Nanoscale Dynamics versus Surface Interactions ... - ACS Publications

Letter pubs.acs.org/JPCL

Nanoscale Dynamics versus Surface Interactions: What Dictates Osmotic Transport? C. Lee,† C. Cottin-Bizonne,‡ R. Fulcrand,‡ L. Joly,‡ and C. Ybert*,‡ †

Department of Mechanical Engineering, Kyung Hee University, Yongin 446-701, Korea Univ Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622 Villeurbanne, France

‡

S Supporting Information *

ABSTRACT: The classical paradigm for osmotic transport has long related the inducedflow direction to the solute membrane interactions, with the low-to-high concentration flow a direct consequence of the solute rejection from the semipermeable membrane. In principle, the same was thought to occur for the newly demonstrated membrane-free osmotic transport named diffusio-osmosis. Using a recently proposed nanofluidic setup, we revisit this cornerstone of osmotic transport by studying the diffusio-osmotic flows generated at silica surfaces by either poly(ethylene)glycol polymers or ethanol molecules in aqueous solutions. Strikingly, both neutral solutes yield osmotic flows in the usual low to high concentration direction, in contradiction with their propensity to adsorb on silica. Considering theoretically and numerically the intricate nature of the osmotic response that combines molecular-scale surface interaction and near-wall dynamics, these findings are rationalized within a generalized framework. These elements constitute a step forward toward a finer understanding of osmotically driven flows, at the core of rapidly growing fields ranging from energy harvesting to active matter.

T

associated with surface attraction (respectively repulsion),7 where x is the direction parallel to the surface. Starting from a homogeneous pressure in the bulk P∞ and imposing a concentration gradient in the bulk c∞(x) along the x direction will result in a pressure gradient within the diffuse layer, which thus drives a liquid flow. Importantly, these simple arguments point to the intimate link, made in standard theories, between the flow direction and the sign of the solute−wall effective interaction.7 Exploring here the (diffusio-)osmotic transport induced by neutral solutes in aqueous solutions, we demonstrate that the previous classical paradigm based on surface interactions alone fails to predict even the direction of the induced flows. Complementing nanofluidic experiments with theoretical approaches and molecular dynamics (MD) simulations, we show that this failure can be rationalized by considering the near-wall dynamics of the solution down to the molecular scale. This stresses the entangled role of interactions and dynamics in surface-driven flows, an element put forward previously in the framework of wall slippage19,20 but whose experimental demonstration remained so far elusive. Diffusio-osmosis experiments have been carried out using nanofluidic chips, following the method developed for electrolyte solutes.12 In short, a nanochannel of height h = 148 or 163 nm, width w = 5 μm, and length L = 150 μm is etched on a silicon wafer using standard nanofabrication

he interest in micro/nanofluidic systems has been quickly growing over the recent years, with huge expectations in domains such as energy or environmental and biomedical applications.1−3 As for any size reduction, this is associated with the prominent role of surfaces, where most useful or new phenomena occurring in confined fluidic systems take place.2,4,5 Among these, surface-driven flows, as exemplified by the widespread electro-osmosis and more generally by the many electrokinetic effects, have constituted a cornerstone of the micro/nanofluidic toolbox.6 Recently, it was shown that beyond electric or thermal driving, these types of transport can also be triggered by osmotic effects associated with concentration gradients.7−13 In a previous work, some of the authors demonstrated that osmotic flows can be generated in nanosystems without the classical requirement of a semipermeable or selective membrane.12 Relieving this constraint, these so-called diffusio-osmotic flows considerably extend the domains for which osmotic transport may contribute. Such phenomena open, for instance, promising routes for efficient blue energy harvesting11 or oil recovery in dead-end pores14 and can have a key contribution in confined or unconfined transport of biomolecules.15−18 Membrane-free osmotic flows result from the local pressure equilibrium normal to the channel surfaces, which interact with the solute of concentration c through a potential of mean force ϕ(z) (with z the distance to the interface), gathering all contributions (enthalpic and entropic) to the solute−wall interactions. Within the diffuse layer set by the range of surface interactions, the static equation of fluids ∂zP = −c(x, z)∂zϕ describes the pressure build up (respectively decrease) © XXXX American Chemical Society

Received: November 23, 2016 Accepted: January 3, 2017

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DOI: 10.1021/acs.jpclett.6b02753 J. Phys. Chem. Lett. 2017, 8, 478−483

Letter

The Journal of Physical Chemistry Letters

Figure 1. Left: Schematic of the experimental setup. Side microchannels are used to impose concentration gradients along a central nanochannel. Generated osmotic flows are quantified by confocal imaging of the longitudinal concentration profile of a fluorescent probe. Right: Experimental images of the fluorescent dye profiles for solute gradients of opposite magnitudes. Profiles are modified by the generated diffusio-osmotic flow, which adds to the dye diffusion (up) or opposes to it (down).

