Specific Ion Binding to Carboxylic Surface Groups and the pH

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Specific Ion Binding to Carboxylic Surface Groups and the pH Dependence of the Hofmeister Series Nadine Schwierz, Dominik Horinek, and Roland R. Netz Langmuir, Just Accepted Manuscript • DOI: 10.1021/la503813d • Publication Date (Web): 12 Dec 2014 Downloaded from http://pubs.acs.org on December 17, 2014

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Specific Ion Binding to Carboxylic Surface Groups and the pH Dependence of the Hofmeister Series Nadine Schwierz,∗,† Dominik Horinek,‡ and Roland R. Netz∗,¶ Chemistry Department, University of California, Berkeley, CA 94720, USA, Institut f¨ ur Physikalische und Theoretische Chemie, Universit¨ at Regensburg, 93040 Regensburg, Germany, and Fachbereich f¨ ur Physik, Freie Universit¨ at Berlin, 14195 Berlin, Germany E-mail: [email protected]; [email protected]

Abstract Ion binding to acidic groups is a central mechanism for ion-specificity of macromolecules and surfaces. Depending on pH, acidic groups are either protonated or deprotonated and thus not only change charge but also chemical structure with crucial implications for their interaction with ions. In a two-step modeling approach, we first determine single-ion surface interaction potentials for a few selected halide and alkali ions at uncharged carboxyl (COOH) and charged carboxylate (COO− ) surface groups from atomistic MD simulations with explicit water. Care is taken to subtract the bare Coulomb contribution due to the net charge of the carboxylate group and thereby to extract the non-electrostatic ion-surface potential. Even at this stage, pronounced ion-specific effects are observed and the ion surface affinity strongly depends on whether the carboxyl group is protonated or not. In the second step, the ion surface ∗

To whom correspondence should be addressed Chemistry Department, University of California, Berkeley, CA 94720, USA ‡ Institut f¨ ur Physikalische und Theoretische Chemie, Universität Regensburg, 93040 Regensburg, Germany ¶ Fachbereich f¨ ur Physik, Freie Universität Berlin, 14195 Berlin, Germany †

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interaction potentials are used in a Poisson Boltzmann model to calculate the surface charge and the potential distribution in the solution depending on salt type, salt concentration and solution pH in a self-consistent manner. Hofmeister phase diagrams are derived based on the long-ranged forces between two carboxyl-functionalized surfaces. For cations we predict direct, reversed and altered Hofmeister series in dependence of the pH, qualitatively similar to recent experimental results for silica surfaces. The Hofmeister series reversal for cations is rationalized by a reversal of the single-cation affinity to the carboxyl group depending on its protonation state: the deprotonated carboxylate (COO− ) surface group interacts most favorably with small cations such as Li+ and Na+ , whereas the protonated carboxyl (COOH) surface group interacts most favorably with large cations such as Cs+ and thus acts similarly to a hydrophobic surface group. Our results provide a general mechanism for the pH dependent reversal of the Hofmeister series due to the different specific ion binding to protonated and deprotonated surface groups.

Introduction Most physico-chemical processes in electrolyte solutions not only depend on the concentration and valency of the ions, but also on the ion type. Remarkably, despite the complex origin of these ion specific effects and the still on-going scientific interest, they have been discovered over a century ago by Franz Hofmeister in his famous protein precipitation experiments. 1 In fact, the series found by Hofmeister, governs a variety of different properties of electrolytes, including the surface tension increment, the solubility of gases and colloids, diffusion processes as well as chemical reaction kinetics. 2,3 Over the last years, the previously believed universal Hofmeister order has been replaced by a diverse spectrum of direct, altered and reversed Hofmeister series while state-of-theart experiments unraveled the influence of temperature, salt concentration, pH, buffer type and other external parameters on the Hofmeister ordering. 4–10 In particular, Hofmeister

