Mechanism of ion adsorption to aqueous interfaces:Graphene/water vs. air/waterDebra L. McCaffreya,b,1, Son C. Nguyena,c,1, Stephen J. Coxb,1, Horst Wellerc,d, A. Paul Alivisatosa,e,f,g,Phillip L. Geisslera,b,2, and Richard J. Saykallya,b,2

aDepartment of Chemistry, University of California, Berkeley, CA 94720; bChemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley,CA 94720; cThe Hamburg Centre for Ultrafast Imaging, University of Hamburg, 22761 Hamburg, Germany; dInstitute of Physical Chemistry, Universityof Hamburg, 20146 Hamburg, Germany; eDepartment of Materials Science and Engineering, University of California, Berkeley, CA 94720; fMaterialsSciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720; and gKavli Energy Nanoscience Institute, University of California,Berkeley, CA 94720

Edited by Michael L. Klein, Temple University, Philadelphia, PA, and approved July 31, 2017 (received for review February 17, 2017)

The adsorption of ions to aqueous interfaces is a phenomenon thatprofoundly influences vital processes in many areas of science,including biology, atmospheric chemistry, electrical energy storage,and water process engineering. Although classical electrostaticstheory predicts that ions are repelled from water/hydrophobe (e.g.,air/water) interfaces, both computer simulations and experimentshave shown that chaotropic ions actually exhibit enhanced concen-trations at the air/water interface. Although mechanistic pictureshave been developed to explain this counterintuitive observation,their general applicability, particularly in the presence of materialsubstrates, remains unclear. Here we investigate ion adsorption tothe model interface formed by water and graphene. Deep UVsecond harmonic generation measurements of the SCN− ion, a pro-totypical chaotrope, determined a free energy of adsorption withinerror of that for air/water. Unlike for the air/water interface,wherein repartitioning of the solvent energy drives ion adsorption,our computer simulations reveal that direct ion/graphene interac-tions dominate the favorable enthalpy change. Moreover, the gra-phene sheets dampen capillary waves such that rotational anisotropyof the solute, if present, is the dominant entropy contribution, incontrast to the air/water interface.

specific ion effects | graphene | SHG spectroscopy | molecular dynamics |adsorption

Over a decade ago, detailed simulations predicted that cer-tain simple ions would exhibit enhanced concentrations atthe air/water interface (1), reinvigorating a century-old debateprimarily addressing the origin of the famous Hofmeister effectsin protein chemistry (2). Experiments subsequently verified thesepredictions (3, 4). Surface enhancement of simple ions has sincebeen widely studied [e.g., see the review by Jungwirth and Tobias(5)] and attributed to various properties of the ions including size,polarizability, dispersion forces, hydration free energy (6–8), andthe degree of interfacial roughness (9–11). Previous temperature-dependent deep UV (DUV) second harmonic generation (SHG)experiments from the Saykally group have determined theenthalpic and entropic contributions to the adsorption of theprototypical pseudohalide, the thiocyanate (SCN−) ion, showingthat a negative enthalpy change drives the ion adsorption, whereasa negative entropy change impedes it (9). Using molecular simu-lations performed in the same study, the following underlyingmechanism was proposed: first, when the ion moves from the bulkto the interface, weakly interacting water molecules are displacedfrom both the surface and the ion solvent shell into the bulk so-lution, where they form stronger water–water bonds, leading tothe negative enthalpy change. Second, the presence of an ion atthe interface dampens its capillary wave fluctuations, leadingto the negative entropy change. Although a consensus has yet tobe reached regarding the complete theory of interfacial ion ad-sorption, these collective, detailed studies of the air/water in-terface have clearly advanced our general understanding (5–13).However, it remains unclear what effect the presence of a material

substrate—which is of central importance with respect to un-derstanding the details of the Hofmeister effects (2)—will have onthe adsorption process. It is therefore essential to investigate theadsorption of ions to other types of aqueous interfaces.A model interface of widespread current interest is graphene/

water. Graphene, a most interesting material in its own right(14), has important practical applications which involve aqueousinterfaces and ion adsorption, e.g., solution-gated field effecttransistors for sensing (15), porous membranes for filtering (16),desalination (17), supercapacitors (18), and lithium-ion batteries(19). In the context of specific ion effects, two properties ofgraphene are particularly relevant: polarizability, which will actto attract ions to the interface (20), and hydrophobicity. Here wedescribe a study of interfacial ion adsorption by DUV–SHGspectroscopy and molecular dynamics (MD) simulations,addressing graphene suspended on the water surface to explorethese issues and compare properties of the resulting interfacewith those determined for air/water (9).

