Monovalent Ion Condensation at the Electrified Liquid/Liquid InterfaceNouamane Laanait,1, a) Jaesung Yoon,1 Binyang Hou,1 Mark L. Schlossman,1, b) Petr Vanysek,2 Mati Meron,3

Binhua Lin,3 Guangming Luo,4 and Ilan Benjamin51)Department of Physics, University of Illinois, Chicago, Illinois 60607, USA2)Department of Chemistry and Biochemistry, Northern Illinois University, DeKalb, Illinois 60115,USA3)The Center for Advanced Radiation Sources, University of Chicago,Chicago, Illinois 60637,USA4)Division of Chemical Sciences and Engineering, Argonne National Laboratory, Argonne, Illinois 60439,USA5)Department of Chemistry, University of California, Santa Cruz, California 95064,USA

X-ray reflectivity studies demonstrate the condensation of a monovalent ion at the electrified interface betweenelectrolyte solutions of water and 1,2-dichloroethane. Predictions of the ion distributions by standard Poisson-Boltzmann (Gouy-Chapman) theory are inconsistent with these data at higher applied interfacial electricpotentials. Calculations from a Poisson-Boltzmann equation that incorporates a non-monotonic ion-specificpotential of mean force are in good agreement with the data.

PACS numbers: 68.05.Cf, 61.05.cm, 61.20.Qg, 82.45.Gj

Interfacial ion distributions underlie numerous electro-chemical and biological processes, including electron andion transfer across charged biomembranes and energystorage in electrochemical capacitors. The solution tothe Poisson-Boltzmann equation for a planar geometry,Gouy-Chapman theory, including modifications with aStern layer, is often used to predict ion distributionsnear those interfaces.1 We showed previously thatthe predictions of such theories are inconsistent withx-ray reflectivity measurements of ion distributionsat an electrified liquid/liquid interface.2 Instead, anion-specific Poisson-Boltzmann equation (PB-PMF)that incorporated a potential of mean force (PMF) foreach ion produced excellent agreement with the x-rayresults.2 The PB-PMF theory accounts for interactionsand correlations between ions and solvents that areleft out of Gouy-Chapman theory. This approach haspromise for understanding ion-specific effects that arerelevant to many chemical processes.3

Here, we demonstrate the condensation of a mono-valent ion at a liquid/liquid interface. Recent theoryproposes that condensation of multivalent ions is theresult of strong ion-ion correlations.4 However, thesetheories do not predict such distributions for monovalentions. Our current results can be understood by PB-PMFtheory. We have chosen to fit our x-ray data to thepotentials of mean force instead of fitting to a modelof the electron density profile because a single PMFfor each ion determines the ion distributions for allinterfacial potentials.

The system under study is the liquid/liquid interfacebetween a 100 mM aqueous solution of NaCl (FisherScientific) including 20 mM HEPES to buffer the pH

a)Electronic mail: nlaana1@uic.edub)Electronic mail: schloss@uic.edu

to 7.0, and a 5 mM solution of bis(triphenyl phos-phoranylidene) ammonium tetrakis(pentafluorophenyl)borate (BTPPA+, TPFB−) in 1,2-dichloroethane (DCE,Fluka). Water was produced by a Barnstead Nanop-ure system and DCE was purified using a column ofbasic alumina. BTPPATPFB was synthesized fromBTPPACl (Aldrich) and LiTPFB (Boulder Scientific).5

 FIG. 1. Circular glass sample cell and x-ray kinematics. Elec-trochemical cell diagram: Ag|AgCl | 0.1M NaCl | water | +20mM HEPES | 5 mM BTPPATPFB | DCE | 10 mM LiCl+1mM BTPPACl | water | AgCl | Ag. A four-electrode poten-tiostat (Solartron 1287) is used to apply potential at counterelectrodes (CE1,2, 9 cm2 Pt mesh) and monitor potential atreference electrodes (RE1,2) in Luggin capillaries within 4 mmof interface. The liquid/liquid interface of 7 cm diameteris pinned by a Teflon strip (affixed to the glass wall) andflattened by adjusting the volume of DCE phase. Volumeratio of water:DCE is 2:1. The x-ray wave vector transfer~Q = ~kout − ~kin.

arX

iv:1

006.

4616

v1 [

cond

-mat

.sof

t] 2

3 Ju

n 20

10

2

Conductance measurements using the method in Ref.6

determined that 54% of BTPPATPFB is dissociated inDCE.

