This paper is published as part of Faraday Discussions volume 146:

Wetting Dynamics of Hydrophobic and Structured Surfaces

Introductory Lecture Exploring nanoscale hydrophobic hydration

Peter J. Rossky, Faraday Discuss., 2010

DOI: 10.1039/c005270c

Papers

Dynamical superhydrophobicity Mathilde Reyssat, Denis Richard, Christophe Clanet and David Quéré, Faraday Discuss., 2010 DOI: 10.1039/c000410n

Superhydrophobic surfaces by hybrid raspberry-like particles Maria D'Acunzi, Lena Mammen, Maninderjit Singh, Xu Deng, Marcel Roth, Günter K. Auernhammer, Hans-Jürgen Butt and Doris Vollmer, Faraday Discuss., 2010 DOI: 10.1039/b925676h

Microscopic shape and contact angle measurement at a superhydrophobic surface Helmut Rathgen and Frieder Mugele, Faraday Discuss., 2010 DOI: 10.1039/b925956b

Transparent superhydrophobic and highly oleophobic coatings Liangliang Cao and Di Gao, Faraday Discuss., 2010 DOI: 10.1039/c003392h

The influence of molecular-scale roughness on the surface spreading of an aqueous nanodrop Christopher D. Daub, Jihang Wang, Shobhit Kudesia, Dusan Bratko and Alenka Luzar, Faraday Discuss., 2010 DOI: 10.1039/b927061m

Discussion

General discussion Faraday Discuss., 2010 DOI: 10.1039/c005415c

Papers

Contact angle hysteresis: a different view and a trivial recipe for low hysteresis hydrophobic surfaces Joseph W. Krumpfer and Thomas J. McCarthy, Faraday Discuss., 2010 DOI: 10.1039/b925045j

Amplification of electro-osmotic flows by wall slippage: direct measurements on OTS-surfaces Marie-Charlotte Audry, Agnès Piednoir, Pierre Joseph and Elisabeth Charlaix, Faraday Discuss., 2010 DOI: 10.1039/b927158a

Electrowetting and droplet impalement experiments on superhydrophobic multiscale structures F. Lapierre, P. Brunet, Y. Coffinier, V. Thomy, R. Blossey and R. Boukherroub, Faraday Discuss., 2010 DOI: 10.1039/b925544c

Macroscopically flat and smooth superhydrophobic surfaces: Heating induced wetting transitions up to the Leidenfrost temperature Guangming Liu and Vincent S. J. Craig, Faraday Discuss., 2010 DOI: 10.1039/b924965f

Drop dynamics on hydrophobic and superhydrophobic surfaces B. M. Mognetti, H. Kusumaatmaja and J. M. Yeomans, Faraday Discuss., 2010 DOI: 10.1039/b926373j

Dynamic mean field theory of condensation and evaporation processes for fluids in porous materials: Application to partial drying and drying J. R. Edison and P. A. Monson, Faraday Discuss., 2010 DOI: 10.1039/b925672e

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Molecular dynamics simulations of urea–water binary droplets on flat and pillared hydrophobic surfaces Takahiro Koishi, Kenji Yasuoka, Xiao Cheng Zeng and Shigenori Fujikawa, Faraday Discuss., 2010 DOI: 10.1039/b926919c

Discussion

General discussion Faraday Discuss., 2010 DOI: 10.1039/c005416j

Papers

First- and second-order wetting transitions at liquid–vapor interfaces K. Koga, J. O. Indekeu and B. Widom, Faraday Discuss., 2010 DOI: 10.1039/b925671g

Hierarchical surfaces: an in situ investigation into nano and micro scale wettability Alex H. F. Wu, K. L. Cho, Irving I. Liaw, Grainne Moran, Nigel Kirby and Robert N. Lamb, Faraday Discuss., 2010 DOI: 10.1039/b927136h

An experimental study of interactions between droplets and a nonwetting microfluidic capillary Geoff R. Willmott, Chiara Neto and Shaun C. Hendy, Faraday Discuss., 2010 DOI: 10.1039/b925588e

Hydrophobic interactions in model enclosures from small to large length scales: non-additivity in explicit and implicit solvent models Lingle Wang, Richard A. Friesner and B. J. Berne, Faraday Discuss., 2010 DOI: 10.1039/b925521b

