Anionic and Cationic Hofmeister Effects on Hydrophobic and

Article pubs.acs.org/Langmuir

Anionic and Cationic Hofmeister Effects on Hydrophobic and Hydrophilic Surfaces Nadine Schwierz,†,‡ Dominik Horinek,§ and Roland R. Netz*,† †

Fachbereich für Physik, Freie Universität Berlin, 141954 Berlin, Germany Physik Department, Technische Universität München, 85748 Garching, Germany § Institut für Physikalische und Theoretische Chemie, Universität Regensburg, 93040 Regensburg, Germany ‡

S Supporting Information *

ABSTRACT: Using a two-step modeling approach, we address the full spectrum of direct, reversed, and altered ionic sequences as the charge of the ion, the charge of the surface, and the surface polarity are varied. From solvent-explicit molecular dynamics simulations, we extract single-ion surface interaction potentials for halide and alkali ions at hydrophilic and hydrophobic surfaces. These are used within Poisson−Boltzmann theory to calculate ion density and electrostatic potential distributions at mixed polar/unpolar surfaces for varying surface charge. The resulting interfacial tension increments agree quantitatively with experimental data and capture the Hofmeister series, especially the anomaly of lithium, which is difficult to obtain using continuum theory. Phase diagrams that feature different Hofmeister series as a function of surface charge, salt concentration, and surface polarity are constructed from the long-range force between two surfaces interacting across electrolyte solutions. Large anions such as iodide have a high hydrophobic surface affinity and increase the effective charge magnitude on negatively charged unpolar surfaces. Large cations such as cesium also have a large hydrophobic surface affinity and thereby compensate an external negative charge surface charge most efficiently, which explains the well-known asymmetry between cations and anions. On the hydrophilic surface, the size-dependence of the ion surface affinity is reversed, explaining the Hofmeister series reversal when comparing hydrophobic with hydrophilic surfaces.

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INTRODUCTION Since the discovery of the Hofmeister series in 1888 in the context of precipitation studies of purified egg white,1 the interest in ion specific effects has steadily grown. It was empirically demonstrated already in 1910 that, for almost all processes in electrolyte solution, the dependence on ion type is ordered according to a universal series both for cations and for anions.2 The widespread applicability of these series in fields ranging from molecular biology to chemical engineering and the unclear origin make the identification of the underlying mechanism one of the grand current challenges in interfacial and colloidal science.3−7 Since identical ion series are observed for bulk electrolyte properties, such as osmotic coefficients, and precipitation studies of various proteins and colloids, ion specific effects have traditionally been attributed to changes that ions provoke in the water surrounding. However, recent experiments demonstrated that ions do not perturb the water structure beyond their first hydration shell,8−10 and the current opinion is that direct ion− macromolecule interactions are mainly responsible for ion specificity of protein and colloidal precipitation.4,7,11 Figure 1 shows the generally accepted Hofmeister series for anions and cations as it is shown in books and review articles,4,6,7 which order the ions with respect to macroscopic properties such as surface tension, solubility of hydrocarbons, © 2013 American Chemical Society

Figure 1. Standard ordering of anions and cations according to the Hofmeister direct series based on precipitation studies of solutions of typical, anionic proteins.6,7 To the left, ions have the smallest stabilization power and typically tend to salt out proteins; to the right, ions have the largest stabilization power and salt in proteins.

or precipitation of a standard protein solution. By a standard protein, we mean in this context a globular protein with a net negative charge, with the precipitation being driven by the aggregation of hydrophobic groups or side chains, which are exposed to the protein exterior. To the left, the stabilization power against precipitation is smallest and one obtains saltingout behavior; to the right, this stabilization power is highest and salting-in behavior is displayed. At the same time, ions to the left tend to be structure-enhancers, conserving the native fold of Received: October 2, 2012 Revised: January 11, 2013 Published: January 22, 2013 2602

dx.doi.org/10.1021/la303924e | Langmuir 2013, 29, 2602−2614

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is in full agreement with the above-mentioned regularities found for proteins. In a series of studies with functionalized organic and inorganic colloidal systems, ionic-specific effects were examined for hydrophobic as well as hydrophilic colloids and both positive as well as negative surface charges, which allowed studying of the full spectrum of different surface characteristics in basically a single model system. In these systems, the cationic and anionic series are reversed when the sign of the surface charge is changed as well as when the surface polarity is changed from hydrophobic to hydrophilic.28−30 An even more basic and controlled experimental setup was recently demonstrated by glueing a silica bead to the tip of an atomic force microscope and measuring the force between the bead and a silicon substrate in various electrolyte solutions at separations down to the subnanometer range.31 Pronounced cationic-specific effects and salt-induced series reversal were observed; toward the end of this paper, we will explicitly address the results of the latter experiments. First, crucial insight into the anionic Hofmeister series came from simulations of halide ions at the air−water interface, where the small F− and Cl− ions were found to be repelled, the larger Br− was quite indifferent to the interface, and the largest I− ion was even slightly attracted to the interface.32,33 These results by themselves explain already the anionic Hofmeister direct series shown in Figure 1: larger ions adsorb on hydrophobic surfaces and therefore give them an effective negative charge which leads to surface−surface repulsion and therefore stabilization of neutral solutes. These findings also qualitatively explain the Hofmeister series observed for the air− water tension increment;34 in fact, simulations with optimized classical force fields 35,36 combined with coarse-grained modeling quantitatively matched the experimental interfacial tension data.37 The series reversal as the surface charge changes from negative to positive is then also easily explained:20 For negative surfaces, the adsorption of large anions will certainly be reduced due to electrostatic repulsion, but the trend will be the same; small anions will be more repelled from the surface than large anions, still giving negative surfaces a more negative surface potential in a NaI solution than in a NaF solution, and therefore, the direct series is retained. On a cationic surface, the trend is reversed, since now the magnitude of the surface potential is reduced by strongly adsorbing I− ions more than by the weakly adsorbing F− ions. This mechanism was explicitly demonstrated in simulations of macromolecules consisting of hydrophobic and cationic patches in different halide solutions.38,39 For cations, the situation is similar in that large cations such as Cs+ tend to adsorb on hydrophobic surfaces and thus give them an effective positive surface charge. For neutral and for cationic surfaces, larger ions thus tend to be more stabilizing than small ions, which is the indirect series. For surfaces of sufficient negative charge, which is the prototypical situation for colloids and proteins, the cationic series will be reversed by the same mechanism that leads to series reversal for anions as one goes from anionic to cationic surfaces, and the direct cationic series is obtained. This asymmetry between cations and anions on hydrophobic charged surfaces is schematically depicted in Figure 2. The experimentally observed double reversal of the anionic series as a function of surface polarity and the surface charge was recently reproduced in a combined simulation−theory approach and rationalized by the different binding affinity of anions on hydrophobic and hydrophilic surfaces.40 Yet, a systematic atomistic theoretical study of anions and cations at