The electric potential difference ∆φw−o(=φwater − φoil) between the water and oil (DCE)phases is given by the applied potential difference acrossthe electrochemical cell (Fig.1) minus the potentialof zero charge (∆φw−o = ∆φw−o

applied − ∆φw−opzc ). We

determined ∆φw−opzc = 318 ± 3 mV by measuring the

interfacial tension as a function of ∆φw−oapplied

7. The ions

Na+ and Cl− stay primarily in the aqueous phase andBTPPA+ and TPFB− stay in the DCE phase through-out the potential range studied. When ∆φw−o 6= 0,the ions form back-to-back electrical double layers atthe interface. For example, when ∆φw−o > 0, theconcentrations of Na+and TPFB− are enhanced at theinterface while those of Cl− and BTPPA+ are depleted.The variation of ionic concentration along the interfacialnormal produces a variation in the electron densityprofile ρ(z) (averaged over the x-y plane) that is probedby x-ray reflectivity.

 FIG. 2. X-ray reflectivity R(Qz) normalized to Fresnel re-flectivity RF (Qz) for various potentials across the water/1,2-dichloroethane interface as a function of wave vector transfernormal to the interface at T=296 K. From top to bottom∆φw−o = 0.33 V (◦), 0.28 V (•), 0.18 V(◦), 0.08 V (•), −0.02V(◦), and −0.12 V(�) (offset for viewing purposes). Dashedlines: Gouy-Chapman theory. Solid lines: PB-PMF. Red andblue lines indicate the use of two different PMFs for TPFB−

(see text).

X-ray reflectivity measurements R(Qz) from theelectrified liquid/liquid interface were carried out atthe ChemMatCARS sector of the Advanced Photon

 FIG. 3. Potentials of mean force for BTPPA+ (black) andTPFB− [W I

TPFB−(z):red,W IITPFB−(z):blue] determined by

fitting the reflectivity data in Fig. 2. PMFs for Na+ (greendots) and Cl− (circles) were calculated by MD simulations(see text) (Ref.10.

Source.8 R(Qz) is the reflected intensity normalized bythe incident intensity (after subtraction of backgroundscattering9) as a function of wave vector transfer Qz =(4π/λ) sinα , where λ (=0.41255 ±0.00005 A) is the x-ray wavelength and α is the angle of incidence (Fig. 1).Figure 2 illustrates R(Qz)/RF (Qz) for different ∆φw−o.The variation of the peak amplitude in R/RF with in-creasing ∆φw−o reveals the formation of a TPFB− layer,as discussed below.

We analyzed the x-ray data using the Poisson-Boltzmann (PB) equation,

d2φ(z)

dz2= − 1

εoε

∑i

eicoi exp[−∆Ei(z)/kBT ], (1)

which relates the electric potential φ(z) along the in-terfacial normal z to the concentration profile of ion i,ci(z) = coi exp[−∆Ei(z)/kBT ] , with Boltzmann constantkB , temperature T , charge ei of ion i (BTPPA+, TPFB−,Na+, and Cl−), permittivity of free space εo, and dielec-tric constant ε of either DCE (10.43) for z < 0 or water(78.54) for z > 0 . ∆Ei(z) is the energy of ion i relativeto its value in the bulk phase. The bulk ion concentrationcoi is calculated from the Nernst equation11 ,12. Fittingto the data involves calculating the electron density ρ(z)and R/RF from the ion concentration profiles ci(z) as de-scribed previously.2 For the purpose of calculating ρ(z)from ci(z) the ions were modeled as spheres of diameter2A for Na+, 3.5A for Cl−, 12.6A for BTPPA+, and 10Afor TPFB−, where the latter were estimated from thecrystal structure of BTPPATPFB.13,14 The TPFB− ionprovides the dominant ionic contribution to the electrondensity profile when ∆φw−o > 0 .

The Gouy-Chapman theory assumes that Ei(z) =eiφ(z) in Eq. 1. Fits of R/RF to predictions of Gouy-Chapman theory (Fig. 2, dashed lines) used only the in-terfacial roughness and a Qz offset ( 10−4A−1, a typicalmisalignment of the reflectometer) as fitting parameters.

3

TABLE I. TPFB− PMF parameters obtained by fitting to the reflectivity data at ∆φw−o = 0.28 and 0.33 V.

