Ibtissen Gammoudi

Marion Mathelié-Guinlet

Zenieb Benabdallah

Fabien Moroté

Houssem Kahli

Laure Beven

Rafik Kalfat

Ali Othmane

M H Delville

Christine Grauby-Heywang
email: christine.grauby-heywang@u-bordeaux.fr

Corinne Dejous

Touria Cohen-Bouhacina

Revisiting of the physico-chemical properties of PAH/PSS polyelectrolyte multilayers for a fine tuning of the immobilization of bacteria or nanoparticles

Keywords: Polyelectrolytes, Layer-by-Layer, Love Wave sensor, Atomic Force Microscopy AFM, Quartz Crystal microbalance with dissipation QCM-D, Cyclic Voltammetry

Introduction

The design of soft assemblies, with controlled properties at the nanoscale, has emerged as a challenging research area over the past decades, due to their implication in various coating applications, in optical devices [START_REF] Lin | Improvement of the surface wettability of silicone hydrogel contact lenses via layer-by-layer self-assembly technique[END_REF], lubrication cosmetics [START_REF] Lee | Adsorption and Lubricating Properties of Poly(l-lysine)-graft-poly(ethylene glycol) on Human-Hair Surfaces[END_REF], environment [START_REF] Gammoudi | Enhanced bio-inspired microsensor based on microfluidic/bacteria/love wave hybrid structure for continuous control of heavy metals toxicity in liquid medium[END_REF], energy [START_REF] Xiang | Layer-by-layer self-assembly in the development of electrochemical energy conversion and storage devices from fuel cells to supercapacitors[END_REF] and medicine [START_REF] Tong | Layer-by-layer assembly of microcapsules and their biomedical applications[END_REF]. Different techniques have been developed for the selfassembly of materials with tunable properties (composition, structure, dimensions) to reach the requirements of the aforementioned fields. Among them, the Layer-by-Layer (LbL) technique, first introduced by Decher et al., consists in the alternate deposition of oppositely charged molecules from aqueous solutions on a solid substrate, mostly through electrostatic interactions [START_REF] Decher | Fine-Tuning of the film thickness of ultrathin multilayer films composed of consecutively alternating layers of anionic and cationic polyelectrolytes[END_REF][START_REF] Decher | Fuzzy Nanoassemblies: Toward Layered Polymeric Multicomposites[END_REF]. By definition, this method allows to tailor the physico-chemical properties of the final assembly by adjusting the intrinsic characteristics of the building blocks. Consequently, numerous studies have been devoted to the understanding of the buildup of these multilayers and of the involved key parameters, as well as to their possible applications [START_REF] Hammond | Form and Function in Multilayer Assembly: New Applications at the Nanoscale[END_REF][START_REF] Zhang | Layer-by-layer assembly: from conventional to unconventional methods[END_REF][START_REF] Dubas | Factors Controlling the Growth of Polyelectrolyte Multilayers[END_REF]. In particular, the LbL technique has been initially and then widely applied to polyelectrolytes (PEs), poly(allylamine hydrochloride) (PAH) and poly(sodium 4-styrenesulfonate) (PSS) being probably the most studied polycation and polyanion, respectively, in this context.

Though the charge overcompensation among these charged polymers is known to control the formation process [START_REF] Schlenoff | Charge and Mass Balance in Polyelectrolyte Multilayers[END_REF], it is still unclear how diverse physico-chemical parameters affect such a buildup. Originally, these stratified films appeared to grow linearly in thickness and mass with the number of deposited layer pairs, which can intertwine each other, leading to a robust structure [START_REF] Lösche | Detailed Structure of Molecularly Thin Polyelectrolyte Multilayer Films on Solid Substrates as Revealed by Neutron Reflectometry[END_REF][START_REF] Yoo | Controlling Bilayer Composition and Surface Wettability of Sequentially Adsorbed Multilayers of Weak Polyelectrolytes[END_REF][START_REF] Caruso | Ultrathin Multilayer Polyelectrolyte Films on Gold: Construction and Thickness Determination[END_REF][START_REF] Guzmán | Growth of Polyelectrolyte Layers Formed by Poly(4-styrenesulfonate sodium salt) and Two Different Polycations: New Insights from Study of Adsorption Kinetics[END_REF]. However, a super linear (or exponential) growth regime was then suggested as another buildup mechanism: depending on the initial conditions and PEs properties, the film thickness increased more rapidly than previously thought, i.e. it was not any more proportional to the number of adsorbed layers [START_REF] Ruths | Polyelectrolytes I: Polyanion/Polycation Multilayers at the Air/Monolayer/Water Interface as Elements for Quantitative Polymer Adsorption Studies and Preparation of Hetero-superlattices on Solid Surfaces[END_REF][START_REF] Elbert | Thin Polymer Layers Formed by Polyelectrolyte Multilayer Techniques on Biological Surfaces[END_REF][START_REF] Picart | Buildup Mechanism for Poly(l-lysine)/Hyaluronic Acid Films onto a Solid Surface[END_REF]. These two regimes, linear and exponential, were associated with the ability of the PEs to build up as either linear chains or aggregated complexes, diffusing in and out of the PE multilayer (PEM) core [START_REF] Picart | Molecular basis for the explanation of the exponential growth of polyelectrolyte multilayers[END_REF] and forming either a smooth film or a rough and heterogeneous one [START_REF] Lavalle | Comparison of the Structure of Polyelectrolyte Multilayer Films Exhibiting a Linear and an Exponential Growth Regime: An in Situ Atomic Force Microscopy Study[END_REF][START_REF] Mcaloney | Atomic Force Microscopy Studies of Salt Effects on Polyelectrolyte Multilayer Film Morphology[END_REF]. Physico-chemical properties such as environmental temperature [START_REF] Salomäki | Effect of Temperature on the Buildup of Polyelectrolyte Multilayers[END_REF], pH [START_REF] Shiratori | pH-Dependent Thickness Behavior of Sequentially Adsorbed Layers of Weak Polyelectrolytes[END_REF] and ionic strength [START_REF] Guzmán | Salt-induced changes in the growth of polyelectrolyte layers of poly(diallyl-dimethylammonium chloride) and poly(4-styrene sulfonate of sodium)[END_REF][START_REF] Kim | Morphology of multilayers assembled by electrostatic attraction of oppositely charged model polyelectrolytes[END_REF] as well as the chemical nature of PE [START_REF] Lavalle | Comparison of the Structure of Polyelectrolyte Multilayer Films Exhibiting a Linear and an Exponential Growth Regime: An in Situ Atomic Force Microscopy Study[END_REF] influence the growth regime of such multilayers. In addition, to overcome the time consuming protocol of traditional LbL, different experimental methods have been proposed, adding new physical parameters playing a potential role in the buildup process.

Thus a spin-coating assisted LbL method has been developed, that also comes along with a better control of PEM properties [START_REF] Li | Layer-by-layer assembly for rapid fabrication of thick polymeric films[END_REF][START_REF] Fadhillah | Development of multilayer polyelectrolyte thin-film membranes fabricated by spin assisted layer-by-layer assembly[END_REF][START_REF] Cho | Fabrication of Highly Ordered Multilayer Films Using a Spin Self-Assembly Method[END_REF]. Similarly to dipping processes, physical parameters such as the PE molecular weight, the salt concentration, and the spin rate can modify the PEM architecture [START_REF] Patel | Combined Effect of Spin Speed and Ionic Strength on Polyelectrolyte Spin Assembly[END_REF][START_REF] Lee | Evidence for Spin Coating Electrostatic Self-Assembly of Polyelectrolytes[END_REF]. Dipping in stirred solutions [START_REF] Fu | Facile and Efficient Approach to Speed up Layer-by-Layer Assembly: Dipping in Agitated Solutions[END_REF] and ultrasonicassisted LbL assembly [START_REF] Jiang | Fabricating Transparent Multilayers with UV and Near-IR Double-Blocking Properties through Layer-by-Layer Assembly[END_REF] were also tested, along with assembly under a high gravity field [START_REF] Jiang | Controlled exponential growth in layerby-layer multilayers using high gravity fields[END_REF] (substrate being in rotation as in spin-coating with PE solutions sprayed as tiny drops).