ResultsFig. 1 diagrams the experimental setup and shows the SHGsignal versus the bulk mole fraction of thiocyanate anions in so-lution. The data were fit to a simple Langmuir model, to extractthe free energy of ion adsorption: ΔGads,gra = −8.5 ± 1.1 kJ/mol(SEs are quoted, and a more detailed description of how they arecalculated is in SI Appendix). This is within error of the free energyof adsorption to the air/water interface (ΔGads,vap = −6.78 ±0.03 kJ/mol). We note that the model used does not account forany surface potential caused by the electrical double layer. Weattempted to use a model that does include the surface potential,as detailed in SI Appendix. However, the parameter errors andparameter correlations were too large to draw conclusions from.

Significance

The Gibbs free energy of adsorption of a prototypical anion toa graphene/water interface is determined by surface-sensitivespectroscopy and interpreted via molecular dynamics simula-tions to establish the adsorption mechanism, which is found tobe qualitatively different from that operative for the air/waterinterface and probably representative of a general water/hydrophobe interface.

Author contributions: H.W., A.P.A., P.L.G., and R.J.S. designed research; D.L.M., S.C.N., andS.J.C. performed research; D.L.M., S.C.N., and S.J.C. analyzed data; and D.L.M., S.C.N.,S.J.C., P.L.G., and R.J.S. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1D.L.M., S.C.N., and S.J.C. contributed equally to this work.2To whom correspondence may be addressed. Email: saykally@berkeley.edu or geissler@berkeley.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1702760114/-/DCSupplemental.

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To elucidate the molecular details underlying the lack ofchange in ΔGads, we performed MD simulations of ion adsorp-tion to the graphene/water interface. Previous studies haveshown that iodide and thiocyanate exhibit very similar behavior(9). Although the effects of thiocyanate anisotropy are moresignificant at graphene/water than for the air/water interface (SIAppendix), the general conclusions drawn from the iodide sim-ulations are the same, and we therefore focus our discussion onthis simpler model. The simulation box contained a graphene/water interface on one end and an air/water interface on theother (Fig. 2A). The potential of mean force (PMF; Fig. 2B,black curve) for an iodide ion above the graphene was con-structed using umbrella sampling, wherein the height of the ionwas biased with a harmonic potential. As discussed in SI Ap-pendix, computing ΔGads directly from the PMF requires the sizeof an adsorption site for an ion at the air/water interface to bedefined. This is avoided by comparing the difference of values,ΔΔGads (SI Appendix, Eq. S17), for the graphene/water and air/water interfaces. Also as discussed in SI Appendix, there is somefreedom in choosing the model parameters. We have found thatour results are surprisingly insensitive to varying the flexibility ofgraphene but that ΔΔGads does depend on the choice of in-teraction strength between the ion and the graphene. We havechosen this interaction to reproduce the experimental free en-ergy difference, which yields an adsorption energy for iodide atgraphene in vacuum (no waters) in reasonable agreement withdensity functional theory (21, 22). This is similar in spirit to the

approach of Williams et al. (23), who capture the effects of thegraphene–ion polarization interaction (as measured by densityfunctional theory calculations) by empirically adjusting the in-teraction strength between the ion and the carbon atoms. De-spite the similarity in the adsorption free energies at the twointerfaces, there are qualitative differences in the PMFs betweenthe two interfaces.The enthalpy was calculated directly from the total potential

energy of the simulations (Fig. 2B, red curve), and the entropywas calculated by subtracting the enthalpy from the free energy(Fig. 2B, blue curve) (Materials and Methods). The air/water in-terface has a more favorable enthalpy change than does thegraphene/water interface, but this is offset by an accompanyingunfavorable entropy change, whereas the graphene/water in-terface exhibits an entropy contribution near zero. To clarify theenthalpy contributions, Fig. 3A compares the total potentialenergy to the direct interaction of iodide with graphene in vac-uum. Comparison of the two curves reveals that the potentialenergy at the graphene/water interface is primarily due to thedirect interaction and not to the solvent repartitioning energy, asfound for the air/water interface, which exhibits no equivalentdirect interaction. Fig. 4 depicts this situation, displaying spatialmaps of water–water interactions (Fig. 4A) and ion–water in-teractions (Fig. 4B), as first described in ref. 9. Notice in Fig. 4A(especially Fig. 4A, Middle) that the water–water interactions areless disrupted at the graphene interface than at the air interface.This leads to a less favorable enthalpy change when these in-terfacial waters are repartitioned back into the bulk solution. Tobetter understand the entropy contributions, Fig. 3B shows theheight fluctuations of the two interfaces relative to the instanta-neous interface (24), an important contribution to the entropy atthe air/water interface (9). The graphene sheet itself severelydampens these fluctuations (Fig. 3B, Left, cyan curve), and theiodide ion actually slightly enhances the fluctuations when it ap-proaches the interface (Fig. 3B, Left, red curve). In contrast, at theair/water interface, large height fluctuations are dampened whenthe ion approaches the interface (Fig. 3B, Right).