W (0) Lo Lw z0 σPMF D

(kBT ) (A) (A) (A) (A) (kBT )

W ITPFB−(z) −5± 0.5 3± 0.1 9± 4 −3.5± 0.2 3.4± 0.2 −9± 0.25

W IITPFB−(z) −25± 0.5 11± 0.5 10± 2.7 −7.5± 0.3 2.6± 0.3 −5.25± 0.2

These fits agree with the data at small ∆φw−o (−0.12V to 0.18 V), but at larger ∆φw−o (0.28 V and 0.33 V)R/RF is greatly overestimated primarily because Gouy-Chapman theory predicts unphysically large ion concen-trations near the interface.

Ion-specific effects can be included in Eq. 1 by express-ing Ei(z) ≈ eiφ(z) +Wi(z), where Wi(z) is the potentialof mean force (PMF) for each ion i.2,15,16 The PMF ofNa+ was calculated from a molecular dynamics (MD)simulation for a single ion.17 The PMF of Cl− was takenfrom an MD simulation in the literature.10 Fig. 3 illus-trates the monotonic variation of Wi(z) for Na+ and Cl−.Due to the computational difficulties of simulating Wi(z)for large molecular ions such as BTPPA+ and TPFB− weused a phenomenological PMF previously introduced inRef.2,

Wi(z) = (Wi(0)−W pi )

erf[|z| − δpi /Lpi ]

erfc[−δpi /Lpi ]

+W pi , (2)

where p(= w, o) refers to either the water phase (z ≥ 0)or the oil phase (DCE,z ≤ 0), W o

i −Wwi is the Gibbs en-

ergy of transfer of ion i from water to oil, δpi is an offset toensure continuity of Wi(z) at z = 0, and Lp

i characterizesthe decay of Wi(z = 0) to its bulk values Ww

i andW oi . We

used this monotonic PMF for BTPPA+, but had to mod-ify it for TPFB−, as described below. Since W o

i −Wwi

for BTPPA+ is known (Ref. 11 ) , the PMF of BTPPA+

is characterized by 3 parameters determined by fitting toR/RF data at ∆φw−o = −0.12 V where it is expectedthat the BTPPA+ interfacial concentration is enhanced:LwBTPPA+(= 14+12/−6A), Lo

BTPPA+(= 20+11/−6A),and WBTPPA+(0)(= 13 ± 2kBT ). The large error barson the PMF of BTPPA+ are due to the small magnitudeof the most negative ∆φw−o that we studied.

The x-ray reflectivity at the two highest positive poten-tials cannot be fit if Eq. 2 is used to model the PMF forTPFB−. The simplest model that will produce the peaksin Fig. 3 is a single layer of TPFB− ions at the interface(note that a layer of Na+, whose concentration is also en-hanced at the interface, cannot provide the x-ray contrastrequired to fit the data). The TPFB− layer is modeledby an attractive well in the PMF. WTPFB−(z) is given byEq. 2 plus a Gaussian function D exp[−(z−z0)2/2σ2

PMF ]for z < 0 along with a constant offset at z = 0 to main-tain continuity (see Fig.3). Analysis with a Lorentzianproduced similar results.

The six parameters of WTPFB−(z) [z0, D, σPMF ,

LwTPFB− , Lo

TPFB− , WTPFB−(0)] along with the Qz offset

and the interfacial roughness ( 4.3A < σ < 5.1A) are de-termined by fitting R/RF measured at ∆φw−o = 0.28V and 0.33 V, where the concentration of TPFB− isenhanced at the interface (Table I). This fitting is per-formed under the constraint that the resultant Wion(z)produces R/RF in agreement with the data over theentire range of potentials. In addition, fitted PMFswere rejected if the fit value of the roughness σ was un-physically small. In those cases an interfacial bendingmodulus18 on the order of 1000kBT would have been re-quired to reconcile the discrepancy of σ with its valuepredicted by capillary wave theory19. In the case of theTPFB− PMF, two local minima in χ2-space (denotedW I

TPFB−(z) and W IITPFB−(z) ) were found to satisfy

these conditions. Potential profiles that are intermediate

between W ITPFB−(z) and W

II(z)TPFB− do not satisfy these

conditions. Most of these fits had values of σ withinone standard deviation of capillary wave theory predic-tions using the measured potential-dependent interfacialtension.2. Fits to W II

TPFB−(z) at ∆φw−o = 0.28 V and0.33 V had values of σ within two standard deviations ofcapillary wave theory.