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series reversal by pH has been observed on oxide surfaces 10–13 and for the aggregation of proteins, 14–16 which forms the motivation for the present theoretical work. There is emerging evidence that ion specific effects, related to the aggregation of particles or macromolecules (including protein folding), are caused by ion binding or depletion from the particle/water interface. 17 Still, the mechanism by which ions are attracted to or repelled from biological interfaces is highly complex and results from the competition of direct ionsurface and indirect hydration-related interactions. 18 For simple planar non-polar surfaces like the air/water interface or the interface between water and a hydrophobic solid or liquid, the adsorption propensity of large anions such as iodide 19,20 was rationalized in terms of interfacial adapted hydrophobic solvation theory. 21–24 Some theories discussed ion-specificity in terms of the ion polarizability 23,25 which is proportional to the ion volume and thus scales similarly as the hydrophobic solvation contribution. Still, a general theory for ion-surface interactions that encompasses hydrophobic as well as hydrophilic surfaces is missing, due to the complex interactions between surface groups, ions and the solvation water. On the other hand, effective ion-surface interactions can be readily extracted from MD simulations 25–27 and incorporated into coarse-grained theories, 25,26,28 thereby providing a link between the microscopic adsorption behavior of the ions and macroscopic, experimentally accessible quantities. For simplified ion-surface interactions the self-consistent equations describing the ion distributions on a mean-field level can even be solved analytically, which allows for a global analysis of the ion-specific behavior of charged surfaces. 29 Acidic surfaces are of special interest in nature and technology. In contact with water such surfaces acquire a negative charge by deprotonation. Prominent examples are minerals with hydroxide surface groups and protein surfaces. 30 In the context of protein folding and denaturation, carboxylate groups are of special interest, since they are frequently present on the surface of proteins. In particular the binding of small ions like sodium to carboxylates and backbone carbonyls can shift the equilibrium from the folded to the unfolded state. 31 In

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this context it is important to note that deprotonation of a carboxylic surface group not only changes the surface charge but also the chemical surface structure, as the absence or presence of a surface hydrogen modifies the interaction with surrounding ions and solvation water in a way that goes beyond the mere description in terms of the surface charge. This distinction between the chemical surface structure and the surface charge is relevant beyond the pure academic interest since it can be resolved in advanced experiments at variable solution pH and under potentiostatic control. 32 So far scientific work has focused on ion-pairing of cations with the carboxylate anions in solution or the pairing of cations with charged carboxylic groups on protein surfaces. 33–36 In water, the binding strength of cations with carboxylate anions decreases with increasing ion size in the sequence Li+ > Na+ > K+ > Cs+ . 17,36 This corresponds to the so-called inverse Hofmeister series and simply reflects that small ions are attracted more strongly to the charged carboxylate group, although the microscopic reason for this is rather subtle and involves solvation water in a nontrivial way. 36 Here, we expand previous studies and investigate specific ion binding to carboxyl-functionalized surface groups in the deprotonated and also in the protonated state, from which we derive pH-dependent Hofmeister series. Using MD simulations with explicit water, we first calculate ion specific interaction-potentials at surfaces containing uncharged carboxyl and charged carboxylate groups. The resulting ion-specific potentials differ substantially for the protonated and deprotonated carboxylic forms, in particular for the cations. Subsequently, the ion-surface potentials are incorporated into Poison-Boltzmann (PB) theory, which describes ion density profiles on a mean-field level. Within this framework the deprotonation degree of carboxylic surface groups is determined by the solution pH, the acidic dissociation constant pKa as well as electrostatic interactions with nearby surface groups in a self-consistent manner. Here, it proves important to account for the hard-core repulsion between ions via a modified PB model that prevents unrealistically high ion densities at the surfaces, in particular for the small cations that bind strongly to the carboxylate surface groups. From the

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PB calculation we derive surface tension increments as well as effective surface charges and surface potentials that depend on the combination of two processes, namely i) surface group deprotonation leading to a bare surface charge and ii) ion-specific surface adsorption. From the effective surface charge, which is indicative of the long-ranged interaction between two similar surfaces, we derive Hofmeister series diagrams that, as a function of salt concentration and pH, show different ion orderings in terms of the strength of the repulsive inter-surface interaction. For cations the Hofmeister series diagram features regions of direct, reversed and altered Hofmeister series in dependence of pH. In fact, a reversal of the Hofmeister ordering with pH has been recently seen experimentally for silica surfaces. 10 Our results suggest that such a pH-dependent Hofmeister reversal is a general fingerprint of acidic surfaces. Moreover, we provide insight into the underlying microscopic mechanism: For low pH most carboxylic surface groups are protonated and thus charge neutral. For COOH, the partial charges of the surface oxygens are quite low and the large Cs+ cation is attracted more strongly to the surface than Li+ and Na+ , which is the normal Hofmeister series as it is also observed on hydrophobic neutral surfaces. 24 At high pH most carboxylic groups are deprotonated. In COO− , the partial charge on the oxygens is increased and now the smaller cations such as Li+ and Na+ are attracted more than the large cation Cs+ . This is nothing but the law of matching water affinities 37 adapted to the pH-dependent protonation-deprotonation equilibrium of acidic surface groups.