Water reorientation, hydrogen-bond dynamics and 2D-IR spectroscopy next to an extended hydrophobic surface Guillaume Stirnemann, Peter J. Rossky, James T. Hynes and Damien Laage, Faraday Discuss., 2010 DOI: 10.1039/b925673c

Discussion

General discussion Faraday Discuss., 2010 DOI: 10.1039/c005417h

Papers

The search for the hydrophobic force law Malte U. Hammer, Travers H. Anderson, Aviel Chaimovich, M. Scott Shell and Jacob Israelachvili, Faraday Discuss., 2010 DOI: 10.1039/b926184b

The effect of counterions on surfactant-hydrophobized surfaces Gilad Silbert, Jacob Klein and Susan Perkin, Faraday Discuss., 2010 DOI: 10.1039/b925569a

Hydrophobic forces in the wetting films of water formed on xanthate-coated gold surfaces Lei Pan and Roe-Hoan Yoon, Faraday Discuss., 2010 DOI: 10.1039/b926937a

Interfacial thermodynamics of confined water near molecularly rough surfaces Jeetain Mittal and Gerhard Hummer, Faraday Discuss., 2010 DOI: 10.1039/b925913a

Mapping hydrophobicity at the nanoscale: Applications to heterogeneous surfaces and proteins Hari Acharya, Srivathsan Vembanur, Sumanth N. Jamadagni and Shekhar Garde, Faraday Discuss., 2010 DOI: 10.1039/b927019a

Discussion

General discussion Faraday Discuss., 2010 DOI: 10.1039/c005418f

Concluding remarks

Concluding remarks for FD 146: Answers and questions Frank H. Stillinger, Faraday Discuss., 2010 DOI: 10.1039/c005398h

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PAPER www.rsc.org/faraday_d | Faraday DiscussionsD

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Amplification of electro-osmotic flows by wallslippage: direct measurements on OTS-surfaces

Marie-Charlotte Audry, Agn�es Piednoir, Pierre Joseph†and Elisabeth Charlaix*

Received 23rd December 2009, Accepted 28th January 2010

DOI: 10.1039/b927158a

The control of water flow in Electrostatic Double Layers (EDL) close to charged

surfaces in solution is an important issue with the emergence of nanofluidic

devices. We compare here the zeta potential governing the electrokinetic

transport properties of surfaces, to the electrostatic potential directly measured

from their interaction forces. We show that on smooth hydrophilic silica these

quantities are similar, whereas on OTS-silanized hydrophobic surfaces the zeta

potential is significantly higher, leading to an enhanced electro-osmotic velocity.

The enhancement obtained is consistent with an interfacial water slippage on the

silanized surface, characterized by a constant slip length of�8 nm independent of

the salt concentration in the range 10�4–10�3M.

1 Introduction

The flow of water close to charged surfaces in solution is of prime importance forelectrokinetic transport, widely used in colloidal science, biological analysis, micro-and nanofluidics, and more generally for bringing into motion fluid or solid phasesat a small scale.1–3 Electrokinetic transport takes its origin in the advection by a flowof the ions contained in the non-neutral fluid layer close to a charged surface, theso-called Electric Double Layer (EDL). The zeta potential which determines theamplitude of electrokinetic properties, e.g. electro-osmotic and electrophoreticvelocities, streaming currents and potentials, depends indeed not only on the electro-static properties of the surface which determine the amount of net mobile charges insolution, but also on the hydrodynamics at the solid interface, which governs theefficiency with which these mobile charges are brought into motion.

Typical size of EDLs range between 1 nm to 100 nm in most usual conditions. Theemergence of applications involving the manipulation of fluids at small scales, suchas micro- and nanofluidic devices for biological analysis, energy storage or con-version, has renewed the interest for a better understanding of the origin of thezeta-potential and its relation with interfacial hydrodynamics.4,5 Traditional model-ling in terms of a no-slip boundary condition (b.c.) at the liquid/solid interface is notsufficient any more in view of the recent findings showing that liquids can undergosubstantial slippage onto solid surfaces.6–8 More specifically, it is now establishedthat water flow onto a range of materials obeys a partial boundary condition, char-acterized by a slip length which increases with the contact angle, and reaches tens ofnanometres on highly hydrophobic surfaces.9–11 It has been recognized that such

Laboratoire PMCN Universit�e Lyon 1, CNRS UMR5586, 43 bd du 11 novembre 1918, F-69622Villeurbanne. E-mail: elisabeth.charlaix@univ-lyon1.fr

