The zeta potential describes the potential at the shear plane of the particle. Here, their diameter is about 130 nm and the shear plane of the particle is about 1 nm far. We neglected this ca. 1 nm difference given the dispersion of the data and the shape of the potential at this r range. From eq.

4 we can calculate the charge q or the charge density (in charge/nm 2 ):

( Both fits show clear trends. For pH<6, the number of interfacial charges is low, and for pH>9, only a small fraction of anionic species available in solution are found at the surface of the particles. Between these two pHs, bicarbonates, the most prominent ions in those conditions, adsorb at interfaces to generate a negative charge. From the literature, we know that an isoelectric point is observed at around pH 3-4. This critical pH value corresponds to the pKa of the H 2 CO 3 /HCO 3 -pair, i.e. where carbonate starts to be naturally formed. Colussi et al, who evaluated the content of charges at air/water interfaces, confirmed this value of pKa. They also reported a second transition at around pH 9.5, which matches with the pKa of the HCO 3 -/CO 3 2pair. [START_REF] Enami | Proton Availability at the Air/Water Interface[END_REF][START_REF] Mishra | Brønsted basicity of the air-water interface[END_REF] These data are in line with the trends observed in our study. If we consider acidic pHs, i.e.

below pH 4, the surface in average becomes positive. Even if the hydronium ion adsorbs, chloride, a chaotropic ion, can also adsorb and neutralize to some extent the surface charge. It is however not clear whether it is CO 2 in its neutral form (H 2 CO 3 ) that is more likely to adsorb or the hydroxonium ion (H 3 O + ). At high pH, OH -and Na + adsorptions compete, whereas bicarbonate anions can definitively be set aside. It can also be anticipated that, due to fast conversion of CO 2 into bicarbonate by reaction with OH -at basic pH, an excess of the latter could form and adsorb onto the interface, thus increasing the overall charge density. Note that the presence of impurities, and also the substantial ionic strength brought by saline solutions, have definitively a role in the stabilization/ionization of hydrophobic surfaces, even if the extent of these are only qualitatively shown here. These assumptions are just open propositions for further works.

Finally, the fact that studies report neutral, negative or positive interfacial charges at water/hydrophobic interfaces from one study to another, depends principally on how measurements are done. For instance, the surface tension of water droplets in air does not change with pH. [START_REF] Beattie | pH and the surface tension of water[END_REF] This is explained by the fact that the very few ions present in the small volume of the droplet (typically 60 µL in our experiment) do not change drastically the IFT. On the other hand, air bubbles in water show negative zeta potentials and low interfacial tensions, because excess ions in water can easily reach the interface. We have found similar differences here when measuring direct or reverse IFT of HD/water systems. A droplet of water shows a constant IFT with time, whereas a reverse one sees its interfacial tension drop with time. As stated at the beginning of this article, water drops in oils have positive zeta values, independent of the pH.

The presence of CO 2 , as slightly soluble in oils as in water, [START_REF] Campos | Solubility of Carbon Dioxide in Water and Hexadecane: Experimental Measurement and Thermodynamic Modeling[END_REF] can protrude to the interface and affect the surface charge, like bicarbonate ions do in the reverse system. Protons in excess cover the few ions present in water, and thus promote a positive charge. Similarly, bubbles of CO 2 in water give stable interfaces below pH 4 and basically dissolve above that value. On the other hand, in a study devoted to the natural electrostatic stabilization of water droplets in supercritical CO 2 emulsions, the authors showed that the natural ionization of interfaces was due to the bicarbonate adsorption. [START_REF] Ryoo | Electrostatic Stabilization of Colloids in Carbon Dioxide: Electrophoresis and Dielectrophoresis[END_REF] In conclusion, we have shown that the carbonation of water is an important parameter to take into account when exploring hydrophobic/water interfaces. Bicarbonate ions, naturally present in water, or generated from atmospheric CO 2 , has a large propensity to adsorb at hydrophobic interfaces, particularly on polymers, on a quantitative level. Whereas these ions do not suffer competition at pHs around neutrality (6-9 range), all other ions present in the aqueous solutions can also adsorb, albeit in part, at lower or larger pHs. The content of interfacial ions is generally too low to ensure efficient colloidal stability, and to be tracked by the different techniques quoted above. We hope that in the future, the several teams cited here will confirm the presence of bicarbonate ions at hydrophobic interfaces from their experimental expertise. For instance, FTIR spectroscopy of the OH band in carbonated aqueous solutions shows signatures not seen for other ions, [START_REF] Kitadai | Effects of Ions on the OH Stretching Band of Water as Revealed by ATR-IR Spectroscopy[END_REF] whereas Raman spectroscopy shows two separated, specific peaks in the carbonyl region for bicarbonate and carbonate ions. [START_REF] Rudolph | Speciation studies in aqueous HCO 3 --CO 3 2solutions. A combined Raman spectroscopic and thermodynamic study[END_REF] Hopefully, Raman coupled to SFS studies could shed some light on interfacial carbonation. It could also be worth to carry out experiments in a glovebox so as to discard any trace of CO 2 from water (and oils) and show its impact on interface charging.