Methods Simulation Details In the simulations the surface is a 3.5 × 3.46 nm2 self-assembled monolayer (SAM) consisting of 56 C20 H41 chains with terminal COOH-groups for the uncharged surface. For the charged surface one COOH-group is replaced by a terminal COO− -group. The chain lattice spacing 5


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corresponds to a gold (111) substrate. The lower six C-atoms of each chain are restrained by harmonic potentials with spring constant k = 5×105 kJ/(mol nm2 ). A tilt angle of 30◦ is fixed by the restrained atoms close to experimental values. The simulation box has an extension of 9 nm in the z-direction and is filled with about 2,700 SPC/E water molecules. The SAM is modeled with the GROMOS96 force field. 38 The force field parameters used for anions and cations were previously optimized to reproduce thermodynamic solvation properties. 39 Using these carefully optimized force field parameters therefore ensures correct water-ion and ion-ion interactions. From the three different cation parameter sets given in 39 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. 40 All force field parameters for the ions and surfaces are listed in the supporting information. The simulations are done at a temperature of 300 K and a pressure of Pz =1 bar maintained by anisotropic pressure coupling, corresponding to the NAPz T ensemble. Periodic boundary conditions are applied, long range Coulomb forces are calculated using the particle-mesh Ewald summation 41 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 potential of mean force (PMF) is calculated by umbrella sampling 42 with a window spacing of 0.025 nm and 3-10 ns simulation time discarding the first 1 ns for equilibration. A time step of 2 fs and the weighted histogram analysis method 43 with force constant kz = 1000 kJ/(mol nm2 ) is used. For the charged surface, we use an additional two-dimensional harmonic potential with kB T /kx,y = 0.0145 nm2 to laterally confine the ion above the charged group. All simulations are performed with the Gromacs simulation package. 44

Poisson-Boltzmann Modeling In the second step of our modeling approach the PMFs obtained in the MD simulations are imported into Poisson-Boltzmann (PB) theory. To account for surfaces of varying degree of deprotonation, we use the so-called molecular-scale approach, where the effective ion6


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surface interaction results from the weighted average of the potentials of the uncharged COOH-groups and the charged COO− -groups. 24 The PB equation including the ion-specific PMFs of anions and cations at the COOH-terminated SAM, ViCOOH (z), and at the charged −

COO− -terminated surface, ViCOO (z), then reads ǫǫ0

X d2 Φ(z) = qi ci (z) dz 2 i=±

(1)

with the ionic densities determined by

ci (z) = c0 e

−

− (1−ξ)ViCOOH (z)+ξViCOO (z)+qi Φ(z) /kB T

.

(2)

Here, z is the distance perpendicular to the surface, qi is the charge of ions of type i, c0 is the bulk salt concentration, ǫ0 is the dielectric constant of vacuum, ǫ is the relative dielectric constant of water, and Φ(z) is the electrostatic potential. In general, the dielectric constant depends directly on the salt concentration 45 and should be used at high salt concentrations. Note that we use a planar surface in this work and neglect the effect of surface curvature. 46,47 The parameter ξ is the degree of deprotonation and corresponds to the fraction of charged COO− -groups on the surface. Thus, ξ = 0 corresponds to an uncharged COOH-terminated surface and ξ = 1 corresponds to a fully charged COO− -terminated surface. In eq 2, the expectation value of the deprotonation degree is used in the exponent. Replacing the expectation value of the exponential by the exponential of the expectation value is equivalent to the mean-field approximation which forms the central assumption in deriving PoissonBoltzmann theory. 48 The PMFs obtained by simulations are fitted by heuristic fit functions which are given explicitly in the supporting information. Eq 1 is solved numerically on a one-dimensional grid with a lattice constant of 1 pm yielding the ion concentration profiles c± (z)/c0 perpendicular to the surface and the electrostatic potential Φ(z) for variable deprotonation degree ξ and bulk salt concentration c0 (see Figure 1A,B for an illustration). The potential satisfies the bulk boundary condition Φ(z → ∞) = 0. In addition, we use 7


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the constant charge boundary condition dΦ(z)/dz = −σsurf /ǫ0 ǫ at the surface located at z = 0. The surface position z = 0 is defined by the mean position of the surface oxygen atoms (see Figure 1C for an illustration) and thus reflects the fact that the surface charge is localized in the oxygen atoms. The surface boundary condition can be rewritten in terms of the deprotonation degree ξ as dΦ(z)/dz|z=0 = −ξσCOO /ǫ0 ǫ, where σCOO = −4.624 e/nm2 corresponds to the surface charge density of the COO− -group. At large surface separation D > κ−1 , the pressure between two charged surfaces that follows from the PB equation can be written as 49 2σ 2 p(D) = DH ǫǫ0

2 + eDκ + e−Dκ (eDκ − e−Dκ )2

!