Unravelling the role of each of these parameters in the PEM buildup is essential to guarantee a control on the properties of the built nanocomposite films. This point is crucial to ensure subsequently their potential in various applications such as those developed in biotechnologies, especially in biosensor applications. Indeed, combined with specific nanoparticles or molecules (for instance proteins) and appropriately tuned, PEMs have already proven to be efficient and successful in the built-up of cytophilic or cytophobic surfaces [START_REF] Mendelsohn | Rational Design of Cytophilic and Cytophobic Polyelectrolyte Multilayer Thin Films[END_REF][START_REF] Chluba | Peptide Hormone Covalently Bound to Polyelectrolytes and Embedded into Multilayer Architectures Conserving Full Biological Activity[END_REF][START_REF] Serizawa | Alternating Bioactivity of Polymeric Layer-by-Layer Assemblies: Anti-vs Procoagulation of Human Blood on Chitosan and Dextran Sulfate Layers[END_REF][START_REF] Gammoudi | Morphological and nanostructural surface changes in Escherichia coli over time, monitored by atomic force microscopy[END_REF] , the immobilization of cells [START_REF] Zhu | Engineered, Robust Polyelectrolyte Multilayers by Precise Control of Surface Potential for Designer Protein, Cell, and Bacteria Adsorption[END_REF][START_REF] Muzzio | Polyelectrolytes Multilayers to Modulate Cell Adhesion: A Study of the Influence of Film Composition and Polyelectrolyte Interdigitation on the Adhesion of the A549 Cell Line[END_REF] or on the contrary in the inhibition of bio-adhesion [START_REF] Kruk | Nanostructured multilayer polyelectrolyte films with silver nanoparticles as antibacterial coatings[END_REF][START_REF] Wang | Direct Loading and Tunable Release of Antibiotics from Polyelectrolyte Multilayers To Reduce Bacterial Adhesion and Biofilm Formation[END_REF][START_REF] Muzzio | Enhanced antiadhesive properties of chitosan/hyaluronic acid polyelectrolyte multilayers driven by thermal annealing: Low adherence for mammalian cells and selective decrease in adhesion for Gram-positive bacteria[END_REF][START_REF] Guo | Tailoring Polyelectrolyte Architecture To Promote Cell Growth and Inhibit Bacterial Adhesion[END_REF][START_REF] Séon | Polyelectrolyte Multilayers: A Versatile Tool for Preparing Antimicrobial Coatings[END_REF] and even in enhancing immunodetection [START_REF] Yang | Layer-by-Layer Construction of Novel Biofunctional Fluorescent Microparticles for Immunoassay Applications[END_REF][START_REF] Caruso | Assembly of Alternating Polyelectrolyte and Protein Multilayer Films for Immunosensing[END_REF]. Though theoretical and experimental data mentioned so far tackle the influence of relevant physico-chemical properties, research focuses often on one parameter at a time, leading to hazardous comparison as PEs and experimental conditions differ from one study to another.

In this context, we investigated here, in a systematic approach, the properties of these PEMs, depending on (i) the pH of the deposition solution and its ionic strength, and (ii) their deposition method (immersion versus spin-coating). Our goal was to define precisely the experimental conditions enabling to obtain PEMs with tunable properties paving the way for application opportunities. Indeed, we finally analyzed the efficiency of such PEMs (i) for the immobilization of bacteria, a pre-requirement for their characterization in physiological media, and (ii) as a coating for biosensor transducers involving nanoparticles. To fully characterize such PEMs and their potential in bioapplications, we combine two acoustic methods, (Love wave sensor [START_REF] Moll | A Love wave immunosensor for whole E. coli bacteria detection using an innovative two-step immobilisation approach[END_REF] and Quartz Crystal Microbalance (QCM) [START_REF] Marx | Quartz Crystal Microbalance: A Useful Tool for Studying Thin Polymer Films and Complex Biomolecular Systems at the Solution-Surface Interface[END_REF]), with Atomic Force Microscopy (AFM) experiments on the one hand and electrochemical analysis on the other hand. To our knowledge, this work is the first to show that Love wave sensor method, an original technique usually developed for biosensor applications [START_REF] Xu | Implementation of guiding layers of surface acoustic wave devices: A review[END_REF], is also well-suited to study PEM buildup.

Materials and methods

Chemical and biological materials

Two types of PE, purchased from Sigma-Aldrich (France), were used: cationic poly(allylamine hydrochloride) or PAH with a molecular weight of 56 kDa, and anionic poly(sodium 4-styrenesulfonate) or PSS with a molecular weight of 70 kDa. Tris Buffered Saline (TBS, 0.05 M Tris, 0.138 M NaCl, pH 7.4), and K4[Fe(CN)6] used for electrochemical measurements were also purchased from Sigma-Aldrich (France). Ultrapure water (Millipore, resistivity higher than 18 MΩ.cm, pH 5.5) was used as a solvent of the PEs, for the rinsing steps and for the preparation of TBS. When necessary, the pH of PE's solutions was adjusted to the required value by adding HCl or NaOH (1 M).

Mica, purchased from Electron Microscopy Sciences (USA), was used for AFM characterizations, when they were not directly performed on the different sensors (Love wave, QCM-D, electrochemical ones). The potentiostat and screen printed electrodes for electrochemical experiments were purchased from Metrohm (Switzerland). Quartz crystals, coated with a gold layer, were purchased from Lot Quantum Design Sarl (France).

Love wave devices were designed in the IMS Laboratory and produced in LAAS (UMR CNRS 8001, Toulouse, France). Gram negative Escherichia coli bacteria (MRE 162 strain) were a kind gift from the Centre d'Etudes du Bouchet, DGA (Direction Générale de l'Armement, France). Bacteria were grown on a solid Luria medium and incubated for 16 h at 37 °C. After scraping, bacteria were suspended in ultrapure water, their concentration being adjusted to 10 8 cells/mL. Negatively and positively charged silica nanoparticles (SiO2-NPs) were home-made, following the procedure developed by Hartlen et al. [START_REF] Hartlen | Facile Preparation of Highly Monodisperse Small Silica Spheres (15 to >200 nm) Suitable for Colloidal Templating and Formation of Ordered Arrays[END_REF] and detailed in our previous work [START_REF] Mathelié-Guinlet | Probing the threshold of membrane damage and cytotoxicity effects induced by silica nanoparticles in Escherichia coli bacteria[END_REF].

Methods

Layer-by-Layer (LbL) self-assembly methods

The LbL method consists in a sequential and alternate deposition of the chosen polycation (PAH) and polyanion (PSS) on a solid substrate. The surface of mica, SiO2 and gold substrates being negatively charged, the nature of the first layer was systematically PAH.

Between each layer deposition, substrates were rinsed with ultrapure water, except in the case of Love wave sensor experiments where no rinsing step was necessary (as similar results were obtained with and without this step). These adsorption and rinsing steps were repeated until reaching the desired number of layers. The final PEMs are denoted thereafter [PAH-(PSS-PAH)n], n being the number of bilayers. The nature of the last layer was also adapted to the targeted application, as shown later on.

Two techniques of deposition were used for this work: by immersion of the substrate into the solutions of PE or by spin coating, referred as I-LbL and SC-LbL methods, respectively.

For the I-LbL method, PAH and PSS solutions (10 µL, 5 mg/mL in pure water) were simply deposited on the substrates for 10 min before rinsing with pure water, for QCM-D, AFM and CV experiments. In the case of Love wave experiments, PE solutions (0.5 mg/mL in TBS) were injected alternatively through a microfluidic system supplying an analysis chamber for 10-20 min at a flow rate equal to 20 µL/min, with breaks for static conditions during PE layers deposition (thus providing conditions similar to those of immersion). In the case of QCM-D experiments, measurements were also performed in static conditions, PE solutions being injected in the analysis chamber through a millifluidic system at a flow rate of 1 mL/min.

For the SC-LbL method, substrates were placed in a spin-coating setup (Suss MicroTec) and PE solutions (10 µL, 5 mg/mL in pure water) were deposited onto the surface before spinning at different rotation speeds (100, 500, 2000 rpm) and times (45, 120, 300 s) and rinsing with pure water (by 4 gentle deposition/aspiration cycles). At the end of the whole deposition process, substrates were left to dry for a few minutes. Under our experimental range, the spinning time did not significantly influence the PEMs roughness as shown by AFM, and was thus kept to its lowest value, 45 s, for a faster buildup. In addition, the roughness increased with the spinning speed and a speed of 100 rpm led to the minimal roughness when increasing the number of layers (data not shown).