ASSOCIATED CONTENT

Supporting Information.

Methods and materials, experimental precodures, NMR spectra, interfacial measurement and ouzo experimetnt are included in supporting information. This material is available free of charge via the Internet at http://pubs.acs.org.

Figure 1 .

 1 Figure 1. Carbonation of water at different pHs and other present ions: water completed either by HCl or NaOH solutions and considered in a closed system. The content of Na + and Cl - are, as a first (but relevant) approximation, based on OH -and H + concentrations, respectively.

Figure 2 .

 2 Figure 2. Interfacial tension measurements: kinetics of ion adsorption. a) Scheme showing

  FigureS2-1), making interfacial tension measurements of a HD drop in deionized water poorly reproducible (section S3 and FigureS3-1a). Purification of HD on alumina columns (X5) allows for quantitatively removing the traces of fatty acids (as confirmed by titration, see section S2, FigureS2-1) while heptadecane remains in HD after treatment. This simple purification step is however sufficient to obtain highly reproducible IFT data (FigureS3-1b). The standard direct pendant drop measurement (Fig.2a(1)) of a distilled water drop in HD is given in Fig.2b. Similar to the report of Goebel and Lunkenheimer in 1997,[START_REF] Goebel | Interfacial Tension of the Water/n-Alkane Interface[END_REF] the IFT does not change for an alkane in which a drop of water is formed. The other IFT measurements shown in Fig.2bwere performed with HD drops in different solvents including water using a reverse pendant drop methodology, (Fig 2a(2), i.e. oil drop in a given medium). In contrast with the direct pendant drop methodology, interfacial tension between HD drop and water progressively decreases whereas, the IFT remains constant for the other oil drop/solvents systems (methanol, ethanol, glycerol). These divergent IFT behaviors (instantaneous IFT stabilization for water drop/HD or HD/solvents vs progressive decrease of IFT for HD drop in water) are consistent with the disparate content of ions present in the two scenarios (Figure2a, vide infra). Complementary experiments were then done at different pHs by adding HCl or NaOH into water prior to measurements. IFT curves are reported in Figure 2c. Basically, there is no clear difference of behavior as a function of pH, except for high pHs and around pH 5. The IFT declines in two steps, a steep decrease in the first minute and then a slow decrease with time. The curves (IFT as a function of time, IFT(t)) can be fitted with a diffusion model in the short time limit. In the first stages of adsorption, IFT(t) depends on the bulk concentration c and the diffusion coefficient D of the adsorbing species (values reported in Table

Figure 3 .

 3 Figure 3. Spontaneous emulsification via Ouzo effect: ion adsorption vs pH. a) Principle of

Figure 4 :

 4 Figure 4: Modeling of interfacial adsorption. a) Calculated content of different ionic species

5 )

 5 as a function of the pH, see Fig.4b. We then compared the surface charge density measured for polymer particles in water in terms of the adsorption of the three molecular species HCO 3 -, H 3 O + , OH -at the water-polymer drop interface. In order to make this comparison, one should estimate the characteristic time of the drop formation. The calculated surface concentration is:(6) assuming that 1 molecule of HCO 3 -(OH -) corresponds to 1 negative charge and 1 molecule of H 3 O + to a positive charge. The best fit was obtained for a characteristic adsorption time t* = 10 5 s, in agreement with the very fast emulsification rate found in Ouzo effect. Note that in this time interval, a Brownian particle travels a distance of about (2Dt*) 1/2 = 141 nm, which agrees with typical distances of adsorption processes. Again, the best agreement is seen for the intermediate range of pH, typically between 6 and 9. Here, we could not state on the adsorption of ions at lower pH than 6, where the size of the particles increase. On the other hand, at basic pH, the zeta potential reaches values that are below those expected for full surface ionization with hydroxide anions.

ACKNOWLEDGMENT F. G. thanks Dr. Martin In for useful discussions. M. D. and X. Y. post-docs were financed by the ANR projects LimOuzInE (ANR-10-BLAN-0942) and PREPROPOSAL (ANR-15-CE09-0021), respectively. DEDICATION This article is dedicated to the memory of Vincent Judais.

AUTHOR INFORMATION

Corresponding Author

*E-mail: francois.ganachaud@insa-lyon.fr

Author Contributions

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

Notes

The authors declare no competing financial interests.