(3)

in terms of the effective Debye H¨ uckel (DH) surface charge density σDH , and where the inverse screening length κ is defined by κ2 = 2q 2 c0 /(ǫ0 ǫkB T ). The DH surface charge density σDH is related to the DH surface potential ΦDH , both can be calculated directly from the numerical solution of the PB equation for a single surface at large separations via ΦDH = lim (Φ(z)eκz ) , z≫d

σDH = lim (ǫǫ0 κΦ(z)eκz )

(4)

z≫d

where d is the range of ion-surface interactions. In our work, the interaction range is set to d = 1.4 nm since the direct ion-surface interactions embodied in the PMFs vanish for larger distances, as demonstrated further below. The DH potential ΦDH and the DH surface charge σDH allow to compare the effective electrostatic repulsion between surfaces in different salt solutions in a fashion that is similar to the common analysis of experimental results. The Gibbs equation at constant pressure and temperature d∆γ = − expressed as

"



8

R zGDS −∞

ci (z)dz +


i=±

Γi dµi can be

!#

(5)

R∞

(ci (z) − c0 ) dz and

X Γi (c0 ) d∆γ(c0 ) ∂ ln y(c0 )  1+ = −kB T  dc0 c0 ∂ ln c0 i=±

with the surface excess of the ionic species Γi =

P

zGDS

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the Gibbs dividing surface zGDS . The activity coefficient y(c0 ) relates chemical potential and concentration and is defined by eµ/kB T = c0 y(c0 ). For ideal solutions the activity coefficient is unity and the last term in eq 5 vanishes. In order to provide insight into non-ideal solution effects, we use experimental values for the activity coefficient 50 and calculate the surface tension increment including non-ideal effects. The experimental data and the fit function used for the activity coefficient are given in the supporting information. Figure 7A shows a comparison for NaCl assuming ideal solution behavior y = 1 (solid blue line) and the result obtained by using the experimental activity coefficient data (dashed blue line). Since non-ideal effects are seen to be small, we assume ideal behavior in the following for all our calculations. For nearly ideal solutions, the activities can be replaced by concentrations and we can write the Gibbs adsorption equation in the following simplified form

∆γ(c0 , σsurf ) = −kB T +

Z σsurf 0

X Z c0

i=± 0

dc′0

Γi (c′0 , σsurf = 0) c′0

′ ′ dσsurf Φ(z = 0, c0 , σsurf ).

(6)

Here Γi denotes the surface excess of ionic species i and Φ(z = 0, c0 , σsurf ) is the surface potential. The Gibbs dividing surface zGDS is calculated from the requirement that the surface excess of water itself vanishes (see supporting information for further details).

Modified Fermionic Poisson-Boltzmann Modeling To ensure that the ionic density does not exceed its physical limit, set by the ionic volume, the hard-core repulsion between ions must be included. In the simplest approach, the proper ionic densities are calculated from the unrestricted ionic densities for anions c˜− (z) and cations c˜+ (z) using the Fermionic distribution 51,52

c± (z) = √

√

2˜ c± (z) 2 + a3+ (˜ c+ (z) − c0 ) + a3− (˜ c− (z) − c0 )

9


(7)

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with the effective diameters of positive and negative ions a+ and a− . Eq 7 restricts the √ maximum density to cmax = a−3 2 corresponding to the density of close-packed spheres ± with diameter a± . Steric effects become important at large salt concentrations, high surface charge densities and for large ion-surface interaction strengths. The maximum density cmax depends on the effective diameter and therefore on the ion type. In order to provide consistent results, the effective diameters of positive and negative ions are taken from the first peak in the ion-water radial distribution function obtained in previous simulations. 24 As before, the unrestricted ionic densities c˜± (z) follow from the Boltzmann distribution

c˜± (z) = c0 e

−

− (1−ξ)V±COOH (z)+ξV±COO (z)+q± Φ(z) /kB T

.

(8)

Combining eq 1, 7 and 8 yields the modified Poisson-Boltzmann equation that will be used in the following unless stated otherwise. Figure 2A shows a comparison of the ionic density profiles ci (z)/cmax for NaCl using the unmodified approach (dotted lines, eq 1 and 2) and the modified approach (solid lines, eq 1, 7, 8). Figure 2B displays the pH as a function of the deprotonation degree ξ for three different concentrations of NaCl using the unmodified Poisson Boltzmann approach defined by eqs 1 and 2. Note that in the limit of vanishing bulk salt concentration, the surface potential diverges and thus the deprotonation ratio ξ approaches zero. 53 For small ξ the pH increases with increasing ξ, as expected, but at larger ξ the pH starts to decrease. This non-monotonic behavior reflects an unrealistically high ionic density close to the charged carboxylate groups caused by the strong interaction between Na+ and COO− (dashed red line in Figure 2A), as will be shown further below. This finding motivates the modified PB modeling which keeps the ionic density below its physical limit (solid red line in Figure 2A). To provide further insight into the role played by the ion-surface interaction strength, we calculate the pH-ξ relation for a simplified ion-surface interaction potential with a square-well