proteins, while ions to the right typically act as denaturants. Throughout this paper, and in agreement with the common literature notation, we refer to the ordering shown in Figure 1 as direct order for both anions and cations. One curious fact immediately catches the eye: The halide anions are ordered according to increasing size, that is, the smallest F− ion to the left has the smallest stabilization power against precipitation, while the largest I− ion to the right has the largest stabilization power. For the cations, the size ordering is just the other way around; here, the largest alkali ion Cs+ to the left has the smallest stabilization power while the smallest Li+ ion to the right has the largest stabilization power. The reason for this asymmetry, which demonstrates that ion-specific behavior is not trivially related to the size and hence to the surface charge density of ions, is one of the central themes in the present work. In this context, it is interesting to note that the cation ranking in Hofmeister’s original work1 was different from the one shown in Figure 1 and corresponds to what we now would call indirect order. The reason is that Hofmeister in his precipitation studies dealt with egg white, which is a complex mixture of proteins of different net charge, so that the ordering he saw is representative of the nonstandard case of charge neutral and cationic proteins. This interpretation is in line with the observation that, for nonpolar solutes such as benzene, the stabilization power of both monovalent anions and cations increases as the ion size goes up12−14 and thus for cations contradicts the ordering shown in Figure 1. All these results highlight the importance of the surface charge of the objects that are dealt with in precipitation studies. In fact, it was observed as early as 1911 by Robertson that the Hofmeister series is reversed when the charge of the precipitating protein is changed,15 and numerous later findings confirmed those observations. To give explicit examples, the solubility of negatively charged proteins such as hemoglobin follows the direct order for anions and cations16,17 while the solubility and crystallization of positively charged lysozyme follow the reversed order.18−20 Moreover, the reversed cationic order is observed for the adsorption of lysozyme to solid silica surfaces.21 In fact, reversal of the Hofmeister series has also been observed when the polarity of the peptide side chain is changed22 and when solution parameters such as the salt concentration19 or the buffer type23 are varied. It transpires that the putative universal Hofmeister ranking in fact has to be replaced by a diverse spectrum of direct, partially altered, and reversed (indirect) series. Protein precipitation phenomena are complex, since it is often not clear whether a protein upon addition of salt first denatures and then precipitates or whether it precipitates in its native state, as was pointed out by Robertson in 1911 already.15 Some of the above-mentioned complexities could thus be argued to be due to the intricate nature of proteins and their ability to undergo conformational changes in reaction to external stimuli. However, Hofmeister series reversal phenomena are not restricted to proteins; they are also well documented for colloidal systems that presumably have no internal degrees of freedom. Here, ion-specific effects are typically studied by measuring the coagulation kinetics, which allows inferring of the stabilization power of various ions. For metal oxide dispersions with low point of zero charge (pzc) such as SiO2 or TiO2, which are negatively charged at normal pH = 7, the cationic sequence is direct.24−26 In contrast, on surfaces with a high pzc such as Al2O3 or Fe2O3, which are positively charged at pH = 7, the ordering is reversed.24,27 This 2603


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concentration. In particular for cations, the small size differences between different cations lead to a more weakly pronounced ordering in series compared to that of the anions.

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METHODS

Simulation Details. The two-scale modeling approach used here has been described in detail in ref 40. Briefly, in the simulations, the surface is a 3.5 nm × 3.464 nm SAM consisting of 56 C20H40 chains with a terminal CH3 group for the nonpolar and a terminal CH2OH group for the polar SAM. The chain lattice spacing corresponds to a gold (111) substrate with a tilt angle of 30° close to experimental values. The lower six C atoms of each chain are restrained by harmonic potentials with a spring constant k = 5 × 105 kJ/(mol nm2). The simulation box has an extension of 9 nm in the z direction and is filled with about 2700 SPC/E water molecules.41 The SAM is modeled with the GROMOS96 force field.42 The force field parameters used for anions and cations were previously optimized to reproduce thermodynamic solvation properties.35 From the three different cation parameter sets given in ref 35, we have used parameter set 2 for all cations in our calculations, since this parameter set yields accurate ion pairing properties as judged by comparison with experimental osmotic coefficient data.36 All force field parameters for the ions and surfaces are listed in the Supporting Information. The terminal CH3 group on the hydrophobic SAM carries a small negative charge, which is negligible with respect to the wetting properties and still renders a very hydrophobic surface.43 For temperature coupling, we use the Berendsen thermostat with a reference temperature of 300 K and a time constant of 0.1 ps. For anisotropic pressure coupling, we use the Berendsen barostat with a time constant of 1 ps and a reference pressure of 1 bar. Periodic boundary conditions are applied, long-range Coulomb forces are calculated using the particle-mesh Ewald summation,44 and for the van der Waals interactions, a cutoff radius of 1.2 nm is used. A single ion is placed into the water phase, and its PMF is calculated by umbrella sampling45 with a window spacing of 0.025 nm and a 3 ns simulation time discarding the first 1 ns using a time step of 2 fs and the weighted histogram analysis method.46 For convenient further usage in our modeling, the PMFs are fitted by fit functions that are given explicitly in the Supporting Information. To ensure converged PMFs, the equilibration at the hydrophobic and hydrophilic surface is analyzed in detail (see the Supporting Information). In all simulations, the ion−oxygen radial distribution function (RDF) g IW(r) is determined. The radius-dependent coordination number is then calculated as

Figure 2. Schematic Hofmeister ordering according to the effectiveness in stabilizing solutions of negatively and positively charged hydrophobic solutes against precipitation. For negatively charged solute surfaces, the direct order (white region) is observed, i.e., larger anions are better stabilizers than small ions. Reversal (black region) takes place when changing the sign of the surface charge, and for intermediate surface charges, partial alterations occur (gray region). For cations, the behavior is opposite; on negative hydrophobic surfaces according to the direct order (white region), small ions are better stabilizers than large ions.