† Present address: LAAS; CNRS; Universit�e de Toulouse; UPS, INSA, INP, ISAE, 7 avenuedu Colonel Roche, F-31077 Toulouse, France

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interfacial slippage should result in a substantial reduction of the friction in EDLs,and accordingly an enhancement of electrokinetic transport.12–16 Such enhancementcould be of major importance in nanofluidic devices, which take explicit benefit ofEDLs overlap to reach new and specific transport functions.17,18 For instance ithas been shown that friction reduction induced by slip lengths of 50 nm couldincrease the efficiency of mechanical to electrical energy conversion by nanofluidicdevices from 3% to 70%.19,20

Few experimental works have addressed quantitatively the issue of the respectivecontribution of surface electrical properties and interfacial hydrodynamics toelectrokinetic transport. This requires an independent measurement of the corres-ponding quantities, however most methods for characterizing surface potential/charges in solution actually rely on measurements of the zeta-potential. Churaevet al.13 have studied the zeta-potential of hydrophobic methylated quartz capillaries.They have shown that adding a surfactant which changes the wetting into hydro-philic, results in a decrease of the zeta-potential, which they attribute to the sup-pression of water slippage. From these measurements they deduce a slip length of�5–8 nm of water on the methylated quartz, but they have to assume that the surfacepotential is unchanged by the surfactant.

More recently Bouzigues et al. performed the first independent characterization ofsurface potential and electro-osmotic flow, and demonstrated an enhancement of100% of the Schmolukovski velocity in a hydrophobic capillary.21 They usea nano-PIV technique to study the velocity field close to the wall, and derive thesurface potential at the same location from the concentration profile of the colloidaltracors. Their data clearly show that the flow enhancement is due to wall slippage.However due to the finite resolution of the optical method, their study is restrictedto a single value of the EDL thickness, (x50 nm) and thus of the salt concentration.

In this work we present and discuss a comparative study of the surface potentialand the zeta potential of two type of surfaces in NaCl solutions: hydrophilic silicaand OTS-silanized hydrophobic glass. We use the colloidal probe Atomic ForceMicroscope (AFM) to measure directly the electrical potential of the surfacesfrom the electrostatic force at equilibrium, and we compare this surface potentialto the zeta potential measured by current monitoring. After a brief reminder ofthe relevant theoretical background in part 2, we describe our experimental proce-dure in part 3 and discuss our results in part 4. We show an enhancement of thezeta potential with respect to the surface potential on hydrophobic surfaces, whichis consistent with a constant slip length of 8 nm independent of the salt concent-ration in the range 10�4 to 10�3M, and in good agreement with the expected slippageof water as a function of the surface wettability.

2 Theoretical background

We recall here briefly the principles of electrokinetic transport at a charged liquid–solid interface and the calculation of the zeta-potential in the case of a partial slipflow boundary condition (b.c.). Without loss of generality we take the case of anelectro-osmotic flow induced by a stationary solid surface located at z ¼ 0 andwearing an electric charge s per unit area (see Fig. 1).

We begin with the Navier expression for the flow partial boundary condition atthe solid surface:

vs ¼ bvv

vzjz¼0 (1)

where vs is the slippage velocity of the solution onto the surface, z the distance to thesolid surface, v(z) the velocity profile and b the slip length (or Navier length). In theEDL, the solution is not electrically neutral and the charge density re(z) is related tothe electrostatic potential V(z) by Poisson’s law:

114 | Faraday Discuss., 2010, 146, 113–124 This journal is ª The Royal Society of Chemistry 2010

Fig. 1 Schematic view of the velocity profile vx(z) near a solid wall where a partial slip occurs,characterized by a slip length b. The electrostatic potential of the surface is VS. The zeta poten-tial z can be understood as the linearly extrapolated potential at the depth z ¼ �b.