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form 29 VS± (z) = V0± Θ(b − z),

(9)

where Θ(b − z) = 1 inside the interaction range z < b and Θ(b − z) = 0 otherwise. The interaction range is chosen to be b = 0.5 nm. To simplify the discussion, the anionic interaction potential is set to zero, V0− = 0. For the cations we compare three different interaction strength values V0+ = -10, -15, -20 kB T, the results are shown in Figure 2C. For cation-surface interaction strengths V0+ more attractive than -10 kB T we reproduce the non-monotonic dependence of the pH on the deprotonation fraction ξ. Although such a non-monotonic dependence of the pH on ξ in principle could happen and would signal a discontinuous jump in the deprotonation degree for a critical pH value, similar to a liquid-gas first-order phase transition, in the present case the non-monotonic behavior is linked to an unrealistically high ion density at the surface. Figure 2D shows the pH as a function of ξ using the modified Fermionic Poisson Boltzmann approach for the same NaCl concentrations as treated in Figure 2B with the ordinary PB model. We see that the non-monotonicity has disappeared. We conclude that the modified Fermionic PB approach has to be used whenever the ion-surface interaction potential is very attractive. The results are presented for unrealistically high pH values in order to demonstrate that the instability present in the unmodified PB theory has disappeared. It should be clear that at very low as well as very high pH values the large concentration of hydronium or hydroxide and their respective counterions leads to additional competitive adsorption effects that should be taken into account.

Self-consistent equation for the deprotonation degree The uncharged carboxyl groups at the solid/liquid interface deprotonate according to the reaction COOH + H2 O ←→ COO− + H3 O+

11


(10)

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with an equilibrium reaction constant

Ka =

i ξ h H3 O + surface 1−ξ

(11)

where the deprotonation degree is denoted as ξ and the H3 O+ surface concentration is [H3 O+ ]surface . The surface H3 O+ concentration is related to the bulk concentration [H3 O+ ]bulk via the Boltzmann factor 54 h

H3 O+

i

surface

h

= H3 O +

i

bulk

e

−eΦ(zH ) kB T

(12)

where e is the elementary charge and Φ(zH ) the electrostatic potential at the carboxyl hydrogen position zH as obtained by the numerical solution of the PB equation. Note that Φ(zH ) takes into account the electrostatic repulsion between surface charges and depends on the deprotonation degree ξ, the salt concentration and the type of salt due to specific ion adsorption. We use a value of zH = 0.11 nm as extracted from the simulations (Figure 1). We do not include any non-electrostatic interaction between hydronium ions and the interface, as they are matter to debate. Using the definitions of pH and pKa h

pH = − log H3 O+

i

bulk

,

pKa = − log Ka ,

(13)

where log is the common logarithm with base 10, eqs 11-13 yield a self-consistent equation for the pH as a function of the deprotonation degree

pH = log

ξ eΦ(zH ) + pKa − . 1−ξ 2.303kB T

(14)

The last term is the electrostatic contribution that takes ion specificity into account via the ion-type dependent surface potential, without this term the ordinary equation for the acid deprotonation equilibrium in bulk solution is obtained. In the following we use a pKa value

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of 4.76 as appropriate for a monolayer with COOH-groups. 55 This approach to model deprotonation treats the binding of protons differently from all the other ions. The reasons are twofold: Firstly, proton binding is largely quantummechanical in nature and the effective potential of mean force is not known to good accuracy. Secondly, there are no reliable classical force fields for hydronium ions that could be used to model proton binding. In the following, we fix the deprotonation degree and the salt concentration and then use the self-consistent equation 14 to calculate the pH. Evidently, this procedure, which we choose for convenience, is opposite to the experimental situation where the pH is fixed and the deprotonation degree adjusts accordingly, which of course does not restrict the generality of our results. Figure 3A shows the pH as function of ξ for different salts at fixed bulk salt concentration. As discussed in the previous section the pH increases with increasing ξ for all salts. This is reflected by a decreasing surface potential at the surface hydrogen position Φ(zH ) as more and more surface groups deprotonate in Figure 3C. The pH as a function of salt concentration for fixed deprotonation fraction ξ = 0.5 decreases with increasing concentration as shown in Figure 3B. The pH for ξ = 0.5 corresponds to the effective or apparent pKa and is larger than the bare pKa of 4.76 due to electrostatic interactions between surface charges. The decrease in Figure 3B is primarily due to salt screening effects but shows significant modulations due to ion-specific adsorption effects, correspondingly, the surface potential Φ(zH ) in Figure 3D increases with rising salt concentration.