simple model solid surfaces, which would encompass both hydrophobic and hydrophilic surfaces and give microscopic insight into these basic questions and yield series reversals for varying surface charge, surface polarity, and salt concentration, has not been reported so far. In this communication, we extend the approach of ref 40 to mixed surfaces consisting of polar and nonpolar surface groups and consider the full coupling of surface charge and surface polarity for both anions and cations. Single-ion interfacial potentials of mean force (PMFs) are obtained using all-atom explicit-water molecular dynamics (MD) simulations for halide and alkali ions at hydrophobic completely CH3-terminated and hydrophilic fully OH-terminated self-assembled monolayers (SAMs). These PMFs are imported into extended Poisson− Boltzmann (PB) theory to yield ionic density profiles, from which interfacial tension increments and surface potentials are derived. Phase diagrams that feature different Hofmeister series as a function of surface charge, salt concentration, and surface polarity are constructed from the long-range force between two surfaces interacting across electrolyte solutions. Two different models for heterogeneous surfaces consisting of mixed polar/ unpolar surface groups are compared. Our two-step approach is validated by favorable comparison with MD simulations at finite salt concentration of c0 = 1 M and by comparison with experimental interfacial tension increments for 1 M sodium halide and alkali chloride solutions. In agreement with the summarized experimental findings, larger ions show less repulsion from a neutral hydrophobic surface with the only exception being lithium, which is less repelled than sodium and potassium. This irregularity, which agrees with experimental interfacial tension increments, is due to the strong binding of the first water solvation shell, which on the unpolar surface, makes Li+ appear larger. We obtain the direct order for both anions and cations on a negatively charged hydrophobic surface. Reversal takes place when changing the sign of the surface charge from negative to positive in agreement with experimental results.18,21,24,28−30 The adsorption at the hydrophilic surface exhibits a complex interplay of ion and surface hydration and of the surface group geometry and the ion size. As a consequence, we obtain a multiplicity of alterations depending on surface charge and salt

nC(r ) =

∫0

r

4πr 2gIW (r′) dr′

(1)

The average number of water molecules in the first hydration shell around an ion is denoted as n1 = nC(r1), where r1 is the position of the first minimum of the bulk RDF. As a check on our modeling assumptions, the density profile for 1 M NaCl at the hydrophobic and hydrophilic SAM surfaces is obtained from 100 ns simulations. All simulations are performed with the Gromacs 3.3.1 simulation package.47 Poisson−Boltzmann Approach for Heterogeneous Surfaces. In our coarse-grained modeling, we consider two limiting scenarios for the interactions of ions with heterogeneous surfaces consisting of hydrophobic and hydrophilic surface groups, as illustrated in Figure 3. In the first scenario, which we refer to as the molecular-scale approach, we assume that ions interact with the surface via an effective potential that corresponds to the weighted average of the hydrophobic and hydrophilic PMFs. This implies that the hydrophobic and hydrophilic groups on the surface are homogeneously distributed down to the molecular scale such that each ion simultaneously interacts with hydrophobic and hydrophilic groups. In this case, the modified PB equation for a planar surface reads q c0 phob phil d2Φ(z) = − ∑ i e−(ξVi (z) + (1 − ξ)Vi (z) + qiΦ(z))/kBT 2 ϵϵ0 dz i 2604

(2)


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ΦDH = lim(Φ(z)e κz), z≫b

RESULTS AND DISCUSSION Cation−Surface Interaction Potentials. In our solventexplicit MD simulations, we study ions at two different surfaces. Figure 4A,B displays the main simulation result, that is, the cation−surface interaction potential at the hydrophobic CH3terminated and at the OH-terminated hydrophilic surface (note that the anionic PMFs are taken from our previous work40 and not reproduced here). The cation adsorption behavior at the hydrophobic surface is similar to the behavior of anions at the air−water interface33,37,49−52 and correlates with the ion size: The largest cation Cs+ adsorbs strongest and shows a pronounced minimum at z = 0.75 nm; at the same separation, K+ is weakly repelled while Na+ is most strongly repelled. However, the behavior of Li+ is more complex and shows a maximum in the PMF at z = 0.7 nm and a local minimum at around z = 0.5 nm, which makes a visual ranking of all cations including Li+ according to their surface affinity difficult. The snapshots in Figure 4D, all taken at the distance z = 0.75 nm where the Cs+ PMF has a minimum, demonstrate that the first hydration layer of all cations is intact at this separation, in contrast to the adsorption behavior of large anions such as I− that partially strip off their hydration shell at the point of maximal surface attraction.40 The snapshots of the hydration structure of Li+ at various surface separations in Figure 4C show that the pronounced free energy barrier of Li+ at intermediate separations of z = 0.7 nm can be associated with the compression of the second hydration layer before hydration water is successively stripped off upon further approaching the surface. The behavior on the hydrophilic surface is different; in Figure 4B, Li+ shows the strongest attraction to the surface with a weak minimum at z = 0.2 nm. The corresponding snapshots of Li+ at z = 0.2 nm in Figure 4E show that Li+ has stripped off the hydration water facing the surface and forms one close contact with one surface oxygen atom. The larger ions Na+ and K+ form contacts with two oxygen atoms, while contact formation of the larger K+ ion requires bending of one alkane chain leading to enlarged repulsion. The minimum of the ion− surface interaction of Cs+ occurs at larger separations (z = 0.55 nm) where this ion has an intact hydration shell, as seen in Figure 4E. Hofmeister Ordering according to Surface Tension. The experimental surface tension at the air−water or oil−water interface exhibits ion-specific effects in a very clear and transparent fashion. Within our approach, the surface tension increment with respect to the uncharged surface at c0 = 0 follows via integration of the Gibbs adsorption equation as

(3)

Note that both scenarios described by eqs 2 and 3 are idealizations and that reality will lie somewhat in the middle, depending on the surface preparation, the size of the surface groups, and the ion sizes. Equations 2 and 3 are solved numerically on a one-dimensional grid with a lattice constant of 1 pm satisfying the boundary conditions (i) Φ(z) = 0 in bulk water (z → ∞) and (ii) Φ(z) = constant for z → −∞. An external surface charge is modeled by the modified boundary condition dΦ(z) |z = 0 = − σsurf dz

(4)

at the surface defined by the mean position of the terminal C and O surface atoms for the hydrophobic and the hydrophilic surfaces, respectively. To calculate the long-ranged forces between two surfaces, we use an asymptotic matching technique.40 In the Debye−Hückel (DH) limit, strictly valid for weakly charged surfaces, the pressure between two charged surfaces reads48 p(D , c0) =

2 ⎛ 2σDH 2 + e Dκ + e−Dκ ⎞ ⎜ Dκ ⎟ ϵϵ0 ⎝ (e − e−Dκ )2 ⎠

(6)

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Here, z is the distance perpendicular to the surface, qi is the charge of ions of type i, c0 is the bulk salt concentration, ϵ0 is the dielectric constant of vacuum, ϵ is the relative dielectric constant of water, (z) is the PMF at the hydrophobic CH3-terminated surface as Vphob i obtained in the MD simulations, Vphil i (z) is the PMF at the hydrophilic OH-terminated surface, and Φ(z) is the electrostatic potential. The parameter ξ corresponds to the surface hydrophobicity, that is, the fraction of nonpolar CH3 groups, where ξ = 1 corresponds to a fully CH3-terminated hydrophobic surface and ξ = 0 to a fully OHterminated hydrophilic surface. In the second limiting scenario, the mesoscale approach, we assume that hydrophobic and hydrophilic groups are segregated and form mesoscale patches on the surface. An ion thus interacts locally either with a purely hydrophilic or a purely hydrophobic surface through the respective PMF. In this case, the ionic densities at the hydrophobic and hydrophilic surface patches are added according to the respective surface fractions ξ and 1 − ξ, and the resulting PB equation reads

ϵϵ0

z≫b

where b is the range of ion−surface interactions. The DH potential ΦDH takes nonlinear charge-renormalization effects at the surface into account; it is calculated directly from the numerical solution of the PB equation at large separations from the surface. Since the interaction pressure in eq 5 is proportional to the square of the effective surface charge σDH, it turns out that the magnitude of σDH is a direct measure of the large-separation interaction between surfaces and thus of the effectiveness of different salt solutions to stabilize solutes against precipitation.