The PB-PMF model with the Wi(z) shown in Fig. 3produces R/RF in good agreement with the data over theentire range of measured potentials (Fig. 2). The attrac-

   FIG. 4. (left) Ion concentration profiles (in units of molar-ity) at ∆φw−o = 0.33V calculated from PB-PMF. BTPPA+

(black), TPFB− [W ITPFB−(z) :red,W II

TPFB−(z) :blue], Na+

(dots) and Cl− (circles). (right) Electron density profiles forvarious potentials calculated from PB-PMF. Top to bottom:∆φw−o = 0.33V [W I

TPFB−(z):red,W IITPFB−(z):blue], 0.28V

(dashed), 0.18V (solid), 0.08(dashed), −0.02V (solid), and−0.12 V (dashed).

4

tive wells for W I,IITPFB− have comparable depths (6 kBT

for W ITPFB−(z) and 5 kBT for W II

TPFB−(z)), FWHM,and centers (Table 1). The ion concentration profilesci(z), are calculated from Eq. 1 using Wi(z). Figure 4shows that the ci(z) at the highest potential, ∆φw−o =0.33 V, take the form of two back-to-back double layerswith a sharply defined layer of TPFB−. The differentci(z) calculated from W I

TPFB−(z) or W IITPFB−(z) differ

mainly in the broadness of the profile, which in the caseof W I

TPFB−(z) returns to its bulk value at z = 0, while

W IITPFB−(z) allows TPFB− to penetrate slightly more

into the water phase. The electron density profiles ρ(z)calculated from the different ci(z) are almost identical(Fig. 3), which demonstrates why our data cannot dis-criminate between W I

TPFB−(z) and W IITPFB−(z) .

The maximum density of TPFB− near the interfaceoccurs at ∆φw−o = 0.33 V and is 1 nm2 per TPFB−

ion when W ITPFB−(z) is used or 1.5 nm2 per TPFB− ion

when W IITPFB−(z) is used. Both values represent a high-

density layer for an ion of 1 nm diameter. Although denseionic layers have been observed in the interfacial adsorp-tion of charged amphiphiles,20 the absence of a denseTPFB− layer at ∆φw−o ≈ 0 indicates that TPFB− is, atmost, weakly amphiphilic.

Simulations and supporting spectroscopy experimentsindicate that highly polarizable ions (such as I− with apolarizability of 7.4A3) are preferentially adsorbed to thewater/vapor interface, though dense layers are not ex-pected or observed.21 We calculated the polarizability ofTPFB− to be 42.9A3.22,23 This large polarizability mayplay a role in forming a dense layer at high potentials.Also, Borukhov et al. suggested that the entropy of thesolvent can stabilize large ion adsorption.24 Additionaltheoretical work is required to determine the relevanceof these two effects for the data presented here.

The MD simulations of the potentials of mean forcethat we used for Na+ and Cl− do not account for ion-ioncorrelations, but they do include ion-solvent and solvent-solvent correlations. Such correlations also account forthe monotonic form of WBTPPA+(z) . However, as aresult of modeling the x-ray reflectivity, the phenomeno-logical WTPFB−(z) in Fig. 3 must implicitly accountfor ion-ion correlations if they are important for the ob-served condensation. The description of this monovalention condensation within PB-PMF theory illustrates theutility of this approach in describing ion-specific effectsthat are important for the behavior of ions in soft matter.

ACKNOWLEDGMENTS

MLS, PV and IB acknowledge support from NSF-CHE.NL acknowledges support from a UIC University Fel-lowship and the GAANN program. ChemMatCARS issupported by NSF-CHE, NSF-DMR, and the DOE-BES.The APS at Argonne National Laboratory is supportedby the DOE-BES.

1G. Gouy, “Constitution of the electric charge at the surface ofan electrolyte,” J. Physique, 9, 457 (1910); D. L. Chapman, “Acontribution to the theory of electrocapillarity,” Philos. Mag. Ser.6, 25, 475 (1913); O. Stern, Z. Elekt. Angew. Phys. Chem., 30,508 (1924).

2G. Luo, S. Malkova, J. Yoon, D. G. Schultz, B. Lin, M. Meron,I. Benjamin, P. Vanysek, and M. L. Schlossman, “Ion distribu-tions at the nitrobenzene-water interface electrified by a commonion,” J. Electroanal. Chem., 593, 142 (2006); “Ion distributionsnear a liquid-liquid interface,” Science, 311, 216 (2006).

3E. R. A. Lima, D. Horinek, R. R. Netz, E. C. Biscaia, F. w.Tavares, W. Kunz, and M. Bostrom, “Specific ion adsorptionand surface forces in colloid science,” J. PHys. Chem. B, 112,1580 (2008).

