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Electrolytes at interfaces: accessing the first nanometersusing X-ray standing waves

Soumaya Ben Jabrallah, Florent Malloggi, Luc Belloni, Luc Girard, DmitriNovikov, Cristian Mocuta, Dominique Thiaudière, Jean Daillant

To cite this version:Soumaya Ben Jabrallah, Florent Malloggi, Luc Belloni, Luc Girard, Dmitri Novikov, et al.. Elec-trolytes at interfaces: accessing the first nanometers using X-ray standing waves. Physical ChemistryChemical Physics, Royal Society of Chemistry, 2016, 19, pp.167 - 174. 10.1039/c6cp06888j. cea-01422226

Electrolytes at Interfaces: Accessing the First

Nanometers Using X-ray Standing Waves

Soumaya ben Jabrallah,† Florent Malloggi,∗,† Luc Belloni,† Luc Girard,‡ Dmitri

Novikov,¶ Cristian Mocuta,§ Dominique Thiaudière,§ and Jean Daillant§

†LIONS, NIMBE, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif surYvette Cedex

‡ICSM UMR 5257 - CEA / CNRS / UM / ENSCM, Site de Marcoule, Bâtiment 426 BP17171 F-30207 Bagnols sur Cèze Cedex

¶Deutsches Elektronensynchrotron DESY, Notkestrasse 85, D-22607 Hamburg, Germany§Synchrotron SOLEIL, L'Orme des Merisiers, Saint-Aubin, BP 48, F-91192 Gif-sur-Yvette

Cedex, France

E-mail: orent.malloggi@cea.fr

Abstract

Ion-surface interactions are of high practical im-portance in a wide range of technological, envi-ronmental and biological problems. In partic-ular, they ultimately control the electric dou-ble layer structure, hence the interaction be-tween particles in aqueous solutions. Despitenumerous achievements, progress in their un-derstanding is still limited by the lack of ex-perimental determination of the surface com-position with appropriate resolution. Tacklingthis challenge, we have developed a methodbased on X-ray standing waves coupled to nano-connment which allows the determination ofion concentrations at a solid-solution interfacewith a sub-nm resolution. We have investigatedmixtures of KCl/CsCl and KCl/KI in 0.1mMto 10mM concentrations on silica surfaces andobtained quantitative information on the par-tition of ions between bulk and Stern layer aswell as their distribution in the Stern layer. Re-garding partition of potassium ions, our resultsare in agreement with a recent AFM study. Weshow that in a mixture of KCl and KI, chlorideions exhibit a higher surface propensity than io-dide ions, having a higher concentration withinthe Stern layer and being on average closer to

the surface by ≈ 1-2 Å, in contrast to the so-lution water interface. Confronting such datawith molecular simulations will lead to a preciseunderstanding of ionic distributions at aqueousinterfaces.

Introduction

The interfacial behavior of ions is of key im-portance in a number of phenomena and pro-cesses ranging from biological systems to micro-and nanouidics. Ion-surface interactions areimportant both in a direct way, e.g. in sorp-tion or ion exchange related eects, or indirectlybecause modifying the eective surface chargethey will aect the structure of the electric dou-ble layer, hence the interaction between chargedparticles in aqueous solutions.1 In this context,particularly interesting are the so-called spe-cic eects, referring to phenomena where ionsof the same valency have a dierent eect.24

These eects resulting from a subtle balancebetween polarisabilty, hydration and interfacialwater structure usually follow Hofmeister se-ries (SCN− > ClO−4 ≈ I− > Br− > Cl− >F− for anions) in direct or reverse order.46

They have a major eect on as diverse phe-

1

liquid heightb)

multilayers membrane

Si

Si

Si

SiO2

W

W

Figure 1: (a) Schematics of the standing wave experiment. Incident (wave vector kin) and reected(wave vector kr) X-ray waves interfere to create a standing wave eld perpendicular to the interface.The species (sketched by blue dots) present in the XSW eld are excited and emit secondaryuorescence photons for absorption edges below the incident beam energy. (b) Schematics ofthe experimental cell. The liquid layer is conned between the multilayer and a exible X-raytransparent membrane.