Results and Discussion Ion-surface Interaction Potentials Figure 4 displays the ionic PMFs at the uncharged COOH-terminated and at the charged COO− -terminated SAM. Note that for the PMFs at the charged surface the electrostatic 13


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interaction between the net surface charge and the ionic charge, which is long-ranged, decays as 1/z for large separations from the surface and is repulsive for anions and attractive for cations, has been subtracted. This subtraction is crucial as the subsequent PB modeling includes the long-ranged electrostatics, leaving the Coulombic interaction in the PMFs would therefore amount to a double-counting of the electrostatic interactions. Our subtraction scheme assumes additivity of electrostatic and non-electrostatic interactions between ion and surface on the single-ion level. This is warranted by our Poisson-Boltzmann modeling we use in the second step, which by construction makes the same assumption. The detailed procedure for this subtraction is explained in the supporting information. The anion surface affinity at the neutral COOH-terminated SAM in Figure 4A decreases with increasing ion size and follows the reverse Hofmeister order F− > Cl− > I− , the small fluoride ion shows a large adsorption minimum of about 6 kB T. The order is exactly opposite compared to non-polar surfaces and the air-water interface but matches the result at a polar OH-terminated SAM, 26 as might be expected since COOH contains an OH group. Surprisingly, the surface affinity of the cations at the neutral COOH-terminated SAM in Figure 4B increases with increasing ion size Li+ < Na+ < Cs+ , different from the anions and in contrast to our previous results for an OH-terminated SAM, 24 and corresponds to the direct Hofmeister series. This size reversed binding affinity of cations versus anions can be rationalized with the frequently used law of matching water affinities: 37 Anions preferentially interact with the small hydrogen on the COOH group which has a high surface charge density, the best match in surface charge densities is obtained for small anions such as F− which therefore preferentially adsorb. This is clearly seen in Figures 5A, B and C that show simulation snapshots of F− , Cl− , and I− at the COOH-terminated SAM. At the position of the minimum in the PMF of F− (z = 0.15 nm), the small F− ion simultaneously makes contact to three partially charged hydrogen atoms. This rather stable configuration more than counterbalances the loss of the

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strongly bound hydration water and leads to the pronounced minimum in the F− -surface PMF in Figure 4A. In contrast, the larger Cl− and I− anions can only form 1-2 contacts with hydrogen atoms due to their larger size and the surface geometry, defined by the separation of the alkane chains of the SAM. As a consequence, larger separations between Cl− , I− and the surface are energetically favorable where both the surface and the ion are hydrated. Cations on the other hand interact with the surface oxygens, which have rather low surface charge densities for the neutral COOH group (lower than the oxygen in a single OH group, which explains the difference to our previous results for a hydroxylated surface 24 ). The best match of surface charge densities is obtained for the large Cs+ ion, for the smaller cations the interaction at small distances becomes repulsive because of the high cost of removing the strongly bound hydration water, see Figure 4B. This is illustrated in Figures 5D, E and F that show simulation snapshots of Li+ , Na+ and Cs+ at the COOH-terminated SAM. At the minimum in the PMF of Cs+ (z = 0.275 nm), this cation contacts 2-3 oxygen atoms. Contacts are formed with both carbonyl (C=O) and hydroxyl (C-OH) oxygens. At the same distance Li+ and Na+ energetically prefer to keep their tightly bound hydration shell and as a consequence Li+ and Na+ ions are repelled at small ion-surface separations. To summarize, small anions like F− and large cations like Cs+ preferentially adsorb at the uncharged COOH-terminated SAM. At the charged COO− -terminated SAM the ion-surface interaction potentials in Figure 4C are strongly repulsive for all anions. There is a minor decrease in the surface affinity with increasing ion size according to F− > Cl− > I− , which is more clearly discerned in the surface tension results that will be shown below. For the cations in Figure 4D, we find strong binding of all cations to the charged COO− -group, the affinity decreases with increasing ion size in the order Li+ > Na+ > Cs+ . This order is in agreement with the ordering of the activity coefficient of LiCl, NaCl and CsCl salt solutions, which is indicative of the anioncationic binding affinity in solution. 17,36 It is not clear what causes the pronounced difference between the anionic and cationic PMFs, with the anions showing overall repulsion from the