Figure 3. Illustration of the two limiting scenarios considered to model heterogeneous surfaces consisting of hydrophobic and hydrophilic surface groups. (A) Molecular-scale approach: ions interact with an effective potential that results from the weighted average over hydrophobic and hydrophilic surface groups. (B) Mesoscale approach: ions locally interact either with a hydrophobic or a hydrophilic surface patch, and the weighted ionic densities are added. Note that the PB equation leads to nonlinear coupling effects in both scenarios.

q c0 phob d2Φ(z) = − ∑ i ξ e−(Vi (z) + qiΦ(z))/kBT 2 dz i ϵϵ0 q c0 phil − ∑ i (1 − ξ)e−(Vi (z) + qiΦ(z))/kBT ϵϵ 0 i

σDH = lim(ϵϵ0κΦ(z)e κz)

(5) −1

where σDH is the effective surface charge density and κ is the screening length determined by κ2 = 8πq2c0/(ϵϵ0kBT). Note that the DH expression becomes exact at large separations D for two highly charged surfaces if the surface charge density σDH is extracted from the PB electrostatic potential distribution far away from the surfaces via

Δγ = −kBT ∑ i

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∫0

c0

dc0′

Γi(c0′) c0′

(7)


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Γw =

z GDS

∫−∞

ρ (z ) d z +

∫z

∞

(ρ(z) − ρ0 ) dz = 0 GDS

(9)

The interfacial tension increments in Figure 5A,B exhibit a linear dependence on the salt concentration c0, in agreement

Figure 5. Surface tension increment Δγ obtained from thermodynamic integration as a function of the bulk salt concentration c0 for different cations at the hydrophobic (A) and at the hydrophilic surface (B). The inset shows schematically how protein folding is driven by Δγ.

with experimental results at the air−water interface.34 The tension increment is positive for all ion pairs, meaning that the repulsion is dominant. The slope of the interfacial tension increment Δγ at the nonpolar surface in Figure 5A correlates with the single ion adsorption displayed in Figure 4A: the less repulsive the PMFs are, the smaller the slope of the interfacial tension. According to the Setschenow equation, the protein concentration of maximum solubility, csol, upon addition of salt is given by log[csol(c0)/csol(0)] = −ksc0

with the salting-out constant ks. The salting-out constant ks is, via the heuristic expression ks = ξAΔγ, assumed proportional to the solvent accessible area of the solute A, the fraction of hydrophobic surface patches ξ, and the interfacial tension increment Δγ, for which typically the value of the air−water interfacial tension is used.22,53 On the basis of the Setschenow equation and using our results displayed in Figure 5A, the maximal solubility increases as the charge density of the ion decreases corresponding to the indirect Hofmeister order, Na+ < K+ < Li+ < Cs+, in agreement with experimental salting-out data of nonpolar solutes.12,22 Note, that the Li+ ion is irregular in the sense that it is located between K+ and Cs+, but note that this is precisely where Li+ is positioned, for example, with respect to its potency in stabilizing benzene in water. At the hydrophilic surface, the order in Figure 5B is altered. Surprisingly, despite the complex ion−surface interactions displayed in Figure 4B, the tension increment again increases linearly with increasing bulk salt concentration. Due to the specific atomic-scale structure of the hydrophilic surface used by us, the smallest and the largest cations are least repelled while the strongest repulsion is predicted for K+. Interestingly, Hofmeister ranking with a maximum around the “neutral cation” K+ has been observed for the catalytic efficiency of enzymes, where the optimum efficiency depends strongly on the active site of the enzyme.54 To quantitatively relate to experiments, we compare in Figure 6 our PB predictions for the interfacial tension increment at c0 = 1 M bulk salt concentration for sodium halide solutions and alkali chloride solutions with experimental data. Our results for the hydrophobic surface in Figure 6A,B are compared with experimental data at the decane and dodecane−

Figure 4. PMFs for cations at the hydrophobic CH3-terminated SAM (A) and at the hydrophilic OH-terminated SAM (B). Vertical dotted lines denote the position of the Gibbs dividing surface zGDS. (C) Simulation snapshots of Li+ at different surface separations z = 0.3 nm, z = 0.525 nm, z = 0.7 nm, and z = 0.875 (from left to right). For small separations, only the first hydration shell containing four water molecules is shown. For larger separations, water molecules within 5.5 or 6.5 Å of the ion are shown. Simulation snapshots of the cations at the hydrophobic SAM (D) are taken at the position of the minimum in the PMF of Cs+ at z = 0.75 nm. Snapshots of Li+, Na+, and K + at the hydrophilic SAM (E) are taken at the position of the minimum in the PMF of Li+ at z = 0.2 nm and for Cs+ at the position of the minimum in the PMF of Cs+ at z = 0.55 nm. Water molecules within 6 Å of the ions are shown. The size of the ions corresponds to their Pauling radii.

where we have replaced activities by concentrations, which is valid for low concentrations for nearly ideal solutions. The ionic adsorption excess Γi is given by Γi(c0) =

z GDS

∫−∞

ci(z) dz +

∫z

∞

(ci(z) − c0) dz GDS

(10)

(8)

PMF

where the ion density is given by ci(z) = c0e−(Vi (z)+qiΦ(z))/kBT and the position of the Gibbs dividing surface zGDS follows from the requirement that the surface excess for water Γw itself vanishes, 2606


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Figure 6. Interfacial tension increment of sodium halide solutions (A) and of alkali chloride solutions (B) at concentration 1 M at the hydrophobic CH3-terminated SAM obtained by PB modeling (filled circles) and at the hydrophilic OH-terminated SAM for sodium halide solutions (C) and alkali chloride solutions (D). Open symbols denote experimental data for decane and dodecane from ref 55, experimental data for dodecanol from ref 56, experimental data for the air−water interface from ref 34. The interfacial tension increment is similar on the different hydrophobic surfaces. The experimental anomaly of Li+ at the air−electrolyte and decane−electrolyte interfaces in (B) is reproduced by the model for the hydrophobic SAM−electrolyte interface.

electrolyte interface55 and the air−water interface.34 The stronger attraction of cations to a hydrophobic liquid compared to the air−water interface, which leads to the shift of the interfacial tension between the air−water and the decane− water and dodecane−water experimental data in Figure 6B, has been discussed previously.57 Our results agree quite nicely with the oil−water experimental data, even the anomaly of lithium chloride, which has a smaller increment than sodium chloride in the experimental data for the air−water interface and the dodecane water interface, is captured in Figure 7B. Our results

Figure 8. Radial distribution function gIW(r) of the anions F−, Cl−, and I− (A) and the cations Li+, Na+, K+, and Cs+ (B) in bulk. The dashed vertical line in (B) denotes the first maximum in the radial distribution function of Cl− for comparison. Cation coordination number in the first solvation shell n1 as a function of the distance z from the CH3 surface (C) and the OH surface (D). n1 decreases for Cs+, K+, and Na+ as the ions approach the hydrophobic surface indicating reduced ion hydration. In contrast, the hydration shell of Li+ remains intact. At the hydrophilic surface, all ions lose part of their first hydration shell. The open symbols denote the position of the minimum in the ion−surface PMF in Figure 4A,B.