Love wave sensor experiments

The real-time Love wave sensor was described previously in details [START_REF] Gammoudi | Enhanced bio-inspired microsensor based on microfluidic/bacteria/love wave hybrid structure for continuous control of heavy metals toxicity in liquid medium[END_REF][START_REF] Gammoudi | High sensitive mesoporous TiO2-coated love wave device for heavy metal detection[END_REF][START_REF] Razan | Radio frequency thin film characterization with polymer-coated Love-wave sensor[END_REF][START_REF] Tarbague | PDMS (Polydimethylsiloxane) Microfluidic Chip Molding for Love Wave Biosensor[END_REF][START_REF] Zimmermann | A love-wave gas sensor coated with functionalized polysiloxane for sensing organophosphorus compounds[END_REF]. Briefly it is made of a piezoelectric quartz substrate (AT cut), with interdigital transducers deposited by lift-off photolithography in order to generate pure shear horizontal acoustic waves propagating perpendicularly along the X crystallographic axis. A 4 µm SiO2 guiding layer, deposited on the substrate through plasma-enhanced chemical vapor deposition, confines the acoustic wave energy near the surface to maximize the sensor sensitivity [START_REF] Razan | Radio frequency thin film characterization with polymer-coated Love-wave sensor[END_REF], resulting in the so-called Love wave. Once placed in the retroaction loop of a radiofrequency amplifier, the synchronous frequency of the bare sensor is close to 117 MHz in agreement with the value previously reported [START_REF] Razan | Radio frequency thin film characterization with polymer-coated Love-wave sensor[END_REF]. Any modification of mass or viscoelastic properties at the sensor surface is electronically measured through a frequency shift (FLove). At last, the analysis chamber of the setup is supplied thanks to a programmable syringe pump (BS8000, Bioseb, France) through a microfluidic network. This device insures a homogenous and controlled flow on the sensitive path of the propagating acoustic wave [START_REF] Gammoudi | Enhanced bio-inspired microsensor based on microfluidic/bacteria/love wave hybrid structure for continuous control of heavy metals toxicity in liquid medium[END_REF][START_REF] Gammoudi | High sensitive mesoporous TiO2-coated love wave device for heavy metal detection[END_REF][START_REF] Tarbague | PDMS (Polydimethylsiloxane) Microfluidic Chip Molding for Love Wave Biosensor[END_REF]. In the case of PEs, the time of deposition was optimized in previous works [START_REF] Gammoudi | Enhanced bio-inspired microsensor based on microfluidic/bacteria/love wave hybrid structure for continuous control of heavy metals toxicity in liquid medium[END_REF][START_REF] Gammoudi | High sensitive mesoporous TiO2-coated love wave device for heavy metal detection[END_REF], and fixed at 10 min, this time being sufficient to adsorb each PE (0.5 mg/mL in TBS) on the SiO2 sensor surface. , where q is the specific density of the quartz crystal (2.648 g.cm -3 ), tq its thickness (30 nm), f0 its fundamental frequency in air (4.95 MHz) and fn is the change of resonance frequency at the first overtone (𝑛 = 1) [START_REF] Ebara | A Kinetic Study of Concanavalin A Binding to Glycolipid Monolayers by Using a Quartz-Crystal Microbalance[END_REF].

Quartz crystal microbalance with dissipation (QCM-D) experiments

The experimental setup was made of a quartz crystal carrying a gold electrode enclosed in an analysis chamber connected to a millifluidic system for injection of solutions. Before each experiment, quartz substrates were sonicated in an ultrapure water bath containing dishwashing liquid for 15 minutes at a temperature of 60°C. After cleaning, substrates were equilibrated by injecting ultrapure water in the analysis chamber for at least 30 min., until observing a constant baseline of frequency shift f. Adsorption-rinsing cycles were then repeated by successive injections to build the PEM on the crystal in static conditions, 1 mL of each PE solution (5 mg/mL in water) being injected in the chamber and incubated for 15 min. Stabilization and experiments were made at room temperature.

AFM experiments

AFM experiments were carried out with a Bioscope II operating with the NanoScope V controller (Bruker, France), PEMs being deposited on mica or SiO2 substrates. All AFM morphological characterizations were performed in tapping mode, in its repulsive dominant regime, for which the contrast of images is predominantly topographic. To this end, data were recorded with commercial cantilevers with a spring constant of about 40 N/m and a corresponding measured resonance frequency around 190 kHz, at a scan rate of 0.5-1.0 Hz. For thickness measurements, the contact mode was on the contrary privileged: AFM tip, with a spring constant of 0.12 N/m, was used as a rake to completely remove the material from its substrate on a defined area and so as to determine the layer thickness from height profiles. Different areas were systematically imaged, using independent samples, to ensure the repeatability and reproducibility of the results.

Cyclic voltammetry measurements

Cyclic voltammetry (CV) is an electrochemical method consisting in the application of a cyclic variable potential of a working electrode in order to measure corresponding oxidation and reduction currents of the species contained in the studied medium. As such, it can also be used to detect and quantify any alteration due to the presence of heterogeneous material adsorbed on the electrode surface. Resulting CV curves show the presence of peaks characterized by a current intensity (mentioned later as Ia and Ic for oxidation and reduction, respectively) and a potential value (Ea and Ec). In particular, the peak-to-peak separation (Ea-Ec) gives access to the electrochemical reversibility of the electron transfer at the working electrode. In addition, the Randles-Sevcik equation enables to calculate the diffusion coefficients of our redox species in the contact of electrodes (nude or functionalized) [START_REF] Elgrishi | A Practical Beginner's Guide to Cyclic Voltammetry[END_REF]. This equation is

𝑖 𝑎/𝑐 = 0.446𝑛𝐹𝐴𝐶 𝑎/𝑐 ( 𝑛𝐹𝑣𝐷 𝑎/𝑐 𝑅𝑇 ) 1/2
, where:

-𝑖 𝑎/𝑐 is the current peak (A);

-𝑣 is the scan speed (V.s -1 );

-𝑛 is the number of electrons transferred in the redox event;

-𝐹 is the Faraday constant;

-𝐴 is the surface of the electrode (cm 2 ); -𝐶 𝑎/𝑐 is the corresponding concentration (mol.cm -3 );

-𝐷 𝑎/𝑐 is the corresponding diffusion coefficient (cm 2 .s -1 );

-𝑅 is the ideal gaz constant;

-𝑇 is the temperature (K).

Voltammetry measurements were carried out using a Metrohm 910 PSTAT mini potentiostat and a commercial and disposable system made of three screen-printed electrodes, a gold working electrode, a carbon auxiliary one and an Ag/AgCl reference one (reference 6.1208.210, Metrohm, France). Experiments were performed at room temperature using a 10 mM solution of K4Fe(CN)6.3H2O in TBS, within a potential range from -0.40 V to +0.60 V, adapted to the concerned Fe 2+ /Fe 3+ redox couple, at a scan rate of 100 mV.s -1 , starting from the potential value at -0.40 V.

Results and discussion

Investigation of the physical parameters affecting the PEM buildup

In the following part, the effect of pH and ionic strength and the influence of the deposition method of PEs (I-LbL versus SC-LbL) on the PEM buildup is investigated by Love wave sensor experiments and more conventional techniques (QCM-D, AFM and CV).

Influence of pH

PEs being intrinsically highly charged, the pH is expected to play an important role in the PEM buildup. Under 'conventional' pH ranges, PSS (pKa = 1 [58]) is always highly negatively charged and its charge density is not significantly affected by varying the pH.

On the contrary, considering the pKa of PAH estimated at 8. more globular chain conformation of PAH is expected [START_REF] Poptoshev | Influence of Solvent Quality on the Growth of Polyelectrolyte Multilayers[END_REF], associated to a more heterogeneous and rougher surface of PEM observed by AFM.