nomena as colloidal stability,2 protein stabil-ity3 or the surface tension of electrolytes.7 Inenvironmental sciences, the interaction betweenions, humics and minerals inuences the mobil-ity and availability of pollutants.8 The interfa-cial behavior of ions is also of key importance inmicro- and nanouidics.9 Phenomena occurringwithin the diuse Gouy-Chapman layer indeedbecome dominant in determining ow prop-erties as channel size, Debye length and sliplength become on the same order of magnitude,leading to unusual phenomena.10 For example,with charged walls, channels can be lled witha unipolar solution of counter-ions, suggestingthat the type and concentration of ions can becontrolled by the surface charge density of thechannel wall.11 12 In addition, "specic eects"could allow for even ner control over the iontype as specic adsorption will eventually de-termine the double layer structure.13

Determining the interfacial distribution ofions with sucient accuracy is, however, a chal-lenge. Indeed, the ionic concentration devi-ates from the bulk concentration only in theStern layer and diuse Gouy-Chapman layer:from 1nm to 100nm depending on the solutionconcentration. Several surface sensitive tech-niques like photoemission,1417 sum-frequencygeneration (SFG), second-harmonic generation(SHG),18,19 X-ray uorescence7 or X-ray re-

ectivity20,21 have been used. More recentlyAtomic Force Microscopy has also been used todirectly probe the electrical double layer.2224

However, SFG and SHG have surface sensitiv-ity but are not directly sensitive to ions andlack depth resolution, X-ray reectivity or neu-tron reectivity have no direct element sensitiv-ity. Though photoemission has recently beenextended to determine surface potential at thecolloid/electrolyte interface,16 it has no directsensitivity to the ion distribution. In this study,we used the X-ray standing waves (XSW) tech-nique which has the advantage of having bothelement and depth sensitivity to probe the rstnanometers at the solid surface. The techniquerst developed to locate atoms in crystals oradsorbed at crystal surfaces25 has also beenapplied to soft condensed matter.26 It has inparticular been used to investigate the adsorp-tion of heavy ions on crystal surfaces from so-lutions.27,28 We show here that the method canbe extended to light ions (down to chlorine orsulfur) on surfaces like silica which are of verybroad interest in colloidal science.

2

Experimental

The x-ray standing wave technique.

The X-ray standing waves (XSW) technique isbased upon creating an electromagnetic stand-ing wave eld by interference between incidentand Bragg reected X-rays (Fig 1a).29 Thestanding wave phase depends on the deviationfrom the exact Bragg angle and can be variedin a controlled way, thus moving the X-ray eldnodes in a range spanning half of the diractionplane spacing. The variation of secondary uo-rescence signal coming from the atoms, that getexcited by this XSW eld, can be then used tolocate the atom positions with (sub)Angstromresolution. The method allows one to simulta-neously investigate positions of dierent atoms,monitoring their specic emission lines. Thestanding waves are present where the incidentand diracted waves overlap, which includesthe solid/liquid interface and the bulk solu-tion above. A specic XSW variant especiallysuited for investigation of liquid/solid interfacesemploys XSW generators, based on articiallygrown multilayer structures (ML). Another ad-vantage of this approach is the possibility totune the resolution by changing the diractingplane spacing as well as the large choice of MLmaterials. In particular it would be possible toapply an external bias by embedding a conduct-ing layer in the ML. The ML-generated XSWwere used for instance for investigation of Zn2+

distribution above a charged lipid layer27 andin studies of electrochemical deposition of io-dine on Pt.30

In order to calculate the uorescence inten-sity, the sample is divided in as many layers jas necessary to describe the elemental distribu-tion. We choose the layers to be thin enough forthe local density of element k in layer j ρk,j(z)to be constant. The uorescence intensity forelement k at grazing angle of incidence θ is thengiven by:

Ik(θ) = Bk

s∑j=0

∫ hj

hj+1

ρk,j(z)Tk,j(z) | Ej(z) |2 dz,

(1)where the constant Bk depends on the uores-

cence yield, detection eciency and geometri-cal factors. Ej(z) is the electric eld in layerj which is calculated in each layer using thematrix method.31 Tk,j(z) is the transmission ofthe uorescence intensity emitted by element kfrom layer j to the detector. As we are look-ing for nanometric layers close to the substrate,Tk,j(z) is in fact independent of j. With thisapproximation,