Figure 2. Nondimensionalized diffusio-osmotic flow velocity Ũ = U/Uref versus scaled concentration difference ΔC̃ = Δc∞/Cref using PEG polymers of MW (▲) 200, (▼) 1000, (▶) 6000, or (◀) 12 000 g/mol or ethanol (red ●) as a solute. Results with a KI electrolyte solute, taken from ref 12, are shown for comparison (blue ■). Lines are linear fits of the experimental data (PEG: black solid line; ethanol: dashed red line; KI: dashed-dotted blue line). Gray shaded (respectively, white) quadrants correspond to “attractive-like” (respectively, “repulsive-like”) behavior, with flow going toward low (respectively, high) concentrations. Reference velocities are, for the KI electrolyte: Uref = DDO/L (with DDO taken from ref 12); for PEG: Uref = kBTR2GC*/(ηwL), where the radius of gyration RG(MW) is taken from ref 21, C*(MW) is the overlap polymer concentration, and ηw is the water viscosity; for ethanol: Uref = kBTδ2Ce0/(ηwL), where δ = 4.4 Å is a characteristic size for ethanol molecules22 and Ce0 is the reference number concentration for pure ethanol. Reference concentrations are Cref = C̅ for KI, C*(MW) for PEG, and Ce0 for ethanol. Inset: Linear response coefficient, U/Δc∞, for PEGs as a function of the squared radius of gyration.

Figure 2 presents the induced diffusio-osmotic flow velocities measured experimentally as a function of solute concentration gradients in water. Nondimensionalized variables Ũ and ΔC̃ are defined for each solute species by taking a reference velocity Uref = kBTS2 Cref/(ηwL), where kB is the Boltzmann constant, T is the temperature, ηw is the solvent viscosity, S is a length scale associated with interactions, and Cref is a reference concentration. Both S and Cref choices will be discussed later on. Experimentally, one should note that both PEG and ethanol significantly modify the solution viscosity. Although this was not accounted for in previous studies on osmotic drift with neutral solutes,15,16,23 this has a consequence on the dye transport and must be corrected for accurately sorting-out osmotic flows (see the SI). Coming back to experimental results, the first noticeable feature is that osmotic flows are generated for all tested solutes. These flows increase essentially linearly with the concentration

techniques. Both ends connect perpendicularly to side microchannels (50 μm height, 300 μm width, and ca. 2 cm length), which act as reservoirs whose concentrations can be easily set by pressure flow control (Figure 1). Solute gradients are generated from aqueous solutions of either poly(ethylene)glycol (PEG) of various molecular weights (MWs) of 200, 1000, 6000, and 12 000 g/mol (Sigma-Aldrich), or ethanol (absolute, Carlo Erba) in Milli-Q water at pH 10 (1 mM TrisHCl, 2 mM NaOH). In addition to the neutral solutes, a molecular dye is added in one reservoir at low concentration (200 μM fluorescein salt). Measurement of the steady-state dye profile along the nanochannel (Leica TCS-SP5 confocal microscope) enables us to detect and quantify the diffusioosmotic convective transport along the channel. Remarkably, the sensitivity achieved on flow rates is below fL/s;12 see the Supporting Information (SI) for details. 479