Influence of the ionic strength

In addition to the effect of the pH, the presence of salt in the PE solutions is expected to strongly modify the architecture of the PEM, since the ionic strength also dictates the strength of the inter-and intra-chain interactions, and their possible rearrangements and detachments. Consequently, hereafter, we investigated the effect of an increased concentration of NaCl (from the intrinsic NaCl concentration in TBS, 0.138 M, to 1.500 M) in both PAH and PSS solutions (Figure 2a). The lowest tested NaCl concentration leads to the typical expected stair-step pattern, showing the actual sequential deposition of PE, as shown previously. At the highest concentration (1.50 M, Figure 2a), the FLove frequency shifts are higher than in the native buffer solution suggesting a thicker PEM, in agreement with previous studies [START_REF] Poptoshev | Influence of Solvent Quality on the Growth of Polyelectrolyte Multilayers[END_REF] , [START_REF] Ruths | Polyelectrolytes I: Polyanion/Polycation Multilayers at the Air/Monolayer/Water Interface as Elements for Quantitative Polymer Adsorption Studies and Preparation of Hetero-superlattices on Solid Surfaces †[END_REF]. However signals are irregular and poorly reproducible.

The plateaus corresponding to a steady state after deposition of either PAH or PSS are often missing, an increase of FLove being even systematically observed in the case of PSS layers. These results suggest that, under such conditions, PEs do not adsorb efficiently on the surface or are even released from it. This can be explained by the conformational changes of PEs induced by the ionic strength. Indeed, at high ionic strength PEs are deposited in a globular conformation whereas at low ionic strength they tend to form rodlike chains [START_REF] Decher | Buildup of ultrathin multilayer films by a self-assembly process: III. Consecutively alternating adsorption of anionic and cationic polyelectrolytes on charged surfaces[END_REF], as schematized in Figure 2b.

This change in the chain conformation is due to the charge screening effect generated by the salts, with a concomitant decrease of the interaction between PEs of opposite charge [START_REF] Decher | Buildup of ultrathin multilayer films by a self-assembly process: III. Consecutively alternating adsorption of anionic and cationic polyelectrolytes on charged surfaces[END_REF]. It has been also reported that salts could act as "lubricants" of the motion of PE molecules interacting with oppositely charged surfaces [START_REF] Sui | Effect of Molecular Weight on the Construction of Polyelectrolyte Multilayers: Stripping versus Sticking[END_REF]. A possible competition between ions and PEs has also been suggested [START_REF] Buron | Surface morphology and thickness of a multilayer film composed of strong and weak polyelectrolytes: Effect of the number of adsorbed layers, concentration and type of salts[END_REF]. When increasing salt concentration, all these proposed mechanisms are expected to lead to thicker but also more fragile films.

The possible detachment of the PEs from the surface and a reduced probability of chain interpenetration could explain the irregular shape of the FLove-versus time curves observed at 1.5 M NaCl in the present work.

Overall, Love wave experiments finally show that [PAH-(PASS-PAH

)n] buildup is much more efficient with the intrinsic NaCl concentration of TBS (0.138 M) and at neutral pH.

Influence of the deposition method

Investigating PEM buildup mechanism, we then wondered if the deposition method would influence its properties, especially in terms of thickness and roughness that are critical parameters for potential biotechnological purposes. Hereafter, we investigate the merits of the I-LbL (immersion) and SC-LbL (spin coating) deposition methods with AFM, QCM-D and CV experiments. For the convenience of AFM characterization, PEs were dissolved in ultrapure water and PEMs were built on a very smooth surface of mica (roughness of 0.5 nm), before being dried at room temperature. Optimal conditions described in Material and Methods were used for deposition by the SC-LbL method (100 rpm, 45 s). masses are higher than other previously reported using QCM-D: for instance, around 1,100-1,300 ng/cm 2 in the case of PEMs made of 10 bilayers of PVA/PAA and PVA/PSS [START_REF] Deligöz | QCM-D study of layer-by-layer assembly of polyelectrolyte blend films and their drug loading-release behavior[END_REF], or around 475 ng/cm 2 in the case of PEMs made of 7 bilayers of PEI/PSS [START_REF] Elzbieciak | Nonlinear growth of multilayer films formed from weak polyelectrolytes[END_REF],

QCM-D measurements

prepared by I-LbL in both cases. Such differences are likely due to different experimental conditions (pH, concentration and nature of PEs …). Furthermore, the two methods show a very different trend when increasing the number of layers. The steady-state frequency shift fQCM, and thus the adsorbed mass, increases with the number of layers in the case of the I-LbL method. Nonetheless, the increasing shift induced by each (PSS-PAH) bilayer is not homogeneous along with the deposition process. When the SC-LbL method is used, the frequency shift after each bilayer is more constant (~20 kHz) but it encompasses oscillations being alternatively positive and negative (Figure 3a).

AFM experiments:

To further understand this phenomenon, AFM imaging, in air, was performed on both systems (Figures 3b-e). Images show that PEMs, formed by SC-LbL or I-LbL methods, are made of aggregates distributed all over the mica surface (Figure 3b).

Despite similar structures, it is clear that PEs aggregates formed by the I-LbL method are larger than those formed by the SC-LbL one. Scratching experiments (Figures 3c-d) at different steps of the deposition process of PEMs showed that, for both methods, the total thickness increases with the number of deposited layers, as expected, the I-LbL method leading to thicker films (whatever the number of layers, 3 or 7) than SC-LbL (Figure 3e).

Mean thicknesses mentioned in this work with the I-LbL method are higher than those reported for instance at 3.5 nm in the similar case of [(PSS-PAH)5] PEMs (70 kDa both)

deposited by immersion in water on a PEI-coated gold substrate [START_REF] Poptoshev | Influence of Solvent Quality on the Growth of Polyelectrolyte Multilayers[END_REF]. On the contrary, the thicknesses obtained with the SC-LbL method are lower, but in the similar range, than values previously reported with a spin method at 1.65 nm per [PSS-PAH] PEM (70 kDa and 15 kDa, respectively) [START_REF] Lefaux | Polyelectrolyte spin assembly: Influence of ionic strength on the growth of multilayered thin films[END_REF], or at 2.1-2.2 nm for a [PAH-PSS] PEM (both 70 kDa) [START_REF] An | Surface modification of hafnia with polyelectrolytes based on the spin-coating electrostatic self-assembly method[END_REF].

In the case of the I-LbL technique, the increase of thickness is not strictly proportional to the number of layers: it increases roughly from 3 nm to 11 nm for 3 and 7 layers, respectively. Such a hypothesis is in agreement with studies revealing an exponential growth regime for [(PAH-PSS)n] systems, where the thickness is not only a function of the PE conformation in the bulk but also of the specific properties of the surface-solution interface [START_REF] Ruths | Polyelectrolytes I: Polyanion/Polycation Multilayers at the Air/Monolayer/Water Interface as Elements for Quantitative Polymer Adsorption Studies and Preparation of Hetero-superlattices on Solid Surfaces †[END_REF]. In particular an increasing roughness at each deposition step would increase the adsorption surface and thus the amount of adsorbed PE. Such an increase is observed by AFM, the roughness increasing from 4-5 nm to 9 nm with 3 and 7 deposited layers, respectively.

In the case of the SC-LbL method, QCM-D measurements confirm the overall deposition of PEMs by the global increase of the frequency shifts fQCM. However, the oscillating behavior of this parameter also suggests that PEs could interpenetrate each other and reorganize into the film according to previously observed properties of adsorbed PEMs made of the alternate deposition of PSS and poly [2-(dimethylamino)ethyl methacrylate] PDEM [START_REF] Liu | Role of Chain Interpenetration in Layer-by-Layer Deposition of Polyelectrolytes[END_REF]. In addition, the AFM measurements show that the thickness and the roughness of each deposited layer remain roughly constant during the SC-LbL deposition process (Figure 3e), and clearly lower than with the I-LbL method. All these results

support the hypothesis of a PEM buildup likely following a linear growth regime by the SC-LbL method, with an interpenetration and a reorganization of PE chains, and leading to thinner and more homogeneous PEMs.

CV measurements: PEMs were then studied by CV, in order to test their permeability layer after layer and also their potential use in electrochemical biosensing devices. They were deposited sequentially onto a gold working electrode which was immersed in a TBS solution containing the Fe(CN)6 3-/4-couple.