Figure 7. Ion concentration profile of NaCl obtained by PB modeling (solid lines) compared to explicit finite-concentration 100 ns MD simulations (open symbols) at the hydrophobic surface (A) and at the hydrophilic surface (B) for 1 M bulk salt concentration.

for the hydrophilic surface in Figure 6C,D are compared to experimental data at the dodecanol−electrolyte interface,56 which presumably forms a polar surface, since the OH groups are expected to arrange at the interface so as to point to the aqueous phase. Also here, the comparison is satisfactory. The almost quantitative agreement between the experimental data and our PB predictions gives confidence in the choice of the optimized ionic force fields and confirms that force fields optimized for bulk can be transferred to interfacial situations. The PB formalism makes some drastic approximations. The neglect of ion−ion correlations and excluded-volume interactions is known to cause failure of the mean-field approach at high salt concentrations.58 To validate our modeling approach, we compare in Figure 7 ion concentration profiles of 1 M NaCl obtained by explicit MD simulations and the PB formalism. The density profiles agree well and thus validate our coarsegrained two-step modeling approach. In order to more closely look into the lithium anomaly at the hydrophobic surface, we analyze the change in hydration as ions approach a surface. Figure 8A,B show the RDF gIW of anions and cations in bulk water. In the regular order F−, Cl−, and I− and Li+, Na+, K+, and Cs+, the first peak in the RDF

decreases and broadens as ions become larger, meaning that small ions have a tighter bound first hydration shell than larger ions. The vertical broken line in Figure 8B denotes the peak position of Cl− for comparison: even the largest cation considered by us, Cs+, is, based on the RDF, considerably smaller than Cl−. To understand the unexpected behavior of Li+ at the nonpolar surface, we show the number of water molecules in the first hydration shell, n1, for all cations as a function of the ion−surface separation z using eq 1. Note that the hydration shell radius used in the calculation of n1 is taken as a constant and is not dependent on the separation. As can be seen in Figure 8C, at the hydrophobic surface, the large cations Na+, K+, and Cs+ partially strip off their hydration shell facing the surface, and the coordination number decreases gradually as the cations approach the surface. In contrast, the first hydration shell of the small Li+ ion remains intact for all separations from the surface, and Li+ behaves as an ion that has an effectively larger radius. This observed behavior of lithium at the 2607


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hydrophobic SAM is identical to the air−water interface37 suggesting that the underlying adsorption mechanism is similar. The situation is different on the hydrophilic surface. Here, all ions strip off their hydration shell to some extent and bind to the negatively charged oxygen atoms of the surface, see Figure 8D. Hydrophobic Solvation at Nonpolar Surfaces. In order to understand the mechanism of the higher surface affinity of large anions such as iodide, we use a simple theory for the interfacial solvation of a hydrophobic solute that was previously used to describe the ion-specific contribution to the adsorption of ions at the air−water interface.37 This theory is a generalization of the information theory approach, according to which the solvation free energy of a hard sphere is proportional to the probability of the spontaneous formation of a cavity matching the hard sphere.59 For the radii of interest, the solvation free energy of a spherical cavity in bulk SPC/E water is excellently described by μex = ζ4πR3/3 with the prefactor given by ζ = 0.195 kJ/(mol Å3).37 The solvation free energy at an interface is assumed proportional to the fraction of the sphere’s volume that penetrates the interface. For a sharp interface located at z = 0, the solvation free energy in dependence of the distance from the interface z reads37,60

Figure 9. (A) Difference in PMF at the hydrophobic SAM−water interface, ΔVPMF(x, F) = VPMF(x) − VPMF(F), of chloride and fluoride (blue) and iodide and fluoride (green). The two noisy curves are the differences obtained from the MD simulations. The smooth curves are the differences according to the hydrophobic solvation theory. The cavity radii are taken from the position of the first peak in the ion− water radial distribution function shown in Figure 8, RF = 0.274 nm, RCl = 0.325 nm, RI = 0.356 nm, Δz = 0.35 nm for Cl−, and Δz = 0.4 nm for I−. (B) Difference in PMF at the hydrophobic SAM−water interface, ΔVPMF(x, Cs) = VPMF(x) − VPMF(Cs), of lithium and cesium (light blue), sodium and cesium (red), and potassium and cesium (green).

parameters only have a minor influence on the interfacial activity of the ions and are not the main driving force for ion specific adsorption. In Figure 9B, the cation PMF differences ΔVPMF(x, Cs) = PMF V (x) − VPMF(Cs) for x = Li+, Na+, and K+ from the simulations at the hydrophobic surface are shown. We do not show the theoretical predictions, because they fail in a dramatic way. By using the cavity radii from the position of the first peak in the ion−water radial distribution function shown in Figure 8B, the theory predicts all ΔVPMF(x, Cs) to be positive, since according to hydrophobic solvation, all cations should be more strongly repelled from the interface than the Cs+ ion. By contrast, we observe that the differences are negative for small separations, since the Cs+ is most strongly repelled. Moreover, the PMF differences show pronounced oscillations that cannot be explained by our simple solvation theory. The reason for the failure is that the cations are smaller than the corresponding anions and strongly hydrated and that the energetic cost of partial dehydration is not included in the theory. Complete Hofmeister Phase Diagram for Anions. Figure 10A,B shows the Hofmeister series phase diagrams for anions with sodium as a counterion at the completely hydrophilic and hydrophobic surfaces as a function of the external surface charge σsurf and the bulk salt concentration c0. These diagrams are based on the previously obtained anionic PMFs.40 We base the ion ordering on the magnitude of the effective surface charge σDH defined in eq 6. For each point in the phase diagram, the PB equation is solved numerically, yielding the electrostatic potential and via eq 6 the effective surface charge σDH for each electrolyte type. The white region corresponds to the direct order according to which |σIDH| > F |σCl DH| > |σDH|; here, two surfaces will repel most strongly when they are immersed in a NaI solution, and thus, the iodide ion has the strongest stabilizing effect. The phase diagrams exhibit four regions with different series, with the completely reversed I series, the indirect series with |σFDH| > |σCl DH| > |σDH| shown in black, being separated from the direct series by two partially reversed series (shown in gray). In agreement with our discussion in the Introduction, negative hydrophobic surfaces are predominantly characterized by the direct anionic series (see Figure 10B), and negative hydrophilic surfaces tend to show the indirect series (see Figure 10A); note that series