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charged surface group while the cations show overall attraction. We remind the reader that the PMFs result after the subtraction of the long-ranged Coulombic repulsion between the surface and ion charges, the symmetry breaking between anions and cations therefore most likely reflects deviations of the actual electrostatic interaction between the ions and the surface charge from the prediction based on continuum electrostatics with a uniform dielectric constant. Since our results indicate that the Coulombic interactions are stronger than simple continuum electrostatics would predict, a possible explanation could have to do with a reduced dielectric constant in the surface layer, 56 which is not correctly accounted for in our subtraction scheme. An alternative explanation would involve the overlap of the surface and the ion’s hydration layers. Some insight into the mechanism of the strong cation binding to COO− visible in Figure 4D is obtained from simulation snapshots: The first minimum in the PMFs in Figure 4D corresponds to a contact ion pair, where the cation and the surface carboxylate level off their hydration shells. As seen in the snapshots in Figure 6D-F, the alkali cations take the middle position between two carboxylate oxygens, in agreement with findings from xray adsorption spectroscopy measurements and ab initio calculations. 34 The small Li+ ion approaches the COO− -group very closely, while the large Cs+ ion induces bending of the alkane chain at small separations, as seen in Figure 6D and F, leading to a less attractive Cs+ -surface interaction at small separations. The second minimum in the cationic PMFs in Figure 4D corresponds to a solvent shared ion pair, in which the hydration shell of the cation and the carboxylate group overlap. We find the second minimum to be less stable than the first minimum corresponding to a contact ion pair, in contrast to simulation results for bulk solutions. 36 The reason for this discrepancy could be related to the very different hydration properties of the carboxylate group at a surface as compared to a bulk solution. To summarize, at the charged carboxylate surface group small cations adsorb preferentially, while anions show overall repulsion with only minor differences between different anion types. This again can be illustrated by the law of matching water affinities, the fact that the

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charged COO− -group has a much higher negative surface charge density than the uncharged COOH group explains that small cations bind preferentially to COO− compared to larger cations. That the anions show very little ion-specific effects on COO− can be explained by the fact that the hydrogen as a potential contact partner is missing in the deprotonated form. We note that our results do not agree with conclusions drawn from charge displacement experiments after rapid solution exchange on lipid monolayers, where small cations and large anions have been found to adsorb preferentially regardless of the charge of the monolayer. 57 Further experimental studies where charge displacement data is correlated with ion distributions or ion surface excesses would be desirable to clarify this discrepancy.

Hofmeister Ordering According to Surface Tension Since the surface tension increment is via the Gibbs adsorption isotherm (eq 6) related to the ionic excess at an interfaces, it allows to conveniently classify different ions with respect to their integral affinity to an interface. Ions that are repelled from an interface thereby lead to a positive tension increment and vice versa. As a matter of fact, in the simplest approach to the ion-specific coagulation of colloids and proteins, the maximal solubility is assumed proportional to the surface tension increment and the solvent-accessible area. Also, the influence that salts have on the protein folding transition has been associated with the interfacial tension increment, for which typically the value of the air-water interfacial tension was used. 18,58 In the following we calculate the surface tension increment at the carboxyl/water interface, which is indicative of the solubility of solutes containing carboxyl groups in different salt solutions. Figures 7A, B show the surface tension increment ∆γ as a function of the bulk salt concentration c0 at the uncharged COOH-terminated surface calculated from eq 6 with σsurf = 0. The tension increases with increasing anion size NaF ≪ NaCl < NaI, the reversed Hofmeister order. For the cations the tension is highest in LiCl solutions and increases with 17


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decreasing size CsCl ≪ NaCl < LiCl, the direct series. The tension increment is positive for NaCl, NaI and LiCl since the repulsion dominates. These salts thus give rise to salting-out behavior and decrease the solubility with increasing salt concentration. In contrast, due to the strong adsorption of F− and Cs+ , the tension increment is negative for NaF and CsCl solutions, leading to salting-in behavior, i.e. NaF and CsCl solutions are predicted to increase the solubility of COOH bearing solutes with increasing salt concentration. Figures 7C and D show the surface tension increment for a surface containing a fixed fraction of ξ = 0.1 charged carboxylate groups. Due to charge screening effects, the tension increment now is negative for all different salts. Among the anions in Figure 7C iodide is most strongly repelled. The surface tension increment is therefore largest in NaI solutions, similar to the uncharged surface. For the cations the surface tension increment is significantly smaller for LiCl and NaCl than CsCl, see Figure 7D. As already apparent from the single ionsurface interaction potentials in Figure 4D, binding of the small Li+ and Na+ ions is preferred over the large Cs+ ion in agreement with previous experimental and theoretical results. 33–36 Due to the large negative increment of LiCl and NaCl, unfolding of macromolecules with charged carboxylate groups on their surfaces is favored in solutions containing Li+ or Na+ ions compared to Cs+ ions. It has been suggested that the reason why the intracellular concentration of Na+ ions is quite low compared to larger cations is to counteract detrimental biological consequences of the denaturant Na+ effects. 35,37

pH dependent Hofmeister reversal In the following we quantify the effect different cations have on the interaction between charged surfaces and compare our results to experiments. In contact with an electrolyte solution, a carboxyl-functionalized surface acquires charge by two processes: Deprotonation and specific ion adsorption. With increasing pH, more and more carboxyl groups deprotonate and yield an increasingly negative surface charge. This negative charge is reduced or increased due to specific cation or anion adsorption. These two processes lead to an effective 18