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Let us come back first to the case of polymer solutes. From PEG adsorption literature, we expect an adsorbed PEG layer to lie on the silica wall and for our concentration range (10−100 g/L) to be essentially at saturation.26 In such a situation, both the extension of the layer and its hydrodynamic thickness are typically of order RG, the polymer radius of gyration.30,31 Outside the adsorbed layer, free polymers are expected to be depleted near the adsorbed layer, with a typical characteristic size again of order RG.32 Hence, for PEG polymer, we propose that the observed flow direction discrepancy arises from effects analogous to dynamical Stern layer (shear-plane location), as introduced in electrokinetic phenomena.33 The adsorbed PEG layer is essentially located below the shear-plane location z = zs, where the fluid velocity vanishes, as indicated by the layer hydrodynamic thickness. In relating the osmotic velocity to the interaction potential, this modifies K and L* definition, with the integrals now running from zs to ∞. In this outer region, free polymers in solution experience a repulsion from adsorbed chains. With a characteristic length scale RG, the KL* term in eq 1 now writes KL* = R2G∫ ∞ 0 z̃cẽ x.(z̃) dz̃, where z̃ = (z − zs)/RG. Because the reduced excess concentration of polymer is negative above the shear-plane, we thus predict

imbalance at the nanochannel ends. However, one should remember that with a nanochannel height h around 150 nm, h is orders of magnitude larger than solute molecular sizes or than solute−wall interaction range. Therefore, the nanochannels are fully permeable to all solutes, and the requirements for classical membrane osmosis are not met, yet an osmotic flow is indeed generated that is thus associated with surface-driven diffusio-osmosis. This underlines the generality of such transport mechanisms in the presence of chemical gradients. Beyond this shared feature of diffusio-osmosis, a striking qualitative difference appears between the present neutral solutes (PEG and ethanol) and previous results for electrolytes. Indeed, salt-induced transport heads toward low concentration, while the two others are heading toward high concentration. Recalling the mechanism underlying osmotic transport, this seems to indicate that PEG and ethanol solutes are repelled from the silica wall surfaces while salt is attracted. Indeed, for salt, the Poisson−Boltzmann equation predicts that ion excess writes 2c∞(x)[cosh(eβV) − 1], where c∞(x) is the imposed salt concentration in the middle of the channel, V is the electric potential near the charged wall, and β = 1/kBT. Ion excess is therefore always positive, corresponding to an attractive wall−solute interaction, in agreement with the observed osmotic flow. For PEG and ethanol, the low-to-high concentration osmotic transport now suggests a repulsive wall interaction, as is observed for membrane osmosis with rejecting membrane. However, this is in strong contradiction with the known behavior of both solutes near silica surfaces, with surface adsorption reported for ethanol24 and PEG.25−27 This clearly questions the theoretical description of diffusioosmosis and requires going beyond the previous qualitative explanation. A full calculation of diffusio-osmotic flows was already carried on in the literature,7,28,29 conducting to U = DDO

⎛ dc ⎞ kT −∇c∞ = B KL*⎜ − ∞ ⎟ ⎝ dx ⎠ η c∞

U=

kBTα 2R G2 ⎛ dc∞ ⎞ ⎜+ ⎟ 2ηw ⎝ dx ⎠

(2)

where α2 is a numerical prefactor that depends on the precise shape of the repulsive interaction with the adsorbed layer and where we choose the solvent viscosity ηw to be the relevant viscosity in the depleted diffuse layer. Note that in the limit of a simple hard-core repulsion, α = 1.12,15,34 Incorporating the molecular-scale dynamics of the near-wall polymers, we thus recover an osmotic velocity of “repulsive” type, directed toward high concentrations, as measured experimentally (Figure 2). Using Uref = kBTR2GC*/(ηwL) and C*/L for nondimensionalizing diffusio-osmotic velocities and concentration gradients, eq 2 reduces simply to Ũ = −(α2/2)ΔC̃ . Therefore, we expect that nondimensionalized data plotted in Figure 2 for different PEG molecular weights should collapse onto a linear master curve, as is indeed observed. Equivalently, we predict theoretically that the linear response coefficient U/Δc∞ varies as R2G. Excellent agreement is obtained, as shown in Figure 2 (inset). For this linear response regime obtained for dilute polymers (ΔC̃ < 1), we obtain a numerical prefactor α = 1.5 ± 0.2. This is fully consistent with our expectation of α ≈ 1. Strikingly, this illustrates the sensitivity of such osmotic phenomenon to probe the wall−solute interactions down to molecular scales, with simple methods relying on optical fluorescence profiles. Finally, one may note that beyond the dilute polymers regime, the linear behavior levels off. Although a detailed examination of the modification of the diffuse layer interactions or dynamics is beyond the scope of the present article, this likely marks deviation from some of the previous hypothesis: ideal gas osmotic pressure,35 splitting and interactions between adsorbed layer and outer solution, and so on. Now turning to the case of ethanol, our guess is that a similar mechanism of reduced near-wall mobility explains the reversed diffusio-osmotic flow compared with adsorption properties. However, the underlying molecular mechanism that we unveil is entirely new and much more subtle, as we show now.