DiscussionGiven the electronic properties of graphene and the qualitativedifferences in the molecular details underlying aqueous ion ad-sorption to graphene and air, it is surprising that the experimentalfree energies are within error of each other. Furthermore, usingUV SHG spectroscopy, Onorato et al. (25) measured similar freeenergies for SCN− adsorption to the dodecanol/water interface.Based on interfacial affinities alone, it would appear that the ef-fect of a hydrophobic boundary is generic, regardless of whetherthe boundary is a rigid material like graphene or instead a coex-isting vapor phase. Our more detailed results suggest, however,that the underlying mechanism of adsorption to the graphene/water interface is qualitatively different from that for air/water.Before presenting a mechanistic interpretation, we note that the

net change in free energy due to solvation is a path-independentquantity that can be parsed in many different (yet exact) ways,each highlighting contributions from different physical factors,such as the entropic costs of solute volume exclusion (7, 26–29),the energetic consequences of charging a microscopic cavity (12,13, 28, 29), intrinsic polarization of an aqueous interface (7, 8), orsurface tension and solute-induced deformations and fluctuationsof such interfaces (9, 11, 30). The complexity of aqueous solvationlimits the simple insight that can be gained from any one analysisof this kind. In particular, the statistics of solvent–solute interac-tions are strongly yet subtly shaped by interactions among solventmolecules, and the entropy of solvation cannot be rigorouslydecomposed into contributions from distinct degrees of freedom[indeed, the entropy that notionally cancels contributions fromsolvent–solvent energetics in approaches like that of ref. 13 is nota measurable entropy at all (31)]. Here we focus on the influence

Fig. 1. Measured SHG signal versus bulk thiocyanate concentration. (A) Theexperimental design. Fundamental (386-nm) pulses are incident on the gra-phene/water surface, and SHG (193-nm) pulses are generated in reflection. Thecollected signal is proportional to the squared number of thiocyanate ions atthe surface. (B) Structure of the interface studied in A. (C) SHG signal (nor-malized to the nonresonant SHG signal of water) versus bulk concentration ofthiocyanate. The data are fit to a Langmuir model (SI Appendix, Eq. S5), and thefree energy of adsorption is extracted. The quoted uncertainty in ΔGads is 1 SE.

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of our simulated graphene substrate on two factors we have pre-viously emphasized in the context of air–water interfaces, namely,the entropic cost associated with capillary wave pinning andenthalpic gain associated with repartitioning undercoordinatedwater molecules at the interface to the bulk. In other parsings ofsolvation free energy, contributions from these factors might ap-pear only implicitly, e.g., through the effect of capillary waves onthe range of fluctuations in the solvent–solute interaction energy.Below, we also discuss how our results may be interpreted in thecontext of cavity formation at the interface and how electrostaticinteractions with the solvent differ at the two interfaces.Solvation of SCN− at the air/water interface exhibits a large

enthalpic contribution, which Otten et al. (9) have attributed tofavorable solvent repartitioning, and a large unfavorable entro-pic contribution, attributed to the dampening of capillary waves.Because previous work has shown that the interface betweenliquid water and a hydrophobic substrate is similar to the air/water interface at the molecular level (24), one might intuitivelyexpect that the similar adsorption free energies arise due to

similar molecular adsorption mechanisms. However, we showhere that the similarity of adsorption affinities actually reflects asubtle cancellation in differences in adsorption enthalpy andentropy. In particular, our simulations clearly show that thegraphene/water interface exhibits a smaller enthalpic contribu-tion dominated by the direct interaction of the iodide and gra-phene (Fig. 3A) and a much reduced entropic contribution,consistent with the fact that the capillary waves are alreadysuppressed by the graphene (Fig. 3B). In this mechanistic in-terpretation, we would expect the role of graphene to generalizeto other material substrates where capillary fluctuations aresuppressed relative to the air/water interface. Indeed, our resultare consistent with the simulation studies of Iuchi et al. (32) andKumar et al. (33), who investigated the adsorption of an excessproton to the air/water interface and a hydrophobic wall. In bothcases, a similar well depth in the PMF as the ion moved to theinterface was observed, and the enthalpic gain and entropic costwas reduced in the presence of the hydrophobic wall. Furtherstudies on other atomically thin, uncharged monolayers are