Figure 4a shows typical CV curves obtained with a gold electrode, bare or covered with a [PAH-(PSS-PAH)n] PEM with n=3, formed either by the I-LbL or the SC-LbL methods. In the absence of any layer at the electrode surface, oxidation and reduction peaks are observed due to the presence in the solution of the Fe(CN)6 3-/4-redox couple. In the case of the I-LbL method, the deposition of sequential [(PSS-PAH)] bilayers induces (i) a decrease of oxidation and reduction currents and (ii) a regular increase of E = (Ea -Ec), both significant of the mass transfer to the electrode (Figures 4b-c). Similar results are observed when PEMs are built using the SC-LbL method (Figure 4).

In both cases (I-LbL and SC-LbL methods), the decrease of oxidation and reduction currents can be assigned to the increasing difficulty for the electroactive complex in solution to reach the electrode's surface after each deposition step. This was also shown by Elzbieciak et al. in the case of (PEI/PSS)n PEMs [START_REF] Elzḃieciak | Influence of pH on the Structure of Multilayer Films Composed of Strong and Weak Polyelectrolytes[END_REF] and Harris and Bruening on (PAH/PSS)n and (PAH/PAA)n PEMs [START_REF] Harris | Electrochemical and in Situ Ellipsometric Investigation of the Permeability and Stability of Layered Polyelectrolyte Films[END_REF]. However, the differences observed in between the two deposition methods both in extent and trend as shown in Figure 4c, support the hypothesis of two different growth regimes.

Quantitatively, the diffusion coefficients of the redox species at the electrode (Da and Dc)

were calculated based on the Randles-Sevcik equation: Da was shown to decrease by 25 % vs. 57 % while Dc dropped by 46 % vs. 84 % after the deposition of three bilayers by SC-LbL and I-LbL respectively (Table 1), convincingly showing that PEMs are less permeable when prepared by the I-LbL method. Isolating efficiency of the coating is thus higher with the I-LbL method (at least after the first bilayer), PEMs made by SC-LbL deposition being more permeable to the electroactive molecules present in solution.

However, our previous results suggest that PEMs by SC-LbL are more organized and homogeneous, implying that higher thickness of PEMs prepared by the I-LbL method might prevail on the more organized structure of PEMs made par the SC-LbL one. Noteworthy is the fact that our diffusion coefficients are higher than those reported by Ghostine and Schlenoff [START_REF] Ghostine | Ion Diffusion Coefficients Through Polyelectrolyte Multilayers: Temperature and Charge Dependence[END_REF] in the range of 10 -9 cm 2 /s, measured with the same redox couple on PEMs made of PDADMA and PSS. Nonetheless, the different nature of one PE and the number of deposited bilayers (10 bilayers in this study) could explain such a difference.

To conclude, though the (PAH-PSS) systems have been widely investigated in the literature, different protocols, with different numbers of layers and / or under different environmental conditions, have led to confusing, even sometimes contradictory, results.

Here, by re-investigating this system at the nanoscale, by studying its properties with complementary techniques (Love waves, AFM, QCM-D and CV), in a systematic approach and under strict conditions free of "parameters interpretation", we showed notably how the deposition process of PEs influences the intrinsic characteristics of the final PEM. I-LbL and SC-LbL methods lead to PEMs likely growing with two different growth regimes.

The former process induces thicker, rougher and less permeable films than those obtained with the latter one. Overall, our results are in agreement with those of previous studies aiming also at developing methods to accelerate the PEM buildup, such as dipping the substrate in stirred solutions or applying a high gravity field. As in the case of the SC-LbL technique, these methods lead to smoother and more homogenous films, as compared to conventional dipping.

PEMs, a way to sense or to attach diverse (bio)systems

Depending on the deposition process, the physico-chemical characteristics of the PEM can thus be tuned. This is especially interesting when targeting biotechnological applications, which do not all require the same characteristics of the support. When the adhesion of cells requires rather soft and hydrated cushions isolating cells from the support, the functionalization of electrodes for biosensing needs on the contrary thinner, organized, more permeable (yet adhesive) films, for the further detection of bio-chemical systems in the nanometric range.

In this context, PEMs built from the I-LbL method and the SC-LbL one appear well adapted in the first and second domains of application, respectively. Brief illustrations in both domains are proposed in the following parts.

Immobilization of bacteria on PEMs built by the I-LbL method

Imaging cellular systems, under physiologically conditions, require their immobilization on substrates. Different methods have been developed for this purpose, including selfassembled monolayers or polymer brushes (poly-L-lysine PEI), but the use of PEMs could also provide an interesting alternative method.

In this work, Gram negative E. coli bacteria were deposited onto either bare mica or mica functionalized with [PAH-(PSS-PAH)3] PEMs built using the I-LbL method, and imaged by AFM either under air ambient conditions or in ultrapure water (Figure 5). When deposited on bare mica and imaged in air, bacteria form more or less dense aggregates which cover only a small fraction of the substrate. Imaged in liquid, all the bacteria are detached from the mica surface, and pushed away by the AFM tip. On the opposite, when deposited on the same mica surface covered with a PEM ending with a PAH layer and imaged in liquid over time, the bacteria population, this time, homogenously covers the surface and remains attached to the PEM. This approach does provide a new alternative to study bacteria in their media. Similar results are obtained with Gram positive B. subtilis bacteria (data not shown).

Even if the organization of E. coli and B. subtilis envelops is different, bacteria surfaces both exhibit a negative charge, which prevents their adhesion on such a negative substrate, as mica. In the presence of PEMs, ending with a positively charged PAH outermost layer, electrostatic interactions with E. coli external membrane or B. subtilis cell wall are favored and are strong enough to prevent the cell motion in liquid under the AFM tip. At the same time, under these conditions, the AFM images suggest the biocompatibility of this kind of substrate, though usually designed as antiadhesion/bactericidal coatings [START_REF] Séon | Polyelectrolyte Multilayers: A Versatile Tool for Preparing Antimicrobial Coatings[END_REF], since bacteria keep their typical rod shape and dimensions, with no sign of cell wall collapse. These results are in good agreement with a previous study dealing with bacteria immobilized on PEMs of various surface charges, and highlighting the crucial role of electrostatic interactions for cell attachment [START_REF] Zhu | Engineered, Robust Polyelectrolyte Multilayers by Precise Control of Surface Potential for Designer Protein, Cell, and Bacteria Adsorption[END_REF].

Immobilization of NPs on PEMs built by the SC-LbL method: nanostructured films for sensor applications

Another great promise of PEMs is their application in biosensors, which require an optimal control not only in terms of surface charge but also in terms of surface roughness.

Hereafter, we present a possible application of PEMs built with the SC-LbL method for the design of nanostructured surfaces based on the adsorption of SiO2-NPs on such PEMs.

Negatively charged 200 nm diameter SiO2-NPs (NPs-) were thus deposited, at a concentration of 5 g/L, by spin coating (20 s, 200 rpm) onto a [PAH-(PSS-PAH)3] PEM.

After a decrease in intensities due to the PEM buildup (as shown above), the electrochemical measurements (Figure 6a) shows a further decrease in CV signals. This proves the actual electrostatic interactions of the NPs on the PEM, that slows down the charge transfer of Fe(CN)6 3-/4 at the electrode.

Positively charged NPs (100 nm NPs + ) were deposited under the same experimental conditions on a [PAH-(PSS-PAH)3-PSS] PEM. Surprisingly, the presence of NPs did not induce any significant modification of the quantity of redox species able to reach the electrode (Figure 6b), though the coating was confirmed by AFM (Figure 6c). This might be explained by the presence of the positively charged surface of the NPs, which interact even less than the PAH layer (Figure 6a) with the kinetics at the electrode surface [START_REF] Chirea | Electrochemical Characterization of Polyelectrolyte/Gold Nanoparticle Multilayers Self-Assembled on Gold Electrodes[END_REF].

Our results show that the coating of PEMs by silica NPs is driven by electrostatic interaction, and confirm other works in the literature [START_REF] Caruso | Electrostatic Self-Assembly of Silica Nanoparticle-Polyelectrolyte Multilayers on Polystyrene Latex Particles[END_REF][START_REF] Zhao | A bacteria-activated photodynamic nanosystem based on polyelectrolyte-coated silica nanoparticles[END_REF].