(1)

where U is the plug-flow velocity outside the near-wall diffuse layers and DDO is the so-called diffusio-osmotic mobility. Equation 1 introduces two length scales, K = ∫ ∞ 0 [exp(−βϕ) − 1] dz and L* = K−1 ∫ ∞ z[exp(−βϕ) − 1] dz (the integrals run 0 from the wall z = 0, where the liquid velocity vanishes, to the middle of the channel, z = ∞). Noting that [exp(−βϕ) − 1] directly accounts for the reduced excess concentration of solute c̃ex. = [c(x,z) − c∞(x)]/ c∞(x), K is simply the Gibbs adsorption length and Kc∞ is the solute surface excess. For a net adsorption, K is thus positive. In most situations, the first moment KL* of the reduced excess concentration will take the same sign as K, so that the diffusioosmotic flow goes from low to high concentration for depleted solutes (negative surface excess) and from high to low for adsorbed ones (positive surface excess). More importantly, the key feature of the classical prediction encompassed in eq 1 is that the knowledge of the static interactions fully determines the direction and magnitude of the generated osmotic response. As we will see now, the discrepancy observed for PEG and ethanol arises from the fact that dynamical elements are actually hidden in the previous derivation and that the molecular-scale aspects of the solution near-wall dynamics must be accounted for accurately. 480


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this layer are practically frozen, even though not all of them are behind the shear plane. More interesting, the diffusion coefficient is already 2.4 times below the bulk one in the second peak and still 1.3 times below in the third peak. In agreement with this reduced mobility, Figure 3 (left) shows that the water and ethanol velocity profiles differ close to the surface, with ethanol molecules moving at a lower velocity.37 The excess solute current can be written as Jex. s ∝ ∞ ex. [c (z)v (z) − c v (z)] dz, which can be rewritten as J ∫∞ zs s s s w s = ex. mob. ex. mob. ∞ J + J , with J ∝ ∫ [cs(z) − cs ]vs(z) dz and J ∝ ∫ c∞ s [vs(z) − vw(z)] dz. It thus clearly appears that while the surface excess contribution Jex. indeed will be positive for attractive interactions, the mobility contribution Jmob. associated with the shift between water and solute velocity profiles can overcompensate the excess term to revert the sign of the global effect. Assuming that the partial decoupling of solute and solvent near-surface velocities writes: vs(z) − vw(z) = ṽex.(z)vw(z), where ṽex.(z) is an excess mobility; this allows us to generalize eq 1. Indeed, eq 1 corresponds to DDO ∝ ∫ ∞ zs (z − zs)c̃ex.(z) dz ∞ ∞ ex. and Js ∝ ∫ zs cs c̃ex.(z)vw(z) dz. Direct analogy thus yields the generalized diffusio-osmotic response coefficient

To investigate such molecular-scale mechanisms, we performed MD simulations of a water−ethanol mixture in a silica slit-channel using the LAMMPS package.36 All details of the numerical setup and protocol can be found in the SI. We used this system to compute the diffusio-osmotic mobility DDO of the water−ethanol/silica interface. According to Onsager reciprocal relations, DDO can also be evaluated from the symmetric configuration, where one measures the solute excess current generated by the solvent Poiseuille flow induced by a pressure gradient;20 see the SI for details. We measured a negative mobility, DDO = −0.23 × 10−9 m2/s, fully consistent with the direction of the measured surface-driven flows (Figure 2). MD simulations can now provide insights into the microscopic mechanisms underlying this “repulsive-like” behavior. In particular, Figure 3 (left) shows the density profile