4A. Y. Grosberg, T. T. Nguyen, and B. I. Shklovskii, “The physicsof charge inversion in chemical and biological systems,” Rev.Mod. Phys., 74, 329 (2002).

5D. J. Fermin, H. D. Duong, Z. Ding, P.-F. Brevet, and H. H. Gi-rault, “Photoinduced electron transfer at liquid/liquid interfacespart ii. a study of the electron transfer and recombination dynam-ics by intensity modulated photocurrent spectroscopy (imps),”Phys. Chem. Chem. Phys., 1, 1461 (1999).

6F. M. Raymond and T. Shedlovsky, “Extrapolation of conduc-tance data for weak electrolytes,” J. Am. Chem. Soc., 71, 1496(1949).

7W. Schmickler, Interfacial Electrochemistry (Oxford UniversityPress, Oxford, 1996).

8M. L. Schlossman, D. Synal, Y. Guan, M. Meron, G. Shea-McCarthy, Z. Huang, A. Acero, S. M. Williams, S. A. Rice, andP. J. Viccaro, “A synchrotron x-ray liquid surface spectrometer,”Rev. Sci. Instrum., 68, 4372 (1997).

9Z. Zhang, D. M. Mitrinovic, S. M. Williams, Z. Huang,and M. L. Schlossman, “X-ray scattering from monolayers off(cf2)10(ch2)2oh at the water-(hexane solution) and water-vaporinterfaces,” J. Chem. Phys., 110, 7421 (1999).

10C. D. Wick and L. X. Dang, “Recent advances in understandingtransfer ions across aqueous interfaces,” Chem. Phys. Lett., 458,1 (2008).

11Gibbs energies of transfer: Na+ (57 kJ/mol), Cl− (53 kJ/mol),BTPPA+ (56 kJ/mol), TPFB− (72.5 kJ/mol), last two mea-sured by partitioning via UV-visible spectroscopy and mass spec-troscopy.

12A. G. Volkov and D. W. Deamer, Liquid-Liquid Interfaces: The-ory and Methods (CRC Press, Boca Raton, 1996).

13Y. Marcus, “Ionic radii in aqueous solutions,” Chemical Reviews,88, 1475 (1988).

14C.Zheng and P. Vanysek (unpublished).15D. Horinek and R. R. Netz, “Specific ion adsorption at hydropho-

bic solid surfaces,” Phys. Rev. Lett., 99, 226104 (2007).16L. I. Daikhin, A. A. Kornyshev, and M. Urbakh, “Ion pene-

tration into an ’unfriendly medium’ and the double layer capac-itance of the interface between two immiscible electrolytes,” J.Electroanal. Chem., 500, 461 (2001).

17I. Benjamin, “Empirical valence bond model of an sn2 reactionin polar and nonpolar solvents,” J. Chem. Phys., 129 (2008).

18S. A. Safran, Statistical Thermodynamics of Surfaces, Interfaces,and Membranes (Addison-Wesley Publishing Co., Reading, MA,1994).

19G. Luo, S. Malkova, S. V. Pingali, D. G. Schultz, B. Lin,M. Meron, I. Benjamin, P. Vanysek, and M. L. Schlossman,“Structure of the interface between two polar liquids: Nitroben-zene and water,” J. Phys. Chem. B, 110, 4527 (2006).

20F. Leveiller, D. Jacquemain, M. Lahav, L. Leiserowitz,M. Deutsch, K. Kjaer, and J. Als-Nielsen, “Crystallinity of thedouble layer of cadmium arachidate films at the water surface,”Science, 252, 1532 (1991).

21B. Winter and M. Faubel, “Photoemission from liquid aqueoussolutions,” Chem. Rev., 106, 1176 (2006); L. X. Dang, “Com-putational study of ion binding to the liquid interface of water,”J. Phys. Chem. B, 106, 10388 (2002).

5

22M. J. Frisch, G. W. Trucks, H. B. Schlegel, et al., “Gaussian 03,”Gaussian,Inc. Wallingford,CT,2004.

23TPFB− geometry optimized at B3LYP/6-311++G(d,p) levelwith tightest constraints on convergence (opt=very tight,int=ultra fine). Resultant geometry agreed closely with crystal

structure. Polarizability tensor calculated from optimized struc-ture at the same level of theory.

24I. Borukhov, D. Andelman, and H. Orland, “Steric effects in elec-trolytes: A modified poisson-boltzmann equation,” Phys. Rev.Lett., 79, 435 (1997).