Ik(θ) = BkTk∑j

∫ hj

hj+1

| Ej(z) |2 dz. (2)

Writing for a plane wave

Ej(x, z) = (A+j e

ikz,jz + A−j e−ikz,jz)e+i(ωt−kx,jx),

(3)where the A±j coecients are determined usingthe matrix method following31 and integratingover layer j, one simply has:∫ hj

hj+1

| Ej(z) |2 dz =|A+

j |22kiz

[1− exp(−2kizδh)]

+|A−j |22kiz

[exp(2kizδh)− 1]

+|A+

j∗A−j |

2ikrz[1− exp(−2ikrzδh)]

+|A+

j A−j∗|

2ikrz[exp(2ikrzδh)− 1].(4)

with δh = hj − hj+1.Though this method is accurate, it does not al-low one to develop an intuition of the expectedshape of the standing wave curve. For a mono-layer located at z, one would have

I(θ, z) = 1 +R(θ) + 2√R(θ) cos(2πz/λ− φ(θ))

(5)where R(θ) is the intensity of the reected beamand φ(θ) is the phase between the incident andreected beam which varies from π to 0 acrossthe Bragg peak. Eq. (5) can help comparingdierent X-ray standing wave curves, even inslightly more complex cases. This is illustratedin Fig. 2 where we have represented the calcu-lated uorescence from a hypothetical 2Å thicklayer of ions adsorbed from a 1µm thick lmof solution. The uorescence intensity is rep-

3

resented for dierent locations of the surfacelayer above the interface when this thin layercontains as many ions as the solution (50% oftotal number of ions), or only 5% of the totalnumber of ions.Obviously, the sensitivity is very high for the

50% case. However the dierent location canstill be distinguished in a t with good qualitydata in the 5% case as the shape of the curve isstill signicantly dierent.

20 A18 A

16 A14 A

12 A10 A

I[a

.u.]

2.22.122.0 x 10− 9

1.8 x 10− 9

1.6 x 10− 9

1.4 x 10− 9

1.2 x 10− 9

1.0 x 10− 9

20 A18 A

16 A14 A

12 A10 A

I[a

.u.]

2.22.12

3.5 x 10− 9

3.0 x 10− 9

2.5 x 10− 9

2.0 x 10− 9

1.5 x 10− 9

1.0 x 10− 9

2A°

Z

50%

5%

Grazing angle of incidence [degree]

Grazing angle of incidence [degree]

Figure 2: Calculated uorescence curves for a2Å thick layer in a 1µm liquid lm. In the bot-tom curves, the layer contains as many ions asthe rest of the lm, and only 5% in the topcurves. The layer is positioned at 10Å, 12Å,14Å, 16Å, 18Å and 20Å above the referenceplane. In the experiments, there is a top sil-ica layer in between the reference plane and thelayer and the interface is located ≈ 10-15 Åabove the reference plane marked by a Cr layerin the experiments.

Experimental methods.

X-ray standing-wave measurements were per-formed at the DiAbs beamline of SynchrotronSOLEIL, Saint-Aubin, France. A schematic ofthe methods used to probe ions at interfacesas well as the setup used at the DiAbs beam-line are shown on Fig. 1. The samples con-sisted in an ultra thin liquid layer sandwichedbetween the multilayer substrate used to createthe standing waves and a 4µm thick ultralene R©X-ray transparent window (Fig. 1b). The ex-periments were performed using a 7 keV inci-dent beam energy with a small parallel beam(250µm× 200µm) allowing to resolve the Braggpeaks.The substrates used in these experiments

were Si-W multilayers (150 periods of 2.5nm)manufactured by AXO (Dresden, Germany).They include a thin (< 0.5nm) Cr layer belowthe top SiO2 to serve as a reference for thephase. Substrates were cleaned following theRCA cleaning procedure33 before being used.KCl, CsCl, CsI (Sigma-Aldrich, 99.9995% pu-rity) and KI (Sigma-Aldrich, 99.999% purity)were used without further purication. Molarstock solutions were prepared using water froma Millipore Milli-Q R© system (18.2 MΩ.cm re-sistivity) and further diluted and mixed justbefore the experiments. Small volumes of so-lution ranging from 250nl to 1.5µl were intro-duced in the cell. The multilayer was thenpressed against the cover ultralene R© lm al-lowing for the control of the sample thickness(Fig. 1b). All manipulations were performedin a clean room to avoid dust contamination.