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reðzÞ ¼ �3v2V

vz2

with 3 is the dielectric constant of the solution.If an external electric field ~E ¼ E~ex is applied parallel to the surface, a body force

~f ¼ re~E acts on the non-neutral fluid and induces a fluid flow obeying the Stokes

equation

hv2vðzÞ

vz2¼ �f ¼ 3E

v2V

vz2(2)

Far from the solid surface the derivative vV/vz vanishes, and the flow reachesa constant electro-osmotic velocity vos. Eqn (2) integrates as:

vðzÞ ¼ vos þ3E

h

�Vðx; zÞ � Vðx;NÞ

�(3)

The z-potential is defined from the electro-osmotic velocity by:

vos ¼ �3z

hE (4)

No-slip boundary condition: the flow velocity vanishes at the solid surface so that

vos ¼ �3E

h

�VsðxÞ � VNðxÞ

�¼ � 3E

hVs (5)

In this case the z-potential reduces to the surface potential. It is sometimes con-sidered that the no-slip b.c. should apply not exactly at the solid surface, but atthe top of the so-called Stern layer which contains the ions adsorbed at the interface.In this case one has also to consider that the surface potential measured in an AFMcolloidal probe experiment should be the potential at the top of this immobile liquidlayer, which is not removed when the surfaces come into close contact. Therefore theequality of the zeta and surface potential is expected on a smooth surface in the caseof a no-slip boundary condition.

Partial slip boundary condition: the flow velocity at the surface is derived from eqn(1) and (3):

vs ¼ b3E

h

vV

vz

!s

eqn (3) then gives the expression of the electro-osmotic velocity:

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vos ¼ �3E

hVs

"1� b

Vs

�vV

vz

�s

#(6)

The z potential is the linear extrapolation of the potential in solution at a depthb under the interface. This enhancement is due to the reduced friction at thesolid–liquid interface. The normal electric field at the solid surface is related to thesurface charge density by s ¼ �3(vV/vz)s. Thus the relative amplification of z-poten-tial due to slippage, (z � Vs)/Vs, is the ratio of the slip length b to the EDL charac-teristic thickness keff

�1:

z� Vs

Vs

¼ b

k�1eff

(7)

keff ¼ �1

V s

�vV

vz

�s

¼ s

3Vs

(8)

In the case of a small electrostatic potential (Vs < 25 mV), the thickness keff�1 reduces

to the Debye length k�1:22

k�1eff ¼ k�1 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3kBTPi nioZ2

i e2

s

with nio the number density of ions of type i and valence Zi in the reservoir solution.In the case of a monovalent electrolyte, the thickness keff

�1 is obtained from the non-linear Poisson–Boltzmann equation for all values of Vs:

23

k�1eff ¼ k�1 2eVs=kBT

sinhð2eVs=kBTÞ (9)

Therefore, if the b.c. does not change with the electrolyte concentration, the relativeamplification of the zeta-potential is expected to scale linearly with the inverse of theeffective Debye’s length.

3 Experimental

We perform independent measurements of the surface potential Vs and of thez-potential of two types of materials: hydrophilic silica, on which water flow obeysthe no-slip b.c.,9,24 and hydrophobic OTS-silanized glass surfaces, on which sub-stantial slippage is expected.9–11 For each of these materials the z-potential ismeasured in capillaries by a current monitoring method, and the surface potentialis measured by colloidal probe AFM on flat surfaces.

3.1 Materials

The following materials are used: silica planes (Suprasil 311, Heraeus, Germany),Pyrex planes (from Pignat, Lyon, France), silica capillaries (Polymicro Techno-logies) in 75 mm internal diameter.

The flat samples are washed with a detergent solution, rinsed with ultrapure water(Millipore, MilliQ, 18.2 MU.cm), and dried with a nitrogen flux. The capillaries areprepared in a similar way by pumping through them successively the detergent solu-tion, the ultrapure water, and clean air under a laminar flow hood. Silanizedmaterials are prepared from silica capillaries and Pyrex surfaces in a single silani-zation operation in order to ensure a similar surface coating for the differentsamples. An octadecyltrichlorosilane (OTS) solution is prepared from fresh OTS(Aldrich) used as received without further purification, and anhydrous toluene(Roth). The solution is prepared under a dry atmosphere (RH < 3%) by mixing

116 | Faraday Discuss., 2010, 146, 113–124 This journal is ª The Royal Society of Chemistry 2010

Fig. 2 Tapping mode topographies of the materials used in this work, from left to right: silicacapillary, Pyrex, silica, silanized silica and silanized Pyrex. The topographies of the inside of thecapillaries have been made thanks to transversal cuts done after the experiments.