A successful example of such a kind of application has been recently shown, with the design of a biosensor with a working electrode previously covered by positively charged silica NPs immobilized on a PEM and easily functionalized by antibodies for the specific detection of bacteria [START_REF] Mathelié-Guinlet | Silica nanoparticles-assisted electrochemical biosensor for the rapid, sensitive and specific detection of Escherichia coli[END_REF]. The presence of the NPs layer greatly enhanced the performances of the sensor, as also shown in other cases in terms of sensitivity and selectivity [START_REF] Howes | Colloidal nanoparticles as advanced biological sensors[END_REF].

In conclusion of this last part, we showed that PEMs properties can be specifically tuned, depending on the experimental conditions used for their design and their outermost layer, for the immobilization of various objects and in a biocompatible manner. We have thus found a common easily and rapidly adaptable protocol, based on the intrinsic architecture of the PEM, well beyond the current multiple different strategies applied for biomedical applications. Such a protocol is likely transferable to other biotechnological applications such as optics and cosmetics for which nanoscale controls and characterizations are critical. Nonetheless, the biologically-relevant applications of PEMs still need to be fully investigated, especially under physiological conditions (pH and temperature). Indeed, our results, obtained at room temperature and neutral pH, might be affected notably at physiological temperature: the cross-correlation of each, and every physical and environmental parameters that could affect the PEM, and in turn its applicability to technological applications, remain to be fully understood.

Conclusion

To conclude, we have combined four complementary methods, from the microscale down to the nanoscale, to fully characterize, optimize and understand in a systematic approach the build-up of PEMs made of PAH and PSS. This build-up was performed by two methods (immersion vs spin-coating) to study the functionalization of three types of surface (mica, silica and gold), leading to systems with tunable properties. To our knowledge, this is also the first time that the Love wave sensor method is applied to such a study. We highlighted the important role of PE charge density (through adapted pH and ionic strength of the solutions) in the growth regime of the PEM. Moreover, the deposition method, i.e.

immersion vs. spin-coating, which has often been neglected even ignored so far in the literature, is in fact a critical parameter that researchers should take into account from now on. Its impact on the PEM subsequent properties is crucial, leading to either a thick isolating film or a thin permeable one. Finally, the two types of PEMs were applied in two domains of bio-applications needing opposite prerequisites in terms of surface functionalization: the immobilization on the one hand of biological samples (bacteria) making possible their observation in biocompatible conditions, and on the other hand of inorganic materials with a size in the nanometric range (SiO2-NPs). These two different applications only require to adjust in a simple way the nature of the outermost layer and the method of deposition, paving the way of many other bio-applications.

Figures legends

  QCM-D was used to study in real-time the changes induced by the PE deposition on the resonance of a quartz crystal (the resonance frequency of the bare device being 5 MHz), by following the frequency shift (fQCM), linked to the changes in adsorbed mass m through the Sauerbrey equation: ∆𝑚 = -𝜌 𝑞 𝑡 𝑞 ∆𝑓 𝑛 𝑛𝑓 0

  5 [59], varying the pH can strongly affect the overall PE charge. We thus studied by Love wave sensor, under static conditions, the deposition of [PAH-(PSS-PAH)n] PEMs at two pH values of the PAH solution, namely below (pH 7.2) and above (pH 9.0) its pKa while the pH of the PSS solution was fixed at 7.2.

Figure 2 (

 2 Figure1ashows the real-time FLove frequency shifts from the reference (bare sensor)

  : similarly to Love wave sensor experiments, the sequential deposition of [PAH-(PSS-PAH)n] PEMs is confirmed by an overall increase of the absolute value of the fQCM frequency shift for both I-LbL and SC-LbL methods (Figure 3a), in QCM-D experiments. However, the lower values of fQCMobtained by the SC-LbL method are significant of lower deposited masses, according to the Sauerbrey equation (see Materials & Methods). Masses are estimated at 3,200 ng/cm 2 and 1,100 ng/cm 2 for the I-LbL and SC-LbL methods, respectively, after the deposition of [PAH-(PSS-PAH)3] PEMs. Such

  Figure 1. a) Real-time evolution of the FLove frequency shifts, measured by Love wave sensors, induced by the sequential deposition of PAH (solution at pH 7.2 or 9.0) and PSS (pH at 7.2). b) AFM height images of bare SiO2 surface and [PAH-(PSS-PAH)3] PEMs at the two studied pH for PAH solutions.

Figure 2 .

 2 Figure 2. a) Real-time variation of the FLove frequency shift, measured by Love wave sensors, induced by the sequential deposition of [PAH-(PSS-PAH)n] PEMs (both solutions at pH 7.2) with two different concentrations of NaCl. b) Scheme illustrating the PEs conformational changes with an increasing ionic strength.

Figure 3 .

 3 Figure 3. Influence of the deposition method on the buildup of [(PSS-PAH)n] PEMs on a first layer of PAH deposited on the gold-coated quartz crystal. a) Variation of the fQCM frequency shift in QCM-D experiments, resulting from the sequential deposition of each layer for both I-LbL and SC-LbL methods. b) AFM height images of [PAH-(PSS-PAH)n] PEMs built from both methods, performed after drying at ambient temperature. c) AFM height image resulting from a scratching experiment on [PAH-(PSS-PAH)n]. d) Height profile along the dotted white line (c) allowing for the determination of the PEM thickness -Because of PEM aggregates and accumulated materials close to the scratched area, higher areas are observed. e) Thickness of PEMs as a function of the number of layers for both I-LbL and SC-LbL methods. Error bars were calculated from three independent experiments.

Figure 4 .

 4 Figure 4. Influence of the presence of [(PSS-PAH)n] PEMs (n=0, 1, 2, 3) made by the I-LbL and SC-LbL methods, after the deposition of a first PAH layer, on the (a) CV curves, (b) intensities of the oxidation (Ia) and reduction (Ic) peaks and (c) E=(Ea -Ec) peak-to-peak separation, normalized by values obtained on the bare electrode. Error bars were calculated from three independent experiments.

Figure 5 .

 5 Figure 5. AFM height images of E. coli bacteria deposited either on a bare mica substrate or on a [PAH-(PSS-PAH)3] PEM, and imaged either in air or in ultrapure water.

Figure 6 .

 6 Figure 6. Influence on the peak intensities determined from CV curves of the deposited layers: a) [PAH-(PSS-PAH)3] PEMs coated with negatively charged NPs, b) [PAH-(PSS-PAH)3-PSS] PEMs coated with positively charged NPs. Error bars are calculated from three independent experiments. c) AFM height image of SiO2-NP + (diameter of 100 nm) covering a [PAH-(PSS-PAH)3-PSS] PEM confirming the actual attachment of such NPs during electrochemical measurements.

Table 1 .

 1 Diffusion coefficients of the redox species through the PEM built either from I-LbL and SC-LbL methods.

	Diffusion coefficients (10 -6 cm 2 .s -1 )

Acknowledgements

The authors thank the Région Aquitaine and CNRS (France) for supporting this work through equipment of plateform used in this work: NanoSpectroImagerie (NSI -CPER COLA2) and TAMIS (IMS). They are also grateful to H. Tabargue (IMS Bordeaux, CNRS UMR 5218) who designed PDMS chips in the frame of the ANR project BIOALERT (Agence Nationale de la Recherche, PRECODD program, ANR-06-ECOT-004), and to J.-L. Lachaud and I. Favre (IMS Bordeaux, CNRS UMR 5218) for the design of microfluidic devices. The authors thank M. Benoît (Réseau Technologique de Base, LAAS-CNRS, Toulouse, France) for realizing acoustic wave delay-lines, and D. Moynet (retired from the University of Bordeaux) for his expertise and participation in experiments with bacteria and Love wave devices.

Funding

The authors are grateful to the Direction Générale de l'Armement (DGA, Ministère de la Défense, France), the Région Aquitaine (France) and LOMA for their financial support

through the Ph.D. grant of M. Mathelié-Guinlet, the CMCU grant of I. Gammoudi (bilateral PHC program France-Tunisia, project No. 10G1103).