Results

Both reectivity curves for sample characteriza-tion and uorescence curves around the Braggpeak were recorded for each sample. The fullanalysis of the results rst requires the deter-mination of the liquid layer thickness by X-ray reectivity. The uorescence of each ionas a function of the grazing angle of incidencearound the Bragg peak (standing wave curve)is then determined by tting the uorescence

4

spectrum for each angle of incidence, and eachstanding wave curve is nally analysed to ob-tain the ionic distribution proles. Bare sub-strates and empty samples with Ultralene win-dow were rst measured as a reference for back-ground subtraction.

200 nm4.7 µm

Empty Cell

qz [A− 1]

Refectivity

0.40.350.30.250.20.150.10.050

100

10− 1

10− 2

10− 3

10− 4

10− 5

10− 6

Figure 3: Measured X-ray reectivity and bestt for an empty cell (no liquid), a 4.7µm and a200nm liquid layer thickness.

Sample thickness determination

using X-ray reectivity.

Reectivity curves were recorded using a scin-tillator detector and carefully normalized tothe incident beam intensity. They were an-alyzed using the Reec software (A.Gibaud,G.Vignaud) based on the matrix method.31

We used a model consisting of the multilayersubstrate, a solution layer and the 4µm thickUltralene R© lm which was tted to the data,allowing to determine the thickness of the liq-uid layer. Obtaining good ts is important inorder to constrain the standing waves analysis.Fig. 3 shows experimental reectivity curves(as measured, without any corrections) as wellas the corresponding ts before and after solu-

tion injection. The tting procedure includes il-luminated area and water layer absorption cor-rections. In order to determine the thicknessfrom the t of reectivity curves, the emptycell curves were tted rst. A solution layerwas then added to the model without allow-ing any change in the multilayer parameters.The change in refractive index when a liquidlayer is present modies the shape of the curvein the qz ≈ 0.1Å

−1region i.e. in between the

critical angle for total external reection at thesubstrate-solution interface and the Bragg peak(Fig. 3). Though the solution layer is generallyeither too thick or not homogeneous enough togive rise to fringes that could be resolved in thereectivity curves, its thickness can neverthe-less be determined from the shape of the re-ectivity curve in the region below and closeto the critical angle (qz ∼ 0.05Å

−1in Fig. 3).

For a very thick layer, the intensity at the crit-ical angle can indeed be reduced by more thanone order of magnitude compared to the emptycell because the incident and reected X-rayswill have to travel hundreds of microns in theabsorbing solution for grazing angles of inci-dence in the mrad range, even for a liquid layerthickness < 1µm. One should also notice thatthe thickness we determine is an average overthe approximately 8 mm long and 250µm widebeam footprint on the sample.

X-ray uorescence measurements

and analysis.

Fluorescence curves were recorded using a 4-element energy sensitive detector and rst ac-curately normalized to the incident beam in-tensity. The uorescence curves were analyzedfollowing the procedure detailed in Ref.7 usinga home made software with a peak model basedon the physics of detection, including a Voigtianpeak shape, a tail and a shelf.34 The dierentpeak parameters have a simple energy depen-dence, thus reducing the number of tting pa-rameters. Another advantage of this methodis that the background from photon countingbeing built up by the shelf contributions, it isautomatically and consistently subtracted. In

5

Sample 2.1 deg.Sample 1.95 deg.

Empty Cell 2.1 deg.Empty Cell 1.95 deg.