DDO =

kBT η

∫z

∞

(z − zs)[cex. ̃ (z) + vex. ̃ (z)] dz s

(3)

thus incorporating dynamical contributions both under the shear-plane location zs and more strikingly under the new mobility-related term ṽex.. Finally, we confirmed this dynamical origin of the reverse diffusio-osmosis direction by considering model hydrophobic surfaces, where the mobility of the adsorbed ethanol molecules is not reduced, and no velocity difference between water and ethanol is observed (see the SI). In that case, eq 1, corrected to account for liquid/solid slip,20 predicts the diffusio-osmotic mobility quantitatively, whose sign is now consistent with the attractive ethanol−surface interactions. In conclusion, we have quantitatively characterized diffusioosmotic flows generated by different neutral solutes, thus evidencing the generality of membrane-free osmotic transport, as recently put forward for electrolyte solutes. Beyond this generalization, we demonstrated that the direction and magnitude of osmotic flows cannot be simply inferred from static (wall interaction) considerations and provided a comprehensive and semiquantitative framework that captures these effects. Strikingly, we evidenced a novel mechanism of differential solvent−solute near-wall mobility that can induce a complete flow reversal for adsorbed solutes. This dramatic entanglement of static and dynamic contribution to surfacedriven flows was previously put forward theoretically in the context of wall-slippage19,20 as a potential response amplifier. However, so far, its experimental investigation had remained elusive, and more complex scenarios leading to response inversion had never been identified. With the importance of osmotic transport, and its upsurge in energy or water treatment contexts, we hope this work will contribute to the onset of innovative and controlled nanofluidic-based strategies as recently proposed.3−6,11,13,18 In a wider perspective, osmotic surface flows have a phoretic counterpart for moving particles, which is at the core of present development in active systems. Our approach can elucidate the direction of swim and interaction, as shown with the ubiquitously used hydrogen peroxide solute (see the SI).38,39

Figure 3. Molecular dynamics simulations of the Poiseuille flow of a water−ethanol mixture (9.2 wt % of ethanol) confined in a slit silica channel. Left: Number density profile of ethanol molecules in the vicinity of the bottom wall (full line); the hydroxyl groups of the silica surface are located at z = −21.5 Å. Water (dotted blue line) and ethanol (dashed red line) velocity profiles are also represented. The vertical black dotted line represents the shear-plane position, zs, where water velocity vanishes. Right: Mean-square displacement along the y direction (parallel to the surfaces and perpendicular to the flow direction) of ethanol molecules located: in the middle of the channel (maroon), in the third adsorption peak (blue), in the second adsorption peak (red), and in the first adsorption peak (green).

of ethanol molecules close to the silica wall. The interaction is clearly attractive, with three successive adsorption layers. From the density profiles, we computed the characteristic lengths K and L* that should control the direction of diffusio-osmosis according to eq 1. In the expressions of K and L*, the integrals were taken between the shear-plane position, zs, where the water velocity profile vanishes in the middle of the channel. Both lengths are positive, with K = 1.99 Å and L* = 1.64 Å. The classical treatment encompassed in eq 1 is therefore unable to predict the mere direction of the measured diffusio-osmotic flow, even when accounting for the notion of shear-plane. Therefore, in the case of ethanol, too, dynamics must play a key role in the “repulsive-like” osmotic flow but in a subtler way than for polymers. Indeed, Figure 3 (right) confirms that adsorbed ethanol molecules are less mobile than bulk ones. This is shown by plotting the mean-square displacement of ethanol molecules along the y direction (parallel to the surfaces and perpendicular to the flow direction) in the middle of the channel and in the three adsorption layers. As compared with the middle of the channel, the first adsorption layer has a diffusion coefficient reduced by a factor 17; that is, molecules in 481