Angélique Deboeuf

Georges Gauthier

Jérôme Martin

Yevgeny Yurkovetsky

Jeffrey F Morris

Particle pressure: A bridge from osmosis to granular dilatancy

The normal stress exerted by particles in a sheared suspension is measured by analogy with a method used to measure osmotic pressure in solutions. Particles in a liquid of equal density are confined by a fine screen to a gap between two vertical concentric cylinders, the inner of which rotates. Pressure in the liquid is sensed either by a manometer or by a pressure transducer across the screen. The particles are large enough so that Brownian motion and equilibrium osmotic pressure are vanishingly small. The measured pressure yields the shear-induced particle pressure Π, which is the nonequilibrium continuation of equilibrium osmotic pressure. For volume fractions 0.3 ≤ φ ≤ 0.5, Π is strongly dependent on φ, and linear in shear rate. Comparisons of the measured particle pressure with modeling, experimental derivations, and simulation show good agreement.

Motion of one component relative to the remainder of a mixture may arise from different sources, including a density difference or concentration gradient. Driving force is often described in terms of a potential, e.g. the gravitational potential energy for settling particles. However, diffusion is usually accounted through a Fickian flux, j = -D∇n, with D the diffusivity and n the solute number density. Because diffusion results from irregular stochastic motion, defining an associated potential is not trivial. The desired potential is, however, obtained from the relation between diffusion and osmotic pressure and this is considered as a prelude to a striking extension of osmotic pressure in flowing mixtures.

Random motion of dissolved molecules and ions, or of submicron particles, results in diffusion scaling as the thermal energy kT . In the absence of other influences, diffusion tends to drive the mixture toward the homogeneous equilibrium state with ∇n = 0. A key development was provided by Einstein [1], who considered a dilute dispersion of particles in an external field of potential energy U . The force F = -∇U , applied to each particle, induces a flux nu with the velocity given by u = M F where M is the mobility of the solute particles. In the resulting inhomogeneous -but nonetheless equilibrium -state, the flux due to the external field balances the diffusive flux so that -nM ∇U -D∇n = 0. Requiring Boltzmann distribution of energy at equilibrium, n ∼ exp[-U/kT ], yields both the thermodynamic force F th = -kT ∇ ln n and the celebrated result D = kT M . Moreover, as pointed out by Einstein, the volumetric thermodynamic force nF th can be written as -∇Π osm , where Π osm is the osmotic pressure which obeys the van't Hoff relation for dilute systems [START_REF] Van't Hoff | hoff-lecture[END_REF], Π osm = nkT . Hence, the Fickian flux may also be written j = -M ∇Π osm . Diffusive flux and osmotic stress are then two complementary descriptions to account for the influence of random motion of a solute. These motions cause diffu-sive mixing but also tend to minimize variations of the Helmholtz free energy A, leading to a thermodynamic definition of the osmotic pressure, Π osm = -( ∂A ∂V ) N,T , with N the number of solute particles.

This thermodynamic approach provides a convenient means to describe osmosis, which occurs when a solution is separated from a lower concentration solution or the pure solvent by a 'semipermeable membrane' allowing the flow of the solvent but restricting the solute to the solution side, as in a U-tube osmometer sketched in the left of Fig. 1. In this context, Π osm is the additional pressure which must be applied to the solution side to stop solvent flow, i.e. to reach the equilibrium state. Note that this solvent flux was first observed in 1748 [START_REF] Nollet | Leçons de Physique expérimentale[END_REF], but its interpretation as a decrease of the free energy by dilution was proposed much later. In practice, osmotic driving forces can be large: As an example, sea water contains ions at n ≈ 1.4 mol/L (2.5 mole %) and has Π osm ≈ 25 -30 atmospheres, surprisingly large yet in line with the van't Hoff relation for dilute solutions.

Here we illustrate that unexpected osmotic phenomena occur in sheared suspensions of large particles. We recall first that for hard spheres, Π osm = nkT [1 + 4φg(2)] where the volume fraction is φ = 4πna 3 /3 for spheres of radius a, and g(2) is the contact value of the pair distribution function [START_REF] Russel | Colloidal Dispersions[END_REF]. Away from the divergence of g at maximum packing, i.e. for concentrations smaller than φ max ≈ 0.64, this expression yields Π osm ∼ kT /a 3 , of O(1) Pa for a = 0.1 µm and O(10 -3 ) Pa for a = 1 µm. For larger particles, osmotic pressure and Brownian motion are then vanishingly small, but these 'noncolloidal' suspensions nevertheless exhibit diffusion in sedimentation or shear [START_REF] Leighton | [END_REF]6], induced by the chaotic particle trajectories [7] caused by hydrodynamic interactions.

The interactions generate 'shear-induced diffusion' which dissipates concentration gradients [8,9]. Rather remarkably, particle interactions driven by a spatially varying shear rate, γ, can generate concentration gradients. For unidirectional flow u x (y) this implies a crossstream particle flux j ∼ -∇ γ, where γ = |du x /dy| [START_REF] Leighton | [END_REF]. As an alternative, a 'particle pressure' Π has been invoked as the driving potential for particle migration [10,11]. Particle pressure and shear-induced diffusion are the counterparts in sheared systems of the thermal osmotic pressure and Brownian diffusion, respectively.

Our purpose is to further develop the connection, described in theory and simulation studies [12,13], between nonequilibrium particle pressure Π and osmotic pressure. In particular, we illustrate that Π may be measured using a method directly analogous to the classical approach for the measurement of osmotic pressure. The experiments show that osmosis in mixtures is a general result of constraining the dispersed phase against spreading. This leads to the notion that Π quantifies the general tendency of a dispersed phase to spread, an idea long associated with Reynolds dilatancy [14] in which a granular assembly, with grains in contact, must expand to shear.

We turn now to the experimental method. When solute or particles are constrained from spreading, stresses arise in the mixture leading to solvent flow into the solution. Osmotic pressure, associated with the drive toward solute spreading and hence a compressive stress in the dispersed component, is thus measured as a reduced pressure in the solvent. We use this as the conceptual basis to measure the pressures induced by shear flow in the two phases of a viscous suspension. Shear-induced particle pressure has eluded direct measurement in large part because opposing stress states of solvent and dispersed phase lead to a cancellation [13,15]. To measure Π requires, as for Π osm , a method which either allows relative motion so the dispersed phase may change its concentration, or alternatively directly senses the driving force for relative motion. We describe both approaches.

We use suspensions of polystyrene spheres (Dynoseeds TS; Microbeads) of diameter 40, 80, or 140 µm (±5% in each case, with AFM-measured roughness ≈ 100 nm), with density ρ = 1.05 g.cm -3 matching the suspending liquid. The viscosity of the Newtonian fluid, poly(ethylene glycol-ran-polypropylene glycol) monobutyl ether, is η f = 3 Pa.s at 20 o C. The bulk suspension viscosity agrees well with the form η(φ)/η f = (1 -φ/φ max ) -2 . The ratio of shear to Brownian motion, or Péclet number, is P e = 6πη f γa 3 /kT = O(10 8 ) at γ = 1 s -1 . Thermal motion is negligible.

The analogy of the device used here to a U-tube osmometer with semipermeable membrane is illustrated in the center sketch of Fig. 1. The actual Couette device is shown at right in Fig. 2. The inner and outer cylinders have radii r 1 = 17.5 mm and r 2 = 20 mm, respectively, leaving an annular gap r 2 -r 1 = e = 2.5 mm. Rotation of the inner cylinder generates a shear rate γ ≈ Ωr 1 /e. Variation of shear rate across the gap is small and we report only the average. The flow is viscous as the Reynolds number is Re = ρ γe 2 /η f ≤ 1. Eight holes of diameter 3 mm pass through the outer stationary cylinder. They are at 90 o intervals, in two sets located 2 and 6 cm from the bottom of the sheared annulus. Screens with 20 µm square openings, small enough to retain the particles, are placed across the holes on the side toward the annulus.