Fluorescence Energy (eV)

Inte

nsity

5000450040003500300025002000

10− 6

10− 7

10− 8

ClαK

ArαK

KαK

CaαK Ca

βK

IβL

IαL

Figure 4: Fluorescence intensity (experi-ments:symbols - ts:solid lines) recorded at1.95 and 2.1 (Bragg peak) from an empty celland a 250nm thick cell lled with a 10mM KCl+ 10mM KI solution.

order to determine the interfacial contributionof ions only, we also need to subtract the con-tribution of elements present in the sample cell,mainly chlorine in the multilayer substrate andcalcium in the ultralene lm. This is done bymanually subtracting the reference sample con-tribution, yielding standing wave curves for theinterface and solution only.Representative spectra are given on Fig. 4

for a mixture of 10mM solutions of KCl andKI. The Cl Kα line at 2622 eV, the Ar Kα lineat 2957 eV (Ar is present in air), the K Kα lineat 3313 eV, the Ca Kα and Kβ lines at 3690 eVand 4014 eV (Ca is an impurity in the Ultra-lene lm, not aecting the measurements) andthe I Lα line at 3938 eV and Lβ line at 4220eV can in particular be identied on Fig. 4.An advantage of uorescence based methods istheir high sensitivity to chemical elements inlow quantities (traces). Samples with minuteconcentration (10−4M) or very thin liquid lay-ers (a few 10s of nms) could in particular bestudied. Integrated over the beam footprint fora 100nm thick sample, the technique allows toresolve 1 femtomole or better.

The dierences in the curves recorded at agrazing angle of incidence of 0.25 below theBragg peak (1.95) and at the Bragg peak (graz-ing angle of incidence of 2.10) in Fig. 4 directlyresult from the interfacial distribution of ions.Indeed, shifting the standing wave eld distri-bution, dierent positions above the interfaceare probed as shown in Fig. 2. This is howevermore clearly seen by representing the uores-cence for each chemical element as a function ofthe grazing angle of incidence around the Braggpeak (standing wave curves).

Standing wave curves.

Typical standing wave curves (uorescence in-tensity for each element as a function of thegrazing angle of incidence across the Braggpeak) are given on Fig. 5.Standing wave curves for the thicker sample

(2.85 µm) have a prole which resembles theBragg peak one. This is expected as thesecurves are dominated by the homogeneous ionicdistribution in the bulk liquid (Fig. 2). Ne-glecting uorescence eects close to the inter-face for a thick solution layer, the uorescencewill be excited by the incident and reectedbeam and will be roughly proportional to theincident beam plus reected beam intensitywhich is peaked at the Bragg angle. Dierenceswith respect to this shape give access to surfaceeects which can be determined and are moreprominent for thinner samples (like the 250nmthick sample) also shown in Fig. 5. In such acase, the position and the shape of the standingwave curve is already indicative of the positionof the ions with respect to the multilayer whichis therefore unambiguously determined.As mentionned above, we analyzed the stand-

ing wave curves using a very simple model con-sisting only of a homogeneous bulk solution anda Stern layer modelled as a stack of 2Å thickionic layers, one for each ion. The sample is di-vided in as many layers as necessary to describethe elemental distribution and the electromag-netic eld is calculated in each layer using thematrix method.31 Fitting the model (Eq. (5))to the experimental curve by minimizing theχ2 function, one obtains the composition, con-

6

BraggS2 - IS2 - KS2 - ClS1 - CsS1 - KS1 - Cl

Grazing Angle of Incidence [degree]I/

I 0

Inte

nsity

0.5

0.4

0.3

0.2

0.1

2.22.152.12.052

10−4

10−5

10−6

10−7

Figure 5: Standing wave curves (experi-ments:symbols - ts:solid lines) for a mixture of1mM solutions of KCl and CsCl (S1) and 10mMsolutions of KCl and KI (S2). Liquid layer sam-ple thickness was 2.85 µm for (S1) and 250nmfor (S2) respectively. Curves have been shiftedfor clarity. The Bragg peak is shown in red asreference. See Table 1 in Supporting Informa-tion for tting parameters.

centration and average position of the dierentions in the Stern layer.In order to get a rst check of the consistencyof the analysis, we have plotted on Fig. 6 (top)the normalized uorescence intensity (i.e. u-orescence is normalized such as any single ionwould give the same uorescence intensity, thisis equivalent to dividing the experimental uo-rescence by BkTk in Eq. (5)) as a function of theproduct concentration times thickness, whichgives the expected number of ions in the cell.As can be seen in Fig. 6 (top), there is goodcorrelation between uorescence intensity andthe expected number of ions: in other wordsuorescence nicely follows the total number ofions. This result shows that both the uores-cence measurements, including the backgroundsubtraction procedure for chloride, and thick-

ness determination using reectivity curves giveconsistent results.