⎧ 4π 3 z < −R , ⎪− R ⎪ 3 0 (z)/ζ = ⎨ 2π 3 V cav π 3 2 ⎪ − R + πR z − z − R < z < R , 3 ⎪ 3 ⎩0 z>R (11)

where R is the radius of the cavity. However, both the SAM− water and the cavity−water interfaces are rough, which leads to broadening of the interfacial density profile that can be extracted from MD simulations.40 The solvation free energy at a broadened interface is given by a convolution ∞

Vcav(z) =

∫−∞ Vcav0(z′)ρ′(z − z′ − Δz)/ρ0 dz′

(12)

where Δz is a shift due to the depletion of water from the hydrophobic surface and the deformation of the interface due to the presence of the ion, ρ′(z) is the derivative of the density profile ρ′(z) = dρ(z)/dz, and ρ0 is the bulk density of water. The water density profile at a hydrophobic surface has been calculated previously, and a fit function can be found in ref 40. The radii of the cavity are taken from the first maximum in the ion−oxygen RDF shown in Figure 8A, B. In Figure 9A, the PMF differences ΔVPMF(x, F) = VPMF(x) − VPMF(F) for x = Cl− and I− are shown. Considering only the difference between anions singles out the ion-specific part of the ion−surface interaction. Since F− is most strongly repelled from the hydrophobic surface, ΔVPMF(x, F) is more negative for I− than for Cl−. The corresponding theoretical predictions are shown as solid lines and agree with the simulated PMFs quite well. Therefore, we see that the ion-specific part of the PMF for the halide anions at the hydrophobic solid−liquid interface is well described by standard hydrophobic solvation theory adapted to the interfacial geometry. We conclude from this that (i) the interfacial affinities of anions at our solid−liquid interface are similar to those at the air−water interface, since at both surfaces, the differences can be explained by the same mechanism and that (ii) polarizability effects that are not captured by the heuristically optimized LJ force-field 2608


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discussed in the Methods section, we use two different procedures for effecting this superposition. Figure 10C shows the Hofmeister series phase diagram for surfaces of varying surface charge σsurf and surface hydrophobicity ξ for constant bulk salt concentration c0 = 200 mM using the molecular-scale approach in eq 2. Note that now the maximal number of 3! = 6 different series orderings that are possible with three distinct ions is obtained; the phase diagram shows besides the direct (white) and indirect (black) order four different alterations. The arrangement of phases is in agreement with the experimental Hofmeister classification of colloids and proteins,18,19,28−30 and the phase diagram is symmetric under the double reversal of the surface charge and the surface polarity. As discussed before, the series reversal when changing the surface from hydrophobic to hydrophilic is a direct consequence of the different surface affinities of the anions to the hydrophobic and the hydrophilic surfaces and occurs at relatively large OH-surface concentrations (ξ < 0.01). The reversal of the ordering when changing the sign of the surface charge originates from the compensation of the explicit surface charge σsurf and the surface charge due to specific ion adsorption. At the hydrophobic surface, strongly adsorbing anions such as iodide increase a negative surface charge further and lead therefore to the highest stabilization. In contrast, at positively charged hydrophobic surfaces, strongly adsorbing anions lead to the most efficient charge compensation and therefore to the weakest stabilization. Figure 10D shows the Hofmeister series phase diagram using the mesoscale approach in eq 3. The results from the two models in Figure 10C,D are qualitatively similar, showing that the molecular-scale and mesoscale heterogeneities have the same ion-specific effects. In the following, we will focus on the molecular-scale approach that is microscopically applicable if the hydrophobic and hydrophilic surface groups are well mixed down to the molecular scale. Stabilization in Dependence of Salt Concentration and Surface Charge. We now return to the cations and start the discussion with Cs+, K+, and Na+ (without Li+) to simplify matters. Before discussing the full phase diagrams, we analyze the relation between the long-ranged forces and the external surface charge and salt concentration. The dependence of ΦDH on the bulk salt concentration is shown in Figure 11A,B for the hydrophobic and the hydrophilic surface. At the hydrophobic surface in Figure 11A, the increasing surface affinity with increasing size of the cations is clearly recognized: The large Cs+ ion adsorbs stronger than Cl−, leading to a positive potential, while for the smaller cations, the potential is negative due to stronger Cl− adsorption. The surface affinity follows the series Cs+ > K+ > Na+ in agreement with cation adsorption at silica surfaces.31 However, the stabilization power depends only on the magnitude of the effective surface charge, since the pressure p is proportional to σ2DH (eq 5). Therefore, the direct Hofmeister series is obtained for the uncharged hydrophobic surface where Cs+ is least stabilizing. At the hydrophilic uncharged surface in Figure 11B, the differences between the cations are much less pronounced, and at intermediate salt concentration, the lines for K+ and Na+ cross, which means that the two ions exchange their position in the series. Figure 11C,D shows the dependence of the magnitude of the DH potential |ΦDH| on the external charge σsurf for a constant bulk salt concentration c0 = 200 mM. At the hydrophobic surface, ΦDH depends linearly on surface charge. For negative surface charges, one obtains the direct order, since the strong

Figure 10. Hofmeister phase diagrams for anions at the hydrophilic OH-terminated SAM (A) and at the hydrophobic CH3-terminated SAM (B) in dependence of the external surface charge σsurf and the bulk salt concentration c0 with Na+ as the counterion. (C) Hofmeister phase diagram for heterogeneous hydrophobic/hydrophilic surfaces according to the molecular-scale approach (eq 2) in dependence of σsurf and the surface hydrophobicity ξ for constant bulk salt concentration c0 = 200 mM. (D) Hofmeister phase diagram for heterogeneous hydrophobic/hydrophilic surfaces according to the mesoscale approach (eq 3). Colored areas denote regions featuring direct order (white), indirect order (black), and four different alterations. The ordering of the ions corresponds to their efficiency in stabilizing solutes against precipitation based on the magnitude of the effective surface charge |σDH|. The dashed lines are the instability lines for NaI (red), NaCl (blue), and NaF (black) on which the longrange repulsion vanishes, i.e., σDH = 0, and thus, the bare surface charge is canceled by ion adsorption .