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100 ml of OTS with 60 ml of toluene. It is stored in a bottle closed by a silicone capand cooled under 10 �C. One side of the capillaries is then introduced through thesilicone cap into the solution, while the other side is connected, also through a sili-cone sealing, to a vacuum bottle containing the Pyrex planes to be silanized in thesame operation. The OTS solution is then pumped through the capillaries byconnecting the bottle to a vacuum pump, until a significant amount of solutioncovers the flat samples. Thus the internal surface of the capillaries and the flatsamples are silanized with the same OTS solution, at the same temperature andhygrometry. The flat samples and the capillaries are then rinsed with chloroformin the same way.

The surface topography of the different samples is recorded by contact modeAFM (Asylum Research MFP-3D) and displayed in Fig. 2. The internal surfaceof the capillaries are imaged after sawing them at a 45� angle, which generatessome debris, therefore the topographies in Fig. 2 and the roughness in Table 1 arerestricted to small areas of 500 � 500 nm lying between the debris. The r.m.s. rough-ness of the plain materials, plane and capillary, are similar. The roughness of thesilanized materials is slightly higher and their topographic image is less homogenous,however there is no significant difference between the OTS-plane and the OTS-capillary.

The advancing and receding contact angle of water on the silianized plane aremeasured with the sessile drop method on several locations of the sample (seeFig. 3). The average contact angle is 98�. The hysteresis is large, about 25�, due tothe nanometre scale roughness and defects revealed on the topographic data.However this hysteresis does not vary significantly with the position tested, whichshows the overall homogeneity of the OTS-surfaces.

After elaboration and cleaning, all samples are stored under a laminar flux hood.They are immersed for a minimum time of 12 h in a NaCl solution prior to any z orsurface potential measurements. Both surface and z-potential values are measuredin 0.1 mM to 1 mM NaCl solutions without buffer, at pH ¼ 5.8 resultingfrom the spontaneous dissolution of carbon dioxide of the atmosphere in thesolutions.

Table 1 Surface roughness of the materials: plain capillary, silanized capillary, plain silica and

silanized Pyrex

Silica capillary Silica plane Silanized capillary Silanized pyrex

Area/mm2 0.5 � 0.5 5 � 5 0.5 � 0.5 0.5 � 0.5

rms/nm 0.3 0.5 2.2 1.4

pk–pk 1.2 3.8 11.6 5.0

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Fig. 3 Advancing (qa) and receding (qr) contact angle of water on the OTS-Pyrex measured indifferent points of the surface. Dashed lines are the mean values.

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3.2 Zeta potential measurements

The current monitoring set-up25 used for zeta potential measurements is shown sche-matically on Fig. 4. Two reservoirs of slightly different NaCl concentrations (about10%) are connected by the studied capillary, previously filled with the solution ofreservoir no1. At time t¼ 0 a high voltage difference DV¼ 1500 V is applied betweenthe reservoirs through platinum electrodes so as to create an electro-osmotic flowfrom reservoir no2 to reservoir no1. The electrical current is recorded as a functionof time and increases linearly as the solution no1 is replaced by solution no2

Fig. 4 Top: schematic description of the current monitoring set-up for the zeta potentialmeasurements. Bottom: Typical current intensity as a function of time.

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(Fig. 4). The solutions do not mix due to the very flat velocity profile of the electro-osmotic flow. At time Dt the capillary is completely filled by solution no2 and thecurrent stabilizes to a constant value. The process is reversed by changing the voltagesign, and cycles are performed. The z-potential is obtained from the electro-osmoticvelocity vos¼ L/Dt, with L the length of the capillary, and the amplitude E¼ DV/L ofthe applied electric field, using eqn (4).

3.3 Surface potential measurements

The electrostatic forces between the flat materials and a sphere in solution aremeasured directly with colloidal probe AFM.26 The surface potential can in principlebe determined from such force curves, but the reliability of the measurementsdepends strongly on the characterization of the colloidal probe in terms of its rough-ness, physico-chemistry, cantilever stiffness, and surface potential. For this reasonwe have built a robust protocol27 which allows accurate measurements of the surfacepotential of flat substrates in a dissymmetric configuration. The colloidal probe usedis a borosilicate sphere from Duke Scientific, cleaned and glued to a micro-cantileverwith a procedure which removes efficiently contamination, and presenting a very lowroughness of less than 1 nm r.m.s. on a 5 mm � 5 mm area of the flattened spheretopography. The cantilever stiffness is measured with 3% accuracy with twoindependent methods.