Thickness × Concentration

Nor

mal

ized

Inte

nsity

65432104.108

4.108

3.108

2.108

2.108

2.108

1.108

5.107

0

I in KCl +KIK in KCl +KICl in KCl +KI

Cs in KCl+CsClK in KCl+CsClCl in KCl+CsCl

Thickness × Concentration

Ste

rn/

Bul

k

1010.10.01

1

0.1

Figure 6: Top: Normalized uorescence of allions as a function of the sample thickness timessolution concentration. Bottom: Ratio of thenumber of ions in the Stern layer to the num-ber of ions in the bulk as a function of productthickness × concentration.

Discussion

Gouy-Chapman-Stern model.

The simplest model used to calculate the dis-tribution of ions at interfaces is the Gouy-Chapman-Stern model.1,35 The electric poten-tial φ in the double layer obeys the Poissonequation:

d2φ

dz2= − ρ

ε0εr. (6)

In Eq. (6), ρ =∑

i niezi is the charge density,with ni the concentration of the ion i of valencyzi. e = 1.602×10−19C is the elementary charge,ε0 = 8.85×10−12F/m is the vacuum permittiv-ity and εr the relative permittivity. Concen-trations in the double layer obey a Boltzmanndistribution:

ni = ni∞ exp

(−zieφkBT

), (7)

7

with kB the Boltzmann constant and T the tem-perature. Insertion of Eq.(7) into Eq.(6) givesafter simple integration the Poisson-Boltzmannequation for the potential:(dφ

dz

)2

=2kBT

ε0εr

∑i

ni∞

[exp

(−zieφkBT

)− 1

].

(8)The charge in the double layer can be written:

σDL =

∫ ∞d

ρ(z)dz = −∫ ∞d

ε0εrd2φ

dz2= −ε0εr

dφ

dz

∣∣∣∣∞d

,

(9)where d is the location of the outer Helmholtzplane which xes the border between the Sternlayer and the diuse layer (Fig. 7).

−Si0

−Si0

−Si0

−Si0

−Si0

−Si0

−Si0

−Si0

+H

+H

+H

+K

+H

+H

+K

+K

+H

+K

−Cl

−Cl

−Cl

+K

+K

−Cl

z=dz=0

Figure 7: Schematics of the Stern layer and thedouble layer. z=d is the location of the outerHelmholtz plane.

By inserting Eq. (8) in Eq. (9), one obtains.

σ2DL = 2kBTε0εr

∑i

zini∞

[exp

(−zieφ(d)

kBT

)− 1

],

(10)known as the Grahame equation, which relatesthe charge in the electric double layer σ2

DL tothe potential at the outer Helmholtz plane φ(d).On the other hand, the composition of the Sternlayer is determined by surface equilibria, relatedto the dissociation of surface silanol groups forour silica surface. For protons and a monova-

lent salt with cation Me+, one would have:

ΓSiO− [H+]z=0 = ΓSiO− [H+] exp

(−eφ(0)

kBT

)= KHΓSiOH , (11)

and

ΓSiO− [Me+]z=d = ΓSiO− [Me+] exp

(−eφ(d)

kBT

)= KMe+ΓSiOC , (12)

where the concentrations involving silanolgroups ΓSiOH , ΓSiO− and ΓSiOC are surfaceconcentrations and it has been made explicitthat H+ ions are located at height 0 and Me+

cations at height d. KH and KMe+ are equi-librium constants. The total density of surfacesites is

Γ = ΓSiO− + ΓSiOH + ΓSiOC . (13)

The potential dependance in the Stern layer canbe obtained by considering the Stern layer as amolecular condenser of capacitance CStern wherethe potential drop is linear:

φ(d)− φ(0) = σ0/CStern. (14)

We now have a full set of equations Eqs. (10)-(14) which can be solved numerically to deter-mine all surface and bulk concentrations.A bare surface density of sites Γ = 8 SiO− sites/nm2 (reduced by protonation and ion com-plexation, Eq. (13)), a capacitance of the Sternlayer CStern ≈ 2.9F/m2 and KH = 10−7.5−10−7

are well established in the literature.36 Thecomplexation constants for cations are less doc-umented. Davis et al.37 report a much weakerspecic adsorption for SiO2 than for the otheroxides, with pKK ≈ 0.5. Sonnefeld38 suggestsan even weaker binding. On the contrary, Taoet al.39 and Zhao et al.24 give pKK = 1 and pKK

= 2 respectively, and the results of Dishon etal.22 are consistent with even larger values (seeFig. 8 bottom).

8

This workpKK = 3pKK = 2pKK = 1

ΓSiOK

3

2.5

2

1.5

1

0.5

0

SiretanuDishonpKK = 3pKK = 2pKK = 1

Concentration [mM]

e−/nm2

1001010.1

0

− 0.02

− 0.04

− 0.06

− 0.08

− 0.1

Figure 8: Top: ΓSiOK as measured in this workand calculated using the Gouy-Chapman-Sternmodel as explained above with pKK=2. Bot-tom: Surface charge calculated using the samemodel with pKK=1,2 and 3 together with mea-surements from Dishon et al.22 and Siretanu etal.,23 showing the consistency with our results.

Partition between Stern layer and

solution.

In contrast to the previous estimates of pKK ,our measurements provide a direct access tosurface concentrations. We nd Potassiumsurface concentrations in the Stern layer of0.14/nm2, 0.3/nm2 and 1.5/nm2 for 0.1mM,1mM and 10mM KCl / KI mixtures respec-tively. As an indication, a 1/nm2 surface con-centration would correspond for a 2Å thicklayer to a concentration of 3mol/l.These results can be compared to the Gouy-Chapman-Stern model presented above in or-der to check whether they are in the expectedrange. With pKK = 2, we obtain ΓSiOK ≈0.13/nm2 for a 0.1mM solution of KCl at pH=7,ΓSiOK ≈ 0.5/nm2 for a 1mM solution andΓSiOK ≈ 1.13/nm2 for a 10mM solution, infairly good agreement with our experimental re-sults (Fig. 8 (top)). As shown on Fig. 8 (top),the agreement is less good with pKK=1 for the

10mM solution and signicantly less good forall concentrations with pKK=3.Previous experiments gave access to the eec-tive surface charge ΓSiO− instead of theK+ con-centration in the Stern layer. Using the Gouy-Chapman-Stern model, we can calculate ΓSiO−

using the same parameters for dierent concen-trations, allowing for an indirect comparison ofour results to previous experiments22.23 Notethat in both Refs.22 and,23 surfaces were pre-pared by plasma cleaning which might lead toa dierent surface chemistry. Whereas Ref.22

shows a better agreement with pKK=3 Ref.,23

shows better agreement with pKK=2 as in ourcase.A dierence between the model and our mea-surements is that there is a nite reservoirof ions in our experiments, in contrast withthe theory which assumes a xed concentra-tion. Using the Gouy-Chapman-Stern model,one expects to have in between ≈ 0.4 × 1014

and ≈ 6 × 1014 ions in the Stern layer on a2 × 2cm2 substrate (for ΓSiOK ≈ 0.1/nm2 andΓSiOK ≈ 1.5/nm2 respectively).We typically spread 500nl - 1 µl droplets con-

taining 3−6×1014 ions for a mM solution. Thiscrude calculation shows that a range of 0.1 to10 is expected for the surface to bulk concen-tration ratio. The ratio of adsorbed ions in theStern layer with respect to the total numberof ions in the bulk is represented on Fig. 6(bottom). This ratio ranges from 0.1 for thickand concentrated samples to ≈ 5 for thin layersand dilute solutions where a signicant amountof ions go to the surface in agreement withthe previous estimate. It also implies that theabove modeling using the Poisson-Boltzmann-Stern approach, which requires an innite reser-voir, cannot be used without caution, at leastfor the least concentrated solutions (0.1mM).A ratio of 0.1 to 10 falls well in the range wherethe dierent elements can be located as dis-cussed earlier and explains why some curves arebulk-like with standing wave curves having ashape which resembles the Bragg peak (con-centrated thick samples) and why surface-likefeatures are more prominent in others.It should be noted here that as the Stern layer ismuch thinner and concentrated than the total