reversal can also be induced by changing the salt concentration, reflected by the fact that the phase boundaries are not horizontal lines. Typical protein surfaces consist of a mixture of polar/ nonpolar groups or patches. Roughly speaking, the surface of a protein contains one-third hydrophobic and two-thirds hydrophilic groups, while the interior of a protein contains only about one-third hydrophilic groups associated mostly with the backbone.61 The same holds for synthetic colloids and many other solutes, which are all characterized by varying amounts of mixed hydrophilic and hydrophobic surface groups. Cosolute effects on a large variety of functional groups have been found experimentally to be additive; the adsorption of ions on polar and nonpolar surface groups can thus to first approximation be viewed as the superposition of both separate processes.62 As 2609


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Figure 11. DH potential ΦDH in dependence of the bulk salt concentration c0 at the uncharged hydrophobic surface (A) and at the uncharged hydrophilic surface (B). Absolute value of the DH potential |ΦDH| for constant bulk salt concentration c0 = 200 mM in dependence of the external surface charge σsurf at the hydrophobic (C) and the hydrophilic surface (D). Dashed vertical lines mark the locations at with ΦDH cross, and thus, two ions exchange their position in the Hofmeister series. Figure 12. Hofmeister phase diagrams for the cations Cs+, K+ and Na+ at the hydrophilic OH-terminated SAM (A) and at the hydrophobic CH3-terminated SAM (B) in dependence of the external surface charge σsurf and the bulk salt concentration c0 with Cl− as the counterion. Colored areas denote regions featuring direct series (white), indirect series (black), and four different alterations. The ordering of the ions corresponds to their efficiency in stabilizing solutes against precipitation based on the magnitude of effective surface charge |σDH|. The dashed lines are the instability lines for CsCl (gray), NaCl (blue), and KCl (green) on which |σDH| = 0.

adsorption of Cs+ compensates the external charge most efficiently and leads to the weakest stabilization. The situation is reversed for positive surface charges where the strong adsorption of Cs+ leads to the highest effective charge and therewith to the highest stabilization. An alteration of two ions occurs when their DH potentials |ΦDH| are equal; in Figure 11C,D, this corresponds to the crossing of two lines and is indicated by vertical dashed lines. An instability point is defined as the external charge, the so-called critical charge σcrit, for which at a given bulk salt concentration, the long-range repulsion vanishes as the external charge is exactly canceled by specific adsorption and ΦDH = 0. At such a point, the effective surface charge σDH changes its sign. Complete Hofmeister Phase Diagram for Cations. Figure 12A,B shows the Hofmeister phase diagram for the cations Cs+, K+, and Na+ in dependence of external surface charge and bulk salt concentration for the cations at the hydrophilic and the hydrophobic surface. At the hydrophilic surface, the phase diagram shows four different series that are arranged in six phase regions. Again, cations are ordered according to their stabilizing ability based on the magnitude of the effective surface charge |σDH|. The indirect order in which Cs+ is most stabilizing and Na+ is most destabilizing occurs at large salt concentrations or large positive surface charges. The direct order is never observed. The critical charge σcrit is always negative, meaning that the surface affinity of all cations is larger than that of Cl−. Due to the complex ion−surface interaction at the hydrophilic surface, a multitude of alterations occur. At the hydrophobic surface, the phase diagram in Figure 12B is similar as for the halide anions: On negatively charged surfaces the series is direct. With increasing surface charge, it undergoes two partial alterations, until finally at large positive charges, one ends up with the indirect order. The critical charge is negative for Cs+, since the large cation has a higher surface affinity than Cl− while the critical charge is positive for Na+ and K+ due to the larger surface affinity of Cl−. Salt concentration dependent alterations are predicted for intermediate positive surface charges such as for anions.

Figure 13A,B shows the Hofmeister phase diagrams for LiCl, NaCl, and CsCl at the polar and nonpolar surfaces. The diagram for the polar surface shows five different series and strikingly no alteration in the ordering if the sign of the surface charge is changed at large salt concentrations in agreement with experimental results for hydrophilic colloids.28 The situation at the hydrophobic surface is as expected, Figure 13B; the cation with the largest surface affinity, Cs+, is least stabilizing at negatively charged surfaces, since it compensates the surface charge most efficiently. At the nonpolar surface, we do not predict the direct Hofmeister series as shown in Figure 1 due to the unusual behavior of the strongly hydrated Li+. Figure 13C shows the Hofmeister phase diagram for LiCl, NaCl, and CsCl for varying surface charge σsurf and surface hydrophilicity ξ for constant bulk salt concentration c0 = 200 mM. The phase diagram for cations differs from the diagram for anions in Figure 10C in that it is not symmetric under the double reversal of surface polarity and surface charge. We do Na Li see the indirect order |σCs DH| > |σDH| > |σDH|, but we do not see the fully reversed direct order. The reason is that (i) Li+ remains hydrated for all ion−surface separations and (ii) the complex adsorption behavior of the cations at the polar surface leads to additional alterations in dependence of external charge and salt concentration. For positive surface charges, the series is quite robust, and no alterations occur when changing the surface hydrophobicity while two partial alterations occur on negatively charges surfaces. Still, these alterations occur only at large OH-surface concentrations (ξ < 0.01). 2610


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where H = 2.2 × 10−21 J is the Hamaker constant for silica surfaces31 and ΦDH is the asymptotic surface potential that follows from our nonlinear PB calculation according to eq 6. In our comparison with the experimental data from ref 31, the ionsurface PMF at the hydrophobic CH3-terminated SAM is used. This amounts to the assumption that the ion-specific ion− surface interactions are dominated by unpolar groups on the surface. Figure 14A shows the effective surface charge σDH in

Figure 14. (A) Effective surface charge σDH vs bulk salt concentration c0 and (B) force between a sphere and a planar surface divided by colloid radius for constant salt concentration c0 = 10 mM vs separation for surface charge σsurf = −0.022e/nm2 and NaCl (red), KCl (green), CsCl (gray), and LiCl (light blue).

dependence of the bulk salt concentration c0 for the four different salts for a negatively charged surface. The bare surface charge σsurf is adjusted such that the effective surface charge σDH at 100 mM NaCl equals the value given in ref 31: σDH = −0.051e/nm2, leading to σsurf = −0.022e/nm2 for our CH3terminated SAM. At small salt concentrations, σDH is negative, indicating negligible cation adsorption. At higher salt concentration, ionic adsorption becomes increasingly important: The large adsorption of Cs+ leads to charge reversal and hence a positive effective surface charge, while for the other cations, σDH stays negative. From Figure 14A, we infer that the adsorption strength at the CH3-terminated SAM follows the series Cs+ > Li+ > K+ > Na+ in agreement with the experimental results at silica surfaces31 (note that the adsorption of Li+ has not been measured in those experiments). Figure 14B displays the force in dependence of the separation D for 10 mM salt concentration. At large separations, the curves decay exponentially, and the effect of van der Waals attraction appears only at small separations. The magnitude of the force is in qualitative agreement with the experimental results for silica surfaces and identical salt concentration.31 Figure 15A−D shows the force in dependence of the separation for different salt concentrations, where the solid black lines show the pure van der Waals attraction. At low salt concentrations (c0 = 50 mM) in Figure 15A, the divergent minimum at D = 0 is separated by a force maximum from the long-ranged repulsive part. The barrier height follows the series Na+ > K+ > Li+ > Cs+, which is opposite to the adsorption strength, since the strongest adsorption for Cs+ leads to the strongest surface charge compensation and therefore to the weakest repulsive force. For c0 = 100 mM in Figure 15B, the force turns attractive for CsCl solutions, and for c0 = 200 mM in Figure 15C, the force barrier is absent for LiCl as well. At large salt concentration c0 = 500 mM in Figure 15D, the force barrier again increases for NaCl and KCl and reemerges for LiCl, whereas the force for Cs+ remains attractive up to the highest concentration used. The reemerging repulsive force barrier at intermediate distances and salt concentration for some of the ions highlight the subtle interplay of ion-specific adsorption at the surfaces and screening of the bare surface charge. The results in Figure 15 recover the trends of the experimental results for silica