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(13) Kar, A.; Chiang, T.-Y.; Rivera, I. O.; Sen, A.; Velegol, D. Enhanced transport into and out of dead-end pores. ACS Nano 2015, 9, 746−753. (14) Shin, S.; Um, E.; Sabass, B.; Ault, J. T.; Rahimi, M.; Warren, P. B.; Stone, H. A. Size-dependent control of colloid transport via solute gradients in dead-end channels. Proc. Natl. Acad. Sci. U. S. A. 2016, 113, 257−261. (15) Jiang, H.-R.; Wada, H.; Yoshinaga, N.; Sano, M. Manipulation of colloids by a nonequilibrium depletion force in a temperature gradient. Phys. Rev. Lett. 2009, 102, 208301. (16) Maeda, Y. T.; Buguin, A.; Libchaber, A. Thermal separation: interplay between the Soret effect and entropic force gradient. Phys. Rev. Lett. 2011, 107, 038301. (17) Wanunu, M.; Morrison, W.; Rabin, Y.; Grosberg, A. Y.; Meller, A. Electrostatic focusing of unlabelled DNA into nanoscale pores using a salt gradient. Nat. Nanotechnol. 2010, 5, 160−165. (18) Hatlo, M.; Panja, D.; Van Roij, R. Translocation of DNA molecules through nanopores with salt gradients: the role of osmotic flow. Phys. Rev. Lett. 2011, 107, 068101. (19) Joly, L.; Ybert, C.; Trizac, E.; Bocquet, L. Hydrodynamics within the electric double layer on slipping surfaces. Phys. Rev. Lett. 2004, 93, 257805. (20) Ajdari, A.; Bocquet, L. Giant amplification of interfacially driven transport by hydrodynamic slip: diffusio-osmosis and beyond. Phys. Rev. Lett. 2006, 96, 186102. (21) Devanand, K.; Selser, J. C. Asymptotic behavior and long-range interactions in aqueous solutions of poly(ethylene oxide). Macromolecules 1991, 24, 5943−5947. (22) Surfactants in Tribology; Biresaw, G., Mittal, K. L., Eds.; CRC Press, 2001; Vol. 2. (23) Paustian, J. S.; Angulo, C. D.; Nery-Azevedo, R.; Shi, N.; AbdelFattah, A. I.; Squires, T. M. Direct measurements of colloidal solvophoresis under imposed solvent and solute gradients. Langmuir 2015, 31, 4402−4410. (24) Zhang, L.; Liu, W.; Shen, Y. R.; Cahill, D. G. Competitive molecular adsorption at liquid/solid interfaces: a study by sumfrequency vibrational spectroscopy. J. Phys. Chem. C 2007, 111, 2069− 2076. (25) Dijt, J. C.; Stuart, M.; Hofman, J. E.; Fleer, G. J. Kinetics of polymer adsorption in stagnation point flow. Colloids Surf. 1990, 51, 141−158. (26) Trens, P.; Denoyel, R. Conformation of poly (ethylene glycol) polymers at the silica/water interface: a microcalorimetric study. Langmuir 1993, 9, 519−522. (27) Derkaoui, N.; Said, S.; Grohens, Y.; Olier, R.; Privat, M. Polyethylene glycol adsorption on silica: from bulk phase behavior to surface phase diagram. Langmuir 2007, 23, 6631−6637. (28) Anderson, J. L.; Lowell, M. E.; Prieve, D. C. Motion of a particle generated by chemical gradients. Part 1. Non-electrolytes. J. Fluid Mech. 1982, 117, 107−121. (29) Prieve, D. C.; Anderson, J. L.; Ebel, J. P.; Lowell, M. E. Motion of a particle generated by chemical gradients. Part 2. Electrolytes. J. Fluid Mech. 1984, 148, 247−269. (30) Killmann, E.; Maier, H.; Kaniut, P.; Gütling, N. Photon correlation spectrometric measurements of the hydrodynamic layer thicknesses of adsorbed polyethylene oxides on precipitated silica. Colloids Surf. 1985, 15, 261−276. (31) Klein, J.; Luckham, P. F. Forces between two adsorbed poly(ethylene oxide) layers in a good aqueous solvent in the range 0− 150 nm. Macromolecules 1984, 17, 1041−1048. (32) Semenov, A. N.; Bonet-Avalos, J.; Johner, A.; Joanny, J. F. Adsorption of polymer solutions onto a flat surface. Macromolecules 1996, 29, 2179−2196. (33) Hunter, R. J. Foundations of Colloid Science, 2nd ed.; Oxford University Press, 2001. (34) Staffeld, P. O.; Quinn, J. A. Diffusion-induced banding of colloid particles via diffusiophoresis. 2. Non-electrolytes. J. Colloid Interface Sci. 1989, 130, 88−100.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.6b02753. Materials and methods; details of MD simulations; supplemental MD results for hydrophobic surfaces; and supplemental experimental results for hydrogen peroxide solute. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

C. Ybert: 0000-0002-2793-7229 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to A.L. Biance, C. Barentin, J. Farago, A. Johner, and C. Drummond for fruitful discussions. We thank P. Joseph (LAAS) for his help with nanofluidics chips fabrication, S. Gravelle for FCS measurements, and I. Theurkauff and S. Guerraz for diffusiophoresis measurements. We benefited from access to clean room facilities at LAAS and INL. This research was supported by the Science and Technologoy Amicable Research Program (STAR) between Korea and France as project #32164XB and through the National Research Foundation of Korea (NRF-2014K1A3A1A21001234).

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