A tube is fixed in each hole and filled with the suspending liquid. These tubes may serve as manometers or for transmission of the liquid pressure to a transducer. Results from the manometer approach for φ = 0.4 and γ = 70 s -1 are illustrated by Fig. 2. Meniscus levels are shown for a screened hole before shearing (left tube) and after forty minutes of shearing, in the top and bottom images, respectively. To demonstrate the role of the screen, the meniscus in a tube attached to an unscreened hole is also shown in Fig. 2 (right tube). Whereas the meniscus associated with the screened hole drops a few cm, the one with the unscreened hole is almost stationary, as liquid suction is balanced by solid phase dispersive pressure.

Although visually convincing and appealing for its direct analogy with the classical U-tube experiment, the manometer approach has drawbacks. The long times (hours) needed to obtain a measurement, and large ∆h when φ and γ are both large render the approach inconvenient. A basic flaw is that the results are sensitive to φ, which is altered by the liquid drawn into the annulus. Note, however, that the manometer measurements are consistent with the approach described below.

To obtain quantitative measurements, a pressure transducer is attached to each tube. The screen is maintained, and the tubing is completely filled with the suspending liquid to provide communication between suspension and transducer. A pre-shear was applied to ensure the suspension was uniform around the annulus. The transducer reading stabilizes within a few seconds of shearing, and measurements are averaged over 1-2 minutes. No liquid is exchanged across the screen. The difference in the transducer reading between sheared and static states is ∆P , and is negative: Flow generates a suction pressure in the liquid. The pressure is averaged over forward and reverse shearing to eliminate flow-induced pressure due to any slight eccentricity of the cylinders.

Results for the suspension of 40 µm diameter particles are shown in the top panel of Fig. 3 as a function of η f γ, with the fluid viscosity η f corrected for temperature. The measured |∆P | is viscously-driven, as inertial effects would be greatest for the pure liquid which gives a null response, ∆P = 0, and |∆P | increases roughly linearly with increasing γ. Note that linearity in γ at P e ≫ 1 differs from the γ2 dependence of normal stress observed for small P e [16]. The magnitude increases strongly with φ, from |∆P |/η f γ = 0.35 at φ = 0.3 to 18.5 at φ = 0.5. Error bars are significant, but are typically small compared to the mean value. Data for the other sizes of particles studied (80 and 140 µm) are similar to the 40 µm case, although ∆P is smaller for the larger particles.

The measured suction pressures, normalized by η f γ, for all φ and particle sizes studied are gathered in the lower panel of Fig. 3. These show that the suction pressure measured in the liquid behaves similarly to the particle normal stress differences [11,17]. In particular, the pressure becomes reliably measured at φ ≈ 0.3 and grows rapidly with φ. A slight radial particle migration, which can be deduced from results in [11], is complete during the pre-shear for all a, and cannot explain the difference in |∆P | with particle size. A particle slip layer [18] will not explain the observation, although there may be a difference in organization when the gap is small (e/2a < 20 for the 140 µm beads) which could enhance apparent slip (as in shear banding). We note that an axial migration to, and even through, the free surface was observed and this reduces φ within the suspension; migration is more pronounced for larger beads. In general, these considerations lead us to expect that small particles yield the most accurate results, in accord with agreement with model and simulation for the 40 µm suspension (see Fig. 4).

There is a conceptual difficulty in the measurement of the particle pressure in a sheared suspension, stemming from the fact that liquid and solid both satisfy incompressibility to a close approximation. Particle pressure is thus offset by an equal and opposite change in liquid pressure [13], i.e. Π = -∆P ( γ). A transducer exposed to both phases measures the sum of these shear-induced stresses to yield a confusing result [15]. Hence, only a method which discriminates between the phases can enable the measurement of the particle pressure, and in our approach we make use of Π = -∆P = |∆P |. This use of the liquid pressure provides the conceptual link to osmotic pressure. The particle pressure [12] in a sheared suspension is the mean normal stress exerted by the particle phase Π = -(1/3)[Σ P 11 + Σ P 22 + Σ P 33 ] and has been shown by simulation to be equivalent to the osmotic pressure for vanishing shear rate [13], i.e. lim γ→0 Π = Π osm .

However, one has to be cautious in equating the measured liquid pressure with the particle pressure, i.e. in using Π = |∆P |. The measured liquid pressure is set by the conditions at the free surface of the suspension, where deformation of the liquid surface allows capillary pressure to balance the mean particle stress in the vertical direction. It follows |∆P | = Σ P 33 , which may differ from Π. Several arguments justify the approximation Π ≈ |∆P |. First, simulation [13] and experimental correlation [17] lead to the conclusion that normal stress differences, N 1 = Σ P 11 -Σ P 22 and N 2 = Σ P 22 -Σ P 33 , are small relative to Π. Furthermore, the small change in the meniscus level for an unscreened hole (Fig. 2) confirms that Σ P rr + ∆P = Σ P 22 -Σ P 33 ≈ 0. The particle pressure measured, using the approxima-tion Π = -∆P , is compared in Fig. 4 with experimental correlation, simulation, and modeling. Analysis of experimental data [17] showed that migration and viscous resuspension could be rationalized by an isotropic particle stress. The resulting correlation developed for Π is plotted. The expression η n (φ) = Π/η f γ, from constitutive modeling for migration analysis [11] is also displayed, together with simulation values of Π at P e = 1000 [13] and infinite P e [19], obtained with weak and zero thermal motion, respectively. Both simulations use Stokesian Dynamics but differ in the treatment of Π. Despite the variation observed for the different particle sizes, our measured particle pressure is in remarkable agreement with simulation and experimental correlation. We conclude that liquid suction pressure in a sheared suspension provides a robust means of measuring the particle pressure. The fundamental link between particle pressure and equilibrium osmotic pressure is strong. Bagnold's notion of particle pressure under shear [START_REF] Bagnold | Proc. R. Soc. Lond. A[END_REF] has a central role in the modeling of shear-induced migration.

The utility of Π ∼ η f γ for modeling is recognized and applied for noncolloidal [12,13] and Brownian dispersions [START_REF] Frank | [END_REF]22]. Simulations have shown that the quantity agrees with equilibrium theory [13]. The present work shows direct measurability of Π, which, these models have argued, drives shear-induced migration flux [10][11][12][13]:

j ∼ ∇•Σ P ≈ -∇Π = - ∂Π ∂φ ∇φ + ∂Π ∂ γ ∇ γ . (1)
Thus, particle stress can be seen to play a similar role both in and out of equilibrium. The shear-induced migration driven by ∇ γ generates gradients in φ, but nonetheless relaxes variations in Π, just as Fickian diffusion relaxes variations in Π osm arising from nonzero ∇φ. One can then speculate that particle pressure pertains to a more general property of mobile particle mixtures, which exhibit rather nonintuitive phenomena when the dispersed phase is confined. The phenomena include the well-known osmosis, observed in thermally-driven systems, and known to be related to the osmotic pressure. Particle pressure is the nonequilibrium continuation of osmotic pressure [13] and drives shear-induced migration, known to generate inhomogeneity in pipe and channel flows [10,23]. Because density matching is possible, Π for viscous suspensions can be explored for any φ, and for arbitrary ratios of shearing to thermal motion. When gravity plays a prominent role, solids loading is not freely variable. Hence, a granular medium or sediment is formed with φ ≈ φ max and particles in contact. Under such conditions, shearing will induce dilation and the granular material will develop normal forces if it is sheared while constrained to the same volume. While the final link with granular dilation remains to be made, particle pressure appears to be a bridge from osmotic pressure driven by kT to the athermal mixture stresses in suspensions and granular materials.

FIG. 1 :FIG. 2 :

 12 FIG. 1: Left: U-tube osmometer. Center: Schematic of the experimental apparatus. Right: Reynolds dilatancy.

FIG. 3 :

 3 FIG. 3: Measured difference in liquid pressure between resting and sheared states, ∆P . Top: 40 µm diameter particle suspension at varying φ, as a function of η f γ. Error bars show the range of transducer measurements for a given condition. Bottom: |∆P |/ γη f as a function of φ for three particle sizes.

FIG. 4 :

 4 FIG. 4: Comparison of experimental correlation, simulation, and modeling of the particle pressure with the experimental values obtained in this study taking ∆P ≡ Π.

We thank RTRA Triangle de la physique for funding, Univ. de Paris 6 for a visiting professorship (JFM), A. Aubertin and R. Pidoux for building apparatus, and D. Bonamy and G. Pallares for the AFM measurements.