Fig. 3. Examining potential energy (PE) and height fluctuations. (A) The total PE (red) of the iodide in solution and the direct interaction energy (blue) of asingle iodide at the graphene sheet (no waters). Graphene is centered at zion = 0 nm. The total PE has contributions from ion–graphene, water–ion, andwater–water interactions. (B) The variance of the height fluctuations of the instantaneous (Left) graphene–water and (Right) air–water interfaces (24), withthe ion positioned at the graphene–water and air–water interfaces and in bulk. Neat simulations (no ion) are also shown. The inset shows the fluctuations atthe graphene interface on a larger scale.

Fig. 2. Simulation results for iodide interacting with both graphene/water and air/water interfaces. (A) A representative snapshot of the simulation box,including iodide (yellow), air/water instantaneous interface (blue), graphene/water instantaneous interface (black), and periodic boundaries (dashed line).The graphene (black) is at z = 0 nm. (B) The potential of mean force (black), total potential energy (red), and entropy (blue) curves for the ion vs. distance fromthe graphene sheet. Graphene is centered at zion = 0 nm. Distances less than zion ∼0.4 nm are effectively disallowed by steric repulsion. Total potential energyis nearly identical to enthalpy at ambient conditions.

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needed to confirm the extent to which this cancellation effectholds in general.To explore interfacial ion solvation from a different mecha-

nistic perspective, we have examined a solvation pathway thatfirst creates an uncharged volume-excluding solute and then in-troduces the ion’s charge. For the air/water interface this routeemphasizes the strong aversion of a neutral solute for the liquidphase and a competing preference for liquid due to electrostaticinteractions. In the case of graphene, both these biases aresubstantially weakened, highlighting again the dominant impor-tance of direct interaction between the ion and graphene (Fig.5). Further results and discussion of these calculations are givenin SI Appendix.In summary, we used DUV–SHG spectroscopy to determine

the free energy of adsorption of thiocyanate to the graphene/water interface as −8.5 ± 1.1 kJ/mol, which is within error of−6.78 ± 0.03 kJ/mol for the air/water interface (9). Moleculardynamics simulations show that although the free energies aresimilar, the corresponding mechanisms are not. For the gra-phene/water interface, the enthalpy is dominated by the directinteraction of the ion and graphene. Entropy changes are neg-ligible in our simulations of an isotropic solute; for a linearmolecule we find them to be accounted for by the solute’s ro-tational anisotropy (SI Appendix). This suggests that even thoughhydrophobe/water interfaces are similar at the molecular scale(24), there are subtle, but important, differences that need to beconsidered when treating interfacial ion adsorption. Otherstudies, both theoretical and experimental, suggest that similaratomically thin, uncharged interfacial layers may also exhibit thiscancellation effect between enthalpy and entropy (25, 32, 33).

Materials and MethodsExperimental Details. Fig. 1A depicts the experiment, wherein 100-fs laserpulses at 386 nm incident on the surface of CVD graphene (three to five layers)suspended on top of solutions of NaSCN generate 193 nm second harmonicradiation, which is resonant with the charge transfer to solvent transition ofthiocyanate (9). A more detailed explanation of the procedure is given in SI

Appendix. In the dipole approximation, such even-order nonlinear processesare inherently surface specific due to symmetry constraints (34); thus, theresonance-enhanced SHG selectively probes thiocyanate ions at the graphene/water interface. Fig. 1B diagrams the interfacial structure, whereas Fig. 1Cshows the actual SHG signal collected (normalized to the nonresonant SHG

Fig. 5. PMFs vs. distance from graphene sheet, for the iodide and neutralcavity. Aside from the charge on the ion, all other parameters are thesame. The iodide result (black) is the same as that presented in Fig. 2. It ismore favorable to move the neutral cavity (teal) to the air/water in-terface than the charged iodide. At the graphene interface (the gra-phene is at zion = 0 nm), the well depths are comparable. The solid blueline shows the direct interaction between the solute and the graphene(Fig. 3). In both cases, the PMF at the graphene interface is dominated bythis direct interaction.

Fig. 4. Spatial maps of water interactions. Graphene is centered at z = 0 nm. (Interactions with graphene are not included.) (A) The average interaction awater experiences with all other waters for the iodide positioned at the (Left) graphene and (Right) air interfaces and (Middle) in the bulk. The zero of energyfor all maps corresponds to bulk values for easy comparison. The depression at the air–water interface is an artifact of the cylindrical averaging. (B) Theaverage interaction a water experiences with the iodide for the iodide positioned at the (Left) graphene and (Right) air interfaces and (Middle) in the bulk.