Figure 13. Hofmeister phase diagrams for the cations Cs+, Na+, and Li+ at the hydrophilic OH-terminated SAM (A) and at the hydrophobic CH3-terminated SAM (B) in dependence of the external surface charge σsurf and the bulk salt concentration c0 with Cl− as the counterion. (C) Hofmeister phase diagram for mixed hydrophobic/ hydrophilic surfaces in dependence of σsurf and the surface hydrophobicity ξ for constant bulk salt concentration c0 = 200 mM. Colored areas denote regions featuring indirect series (black) and four different alterations. The direct Hofmeister order is not observed due to the unusual behavior of Li+ at the hydrophobic surface and Cs+ at the hydrophilic surface. The ordering of the ions corresponds to their efficiency in stabilizing solutes against precipitation based on the magnitude of the effective surface charge |σDH|. The dashed lines are the instability lines for CsCl (gray), NaCl (blue), and LiCl (green) on which |σDH| = 0.

Cationic Specificity in Force Profiles between Silica Surfaces. In the following, we calculate force profiles between a planar surface and a sphere with parameters matching recent measurements of the force between a silica colloid and a silica surface using an atomic force microscope.31 By using the Derjaguin approximation, the force in the asymmetric planesphere setup is given by63 F(D) plane (D) = 2πVtot (13) R with the total interaction potential between two planar half spaces given by plane Vtot (D) = −H /(12πD2) + 2ϵϵ0κ Φ2DHe−κD

(14) 2611


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Hofmeister series is not intrinsically weaker for cations compared to anions; it just so happens that ordinary cations are smaller than anions typically considered. On the hydrophilic surface, the single cation adsorption behavior is complex. This complexity leads to small differences in macroscopic quantities and to a multiplicity of alterations in dependence of surface charge and bulk salt concentration. With so many specificities even for the relatively simple polar model surface presented here, it is clear that there is not a universal series that describes cationic Hofmeister trends on all different polar surfaces. In the following, we point out directions for future research: (i) In our approach, we obtain ion−surface PMFs from simulations for uncharged surfaces, while a net surface charge is only accounted for in the PB approach in a homogeneous, smeared-out fashion. Real charged surfaces show varying degrees of charge localization around charged groups, which is expected to have important consequences on the ion binding. (ii) Different hydrophilic surface groups are known to differ in their ionbinding characteristics and give rise to what can be called surface-group specific behavior.65−67 More studies in that direction are needed. (iii) More complex molecular or multivalent ions can in principle be modeled as well, but the development of suitable force fields is challenging and will require modification of the force-field combination rules, as was recently shown for divalent cations.68 (iv) The PB theory neglects nonelectrostatic ion−ion interactions, which become important at higher salt concentrations. Theories that account for ion−ion interactions beyond the mean-field level can also incorporate ion−ion PMFs from explicit-solvent MD simulations69 and shall be used in the future.

Figure 15. Force between a sphere and a planar surface divided by colloid radius vs separation for NaCl (red), KCl (green), CsCl (gray), and LiCl (light blue) for bare surface charge σsurf = −0.022e/nm2 and different bulk salt concentrations: (A) c0 = 50 mM, force exhibits a repulsive range for all salts; (B) c0 = 100 mM, no repulsion for Cs+; (C) c0 = 200 mM, no repulsion for Li+ and Cs+; (D) c0 = 500 mM, increased repulsion for Na+ and K+ and a re-emerging maximum for Li+. The black line corresponds to pure van der Waals attraction.

surfaces.31 Hence, we suggest that ion adsorption at silica surfaces can in a certain pH range be modeled to first approximation similar to ion adsorption at hydrophobic surfaces.

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CONCLUSION Theories addressing Hofmeister series effects are abundant. None of the proposed theoretical frameworks accounts for the full spectrum of direct, reversed, and altered sequences as the charge of the ion, the charge of the surface, and the surface polarity are varied. In our two-step approach, we first use explicit-water MD simulations and extract realistic single-ion surface potentials at hydrophilic and hydrophobic surfaces. These potentials include (i) direct ion−surface interaction at the atomistically resolved surfaces and (ii) hydration effects of the ion and the surface. The ion-specific part of the anion− hydrophobic surface interaction can be explained by interfaceadapted hydrophobic solvation theory, but the same approach fails for cations, which clearly shows that the small size of cations compared to anions makes cations less regular. In the second step, we incorporate single-ion PMFs into PB theory and calculate ion density and potential distributions at heterogeneous surfaces. The resulting interfacial tension increments agree quantitatively with experimental data, capture the Hofmeister trend, especially the anomaly of lithium, and thereby justify our choice of ionic force fields. In addition, the satisfactory agreement of our PB predictions with explicit MD simulations at finite salt concentration further justifies our approach. The capability of ions to stabilize a colloidal or protein solution against precipitation is measured based on the effective charge due to ions adsorbing on a surface. On hydrophobic surfaces, the effective charge is similar for anions and cations of comparable size, in agreement with recent experimental measurements.64 Large anions such as iodide have a high hydrophobic surface affinity and increase the effective charge on negatively charged surfaces further. In contrast, large cations such as cesium also have a large hydrophobic surface affinity and thereby compensate an external negative charge surface charge most efficiently, which explains the difference between cations and anions displayed in Figure 2. As a matter of fact, the

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ASSOCIATED CONTENT

S Supporting Information *

The fitting functions used for the PMFs and tables containing all fitting parameters; further information about the equilibration of the simulations and the influence of the ionic force field. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge financial support from the International Doctorate Program NanoBioTechnology (IDK-NBT), the Elite Netzwerk Bayern (ENB) and the German−Israeli Foundation for Scientific Research and Development (GIF) in the project “Ion specific interactions between functionalized surfaces". The Leibniz Rechenzentrum Munich is acknowledged for supercomputing access (project pr63ca).

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REFERENCES

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