9

lm, the standing wave curve is mainly sensi-tive to the Stern layer and it is more dicult todetermine a concentration prole in the rest ofthe lm.

Distribution within the Stern layer.

The standing wave technique also allows for thedetermination of the position of ions relative tothe multilayer lattice, and therefore relative toeach other. Most interesting is of course thecompetition between K+ and Cs+ in KCl andCsCl mixtures and between Cl− and I− in KCland KI mixtures.

d [A]

105

d [A]

1510

IKCl

8.0 10−6

7.0 10−6

6.0 10−6

5.0 10−6

4.0 10−6

3.0 10−6

2.0 10−6

1.0 10−6

CsKCl

Grazing angle of incidence [degree]

2.162.142.122.12.082.062.04

1.4 10−5

1.2 10−5

1.0 10−5

8.0 10−6

6.0 10−6

4.0 10−6

Figure 9: X-ray standing wave curves and ionicdistributions (insets) for a 1mM KCl/CsCl mix-ture (bottom) and a 1mM KCl/KI mixture(top). The KCl/CsCl sample was 50nm thickand the KCl/KI sample was 120nm thick sam-ple. The width of the distributions has been setequal to the surface roughness. As we do notdetermine absolute concentrations, the distri-butions have been scaled arbitrarily. See Table1 in Supporting Information for tting param-eters.

Two representative examples are given on Fig.9 for a 1mM KCl/CsCl mixture in a 50nm thicksample and a 1mM KCl/KI mixture in a 120nmthick sample. The XSW curves have been anal-ysed using the model described above, wherethe ionic distributions have been convolved withthe surface roughness. We rst note that thereis a large concentration of both cations and an-ions in a 4 to 5 Å thick layer, with concentra-tions ≈ 100 times larger than in the bulk of thelm. Then, looking more deeply into the de-tails, we see that in all cases, cations are locatedcloser to the surface than anions, as expectedfor a negatively charged surface, and K+ andCs+ show an almost equal propensity for thesurface. Regarding the competition betweenCl− and I−, we nd that the center of the Cl−

distribution is systematically closer to the sur-face, compared to the I− distribution. In thiscase the shift is 2.5Å (see top insert of Fig.9).This is in contrast with the air-water interfacewhere I− was shown to have a higher propen-sity for the surface compared to Cl−.7 Interest-ingly enough, this higher propensity of the Cl−

ions for the surface is also reected in the Sternlayer concentration as we nd a ≈ 1.6 ± 0.3larger concentration of chloride ions comparedto iodide ions. These two ndings are not nec-essarily in contradiction since both the surfacechemistry (aecting short range interactions),including interaction with the other ions, andthe dielectric function (aecting the dispersionforces) are dierent.

Conclusion

In this paper, we have shown that X-ray stand-ing waves can be used to investigate ionic distri-butions in nanometer thick liquid layers usingsurfaces and ions of broad interest in colloidalscience and nanoscience. Not only the amountof ions in the bulk and Stern layer can be deter-mined, but also their distribution in the direc-tion perpendicular to the surface. Confrontingsuch data to simulations taking into account allmolecular interactions40,41 should lead to a de-tailed understanding of ionic distributions ataqueous interfaces which is of utmost impor-

10

tance for several areas of science.Acknowledgements: The authors gratefully

thank Christian Blot for manufacturing thesample cell and Elodie Barruet for concentra-tion measurements of the solutions using cap-illary electrophoresis. The Marie SklodowskaCurie initial Training network SOMATAI un-der EU Grant Agreement No. 316866 is grate-fully acknowledged for funding the PhD grantof Soumaya ben Jabrallah.

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