Fig. 5 Top: AFM topography of the borosilicate colloidal probe used in this study. Theparticle radius is 8.7 mm. Bottom: force curves measured between the borosilicate probe andthe Pyrex substrate, in logarithmic scale, for four different NaCl concentrations. Black curvesare fits with the DLVO theory where the non-linear Poisson–Boltzmann equation is solvedwith a constant charge density condition and with a Hamaker constant fixed to the value of1. � 10�20 J.

This journal is ª The Royal Society of Chemistry 2010 Faraday Discuss., 2010, 146, 113–124 | 119

Table 2 Charge density s and surface potential Vs of the colloidal probe issued from AFM

force measurements between the borosilicate probe and a flat Pyrex substrate in NaCl solutions

of various concentration. The targeted concentrations c0 vary from 0.1 mM to 1.0 mM. The

actual salt concentrations measured from the force curves are noted c0r. The values of pC ¼

�log(c0r) and of the Debye length k�1 are mentioned as well

c0 (mM) 0.10 0.20 0.30 0.50 1.00

|s| (mC/m2) 0.79 1.06 1.12 1.27 1.72

|Vs| (mV) 27.3 31.0 26.9 23.4 22.0

k�1 (nm) 24.9 21.5 17.3 13.2 9.1

c0r (mM) 0.14 0.20 0.31 0.52 1.12

pC 3.83 3.70 3.511 3.28 2.95

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The surface potential of the colloidal probe is calibrated by performing AFMforce measurements on a flat Pyrex sample of the same composition as the probe.It is determined by adjusting the curve forces to the Deryaguin–Landau–Verwey–Overbeek (DLVO) theory as explained in the Appendix. Two quantities areadjusted: the Debye length k�1 and the common value Vp of the probe/Pyrex surfacepotential, so that the actual ion content of the solution is checked. The adjusted forcecurves obtained for different NaCl concentration are shown in Fig. 5 and the cali-brated probe potentials are summarized in Table 2.

Once the probe is calibrated, the surface potential of the samples studied is deter-mined by adjusting the force curves measured in each solution with two adjustableparameters, the sample surface potential and the Debye length. The probe potentialis interpolated from the calibration curve to its expected value at the electrolyteconcentration corresponding to the Debye length found, and kept fixed.

4 Results and discussion

The values found for the surface potential and the z-potential of plain silica arereported on Fig. 6 as a function of pCo ¼ �log[NaCl]. They are compared to otherz-potentials and AFM-measured surface potentials of silica at the same pH, from theliterature. A general agreement is found with the previously reported values of thez-potential28–30 as well as the surface potential of silica measured by colloidal probeAFM.26 We find that the z-potential of silica is similar to its surface potential, withinthe resolution of our determination of those quantities, which is also in good

Fig. 6 Comparison of our surface potential (pink circles C) and zeta potential (blue triangles:) of plain silica, as a function of pC. These values are compared as well with others from theliterature (grey symbols): 5 Weiss, pH 6.0, NaCl; > Ducker, pH 5.7, NaCl; @ Scales pH 5.8,KCl; � Gaudin, pH 7, NaCl; * Giesbers, pH 6.0, NaCl.

120 | Faraday Discuss., 2010, 146, 113–124 This journal is ª The Royal Society of Chemistry 2010

Fig. 7 Force curves obtained on plain silica and on OTS-silanized Pyrex at 0.5 mM NaClconcentration. The repulsive force shows the negative charge of the OTS surface.

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agreement with the previous results. This behaviour is coherent with a no-slip b.c.applied on, or very close to the solid surface, as expected on hydrophilic silica.This result supports the validity of classical hydrodynamics with a b.c. applied onthe solid surface, to account for water flow and electrokinetic transport inside theEDL.

In contrast the results on silanized surfaces show a negative z-potential whoseamplitude is substantially higher than the negative surface potential (see Fig. 7).

Early experiments have indeed shown that interfaces between water and hydro-phobic materials, such as liquid alkanes/water interfaces,31,32 or self-assembled-monolayers made of alkane-chains in water,33,34 are negatively charged. The negative

Fig. 8 (a) Surface potential of OTS-silanized Pyrex (orange circles) and zeta potential of silan-ized silica (blue diamonds) as a function of pC ¼ �log([NaCl]). (b) Relative difference betweenthe zeta potential and the surface potential of the OTS-coated surfaces as a function of the in-verse of the effective Debye length. The linear fit corresponds to a slip length b ¼ 7.3 � 0.8 nm.