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signal of water) versus bulk concentration of thiocyanate. The data were fit toa simple Langmuir model (SI Appendix, Eq. S5), as described in SI Appendix.

Simulation Details. To calculate the PMF,we used umbrella sampling. The systemconsisted of 264 SPC/E water molecules (35) placed above a 2.13 × 1.97 nm2

graphene sheet consisting of 160 carbon atoms. Initial simulations of a largersystem with 1,151 water atoms above a 2.55 × 2.46 nm2 graphene sheet with novapor phase found only a small effect on the PMF (the adsorption free energy ofa single ion was more favorable in the small system by only 0.3 kBT). Wetherefore opted to use the smaller system size of 264 water molecules becausethis permits the calculation of the energy and entropy profiles shown in Fig. 2with reasonable computational resources. The plane of the graphene sheet wastaken to be the xy plane, with the normal direction taken to be z. Periodicboundary conditions, commensurate with the graphene sheet, were used withthe length of the z direction set to 4.5 nm. The simulation setup could thus bedescribed as a thin slab of liquid water (approximately 2 nm thick), with onegraphene/water interface and one air/water interface. An iodide ion withcharge qI = −0.8e, where e is the elementary unit of charge, was restrained atdifferent heights z0 above the graphene sheet with a harmonic bias potential

UbiasðzÞ= kbias2 ðz− z0Þ2, [1]

where z is the instantaneous height of the iodide above the graphene sheet.A total of 23 windows with z0 = 0.3, 0.4, . . ., 2.5 nm were used, with kbias =836.8 kJ/mol/nm2. Dynamics were propagated at a temperature of 298 K usingLangevin dynamics (36, 37) as implemented in the LAMMPS simulationpackage (38) (available at lammps.sandia.gov), with a time step of 1.0 fs and adamping constant of 1 ps. For each window, a simulation of 7 ns was per-formed. To reconstruct the PMF, the multistate Bennett acceptance ratio (39)method was used. At ambient conditions, it is reasonable to ignore contri-butions due to pressure–volume work, and contributions from kinetic energyare independent of z. We therefore equate the changes in enthalpy to thechanges in potential energy. Potential energy profiles were measured directlyfrom the umbrella sampling simulations by binning the samples according tothe z coordinate of the ion, with a bin width 0.1 nm. The autocorrelation time

of the potential energy in each window was used to construct uncorrelateddata sets, and the SE for each height was computed as

s=σffiffiffiffiffiffiffiffiffiffiffin− 1

p , [2]

where σ is the SD of the potential energy at a given height, and n is thenumber of samples. The entropy profiles were calculated by subtracting thepotential of mean force from the enthalpy TΔS(z) = ΔU(z) − ΔF(z), and errorbars were calculated by simple propagation of errors.

Long-ranged Coulomb interactions were computed using the particle–particle particle–mesh solver (40) with an interpolation order 5, a neutral-izing background charge, a k-space grid of 18 × 16 × 30, and a screeningparameter of 2.95 nm−1. Short-range Lennard–Jones (LJ) interactions werealso defined between atomic species i and j,

ULJ�rij�= 4«ij

"�σijrij

�12−�σijrij

�6#, [3]

with parameters given in SI Appendix, Table S4 (35, 41, 42). There were noCoulomb interactions between graphene carbon atoms and other species.Furthermore, because their equations of motion were not integrated, no in-teraction potential between carbon atoms was defined (although tests with aflexible graphenemodel were performed; SI Appendix). Similarly, because onlya single iodide ion was present, no iodide–iodide LJ parameters were defined.

ACKNOWLEDGMENTS. We thank William Parkin and Marija Drndi�c for provid-ing graphene samples during the initial stages of this project, Magnus Johnsonfor testing the purity of solutions with sum frequency generation, Tod Pascal andMing Ma for helpful discussions about simulation methods, and Christopher Hullfor help with data analysis. This work was supported by the Director, Office ofBasic Energy Sciences, Office of Science, US Department of Energy under Con-tract DE-AC02-05CH11231, through the Chemical Sciences Division (to D.L.M.,S.J.C., P.L.G., and R.J.S.) and the Physical Chemistry of Inorganic NanostructuresProgram, KC3103 (to S.C.N. and A.P.A.), of the Lawrence Berkeley National Lab-oratory; the work was also supported by the German Federal Cluster of Excel-lence The Hamburg Centre for Ultrafast Imaging (S.C.N. and H.W.).

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