This journal is ª The Royal Society of Chemistry 2010 Faraday Discuss., 2010, 146, 113–124 | 121

Fig. 9 Slip length of water on various surfaces as a function of their wettability, from [18]. Thearrow shows the value derived from the comparison between the z-potential and the surfacepotential of our OTS surfaces.

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charge is attributed to the preferential adsorption of hydroxide ions (OH�) relativeto hydronium ions (H3O+). Theoretically, the preferential adsorption of OH� ionson n-alkane SAMs has been supported by density functional (DFT) simulations35

with surface charges as large as �10�2 C m�2, and molecular dynamics simulationshave shown that Cl� ions are also likely to adsorb at hydrocarbon/water interfaceswhereas Na+ are repelled from it.36 Recent experiments of Tian et al.37 using sum-frequency-vibrational-spectroscopy on OTS/water interface, evidence clearly thepreferential adsorption of OH� ions as well as other negatively charged ions suchas Cl�. In view of these recent works we conclude that the origin of negative chargein our silanized samples lies at the OTS/water interface, and that the difference in thegrafting substrate, Pyrex or silica, does not play a significant role on the chargedensity.

We can then compare the z-potential to the enhancement provided by a partialslip b.c. Fig. 8 plots the relative difference (z � Vs)/Vs as a function of the effec-tive Debye length keff

�1 evaluated from eqn (9). The relative enhancementincreases with keff, that is when the thickness of the Debye layer decreases,although the absolute value of the z- and the surface potential also decrease.This supports the idea that the enhancement is due to a friction reduction effect.The best linear fit corresponds to a slip length b ¼ 7.3 � 0.8 nm. The magnitudeof this slip length is in very good agreement with the slippage expected for theseOTS-surfaces wettability, taking into account their nanometric roughness, as illu-strated in Fig. 9.

5 Conclusion

This work extends the previous results of Churaev et al.13 and Bouzigues et al.21

showing the enhancement of electrokinetic transport due to the finite slippage ofwater on a hydrophobic solid surface. We show by independent measurements ofthe z-potential and the electrostatic surface potential of OTS-coated surfaces thatthis enhancement is well described by a constant slip length of nanometric ampli-tude, for a range of electrolyte concentration. The enhancement reaches values of100% and more at a mM concentration in NaCl, when the slip length becomes largerthan the thickness of the Debye layer.

Our approach opens the way to a systematic investigation of the electrostaticand electrokinetic properties of hydrophobic surfaces in solution, and the searchof highly slippery and charged surfaces to increase electro-osmotic effects andthe efficiency of micro- and nanodevices using them. Work is under progress tostudy the effect of ion specificity on the electrokinetic properties of hydrophobicsurfaces.

122 | Faraday Discuss., 2010, 146, 113–124 This journal is ª The Royal Society of Chemistry 2010

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Appendix

The surface potentials are determined from fitting the experimental force curves toDLVO forces calculated using the Derjaguin approximation and the disjunctionpressure acting between two parallel surfaces separated by a distance D [23]:

FðDÞ ¼ 2pR3ðkBTkÞ2

e2ðcosh jm � 1Þ � AR

6D(10)

where A is the silica–water–silica Hamaker constant (kept fixed to the value

1.10�20J), k ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2noe2=3k

BT

qis the inverse of the Debye length for the number

density no of the monovalent electrolyte, and jm is related to the normalized surfacepotentials j1 ¼ eVs1/kBT and j2 ¼ eVs2/kBT by the elliptic integral:

kD ¼Ð j1

jm

djffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2cosh j�2cosh jm

p þÐ j2

jm

djffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2cosh j�2cosh jm

p

The calculation of the electrostatic force is directly implemented on the Igor Prosoftware of the MFP-3D AFM. The DLVO forces are calculated for each valueof the distance D at constant surface charge on each surface

si ¼3kBT

ek�1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2cosh js;i � 2cosh jm

qThe fitting is done by adjusting two parameters: the Debye length k�1 and thevalue of the unknown surface charge (in dissymmetric configurations). The surfacepotential of the isolated surface in solution is then obtained from the Grahameequation:22

V s ¼2kBT

eArg sh

�esk�1

23kBT

�

Acknowledgements

This work has been supported by the Region Rhone-Alpes and by the program Syn-odos of the ANR-PNano.

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