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surface charge, which determines the long-ranged interaction between two surfaces according to eq 3. Note that the effective surface charge σDH enters eq 3 as a square. Therefore, the double layer interaction between similar surfaces is always repulsive and increases with an increasing magnitude of the effective surface charge. Using eq 4 the effective surface charge σDH can be calculated from the long-ranged part of the electrostatic potential. Correspondingly, σDH has been determined experimentally from the long-ranged repulsion between charged surfaces using an atomic force microscope. 7,10 Figure 8 shows σDH as well as the DH surface potential ΦDH as a function of the pH for a fixed small bulk salt concentration c0 = 0.01M that was chosen to match the experimental conditions in Ref. 10 There are striking similarities between the experimental results reported for silica surfaces and our carboxyl-terminated SAMs. Both, in experiments and simulations, σDH and ΦDH decrease monotonically with increasing pH at low pH, exhibiting the direct Hofmeister series according to |ΦDH (LiCl)| > |ΦDH (NaCl)| > |ΦDH (CsCl)|. At a pH of around 8.5 the ordering in Figure 8 is reversed, in the experimental data the same reversal occurs at a slightly shifted pH of around 7. Our modeling links this reversal of the repulsion between two surfaces from the direct Hofmeister series at low pH to the reversed series at high pH to a reversal of the surface affinity of the cations as the carboxyl groups deprotonate with increasing pH. The magnitude of the effective surface charge differs by a factor of 5 in the experiments and the simulations due to the different types of surfaces used. Still, the overall good qualitative agreement between experiments on silica surfaces and our simulations for carboxyl surfaces suggests a common mechanism for the pH dependent reversal of the Hofmeister series at surfaces that acquire negative charge via deprotonation.

Salt-concentration dependent Hofmeister reversal In this section, we focus on the dependence of the effective DH surface potential ΦDH on the bulk salt concentration. In Figure 9A and B we show ΦDH (solid lines) and its magnitude |ΦDH | (broken lines) for fixed high salt concentration c0 = 0.5 M as a function of pH. With 19


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increasing pH ΦDH tends to decrease for all salts which reflects the deprotonation of surface groups. For the anions in Figure 9A, ΦDH is minimal for F− since it has the highest surface affinity of all anions both for uncharged carboxyl and for charged carboxylate groups. Note that the starting point of the curves (ξ = 0) depends on the value of the electrostatic potential at the surface hydrogen position Φ(zH )according to eq 13. For NaF the curves starts at a higher pH value since Φ(zH ) is negative and larger than for NaCl and NaI. At low pH < 3.5, ΦDH is positive for NaI, since the repulsion of I− is stronger than the adsorption of Na+ . In this pH range charge reversal is observed, meaning that the effective and the bare surface charge differ in sign. At pH=3.5 the effective surface potential vanishes for NaI, corresponding to an instability point (indicated by a red circle) since there is no effective electrostatic repulsion at large separations. As the effective electrostatic interaction is proportional to the square of ΦDH , the magnitude |ΦDH | allows to present the Hofmeister ordering in terms of the effective surface-surface interaction in a rather transparent fashion. While ΦDH for the anions in Figure 9A shows no crossing, the magnitude |ΦDH | shows a crossing between NaCl an NaI at a pH of about 3, which corresponds to a partial alteration of I− and Cl− in the Hofmeister ordering based on the electrostatic repulsion between surfaces, indicated by a vertical arrow. For higher pH the reversed Hofmeister series is observed, |ΦDH (NaF)| > |ΦDH (NaCl)| > |ΦDH (NaI)|. For the cations in Figure 9B the situation is more involved with reversals of the Hofmeister order occurring at low and high pH as indicated by vertical arrows. At low pH where the surface is mostly protonated, Cs+ adsorbs strongly to the uncharged carboxyl-groups, overcompensating the negative surface charge of deprotonated surface groups. The effective surface charge vanishes for CsCl at a pH of about 4.5. In contrast, ΦDH is always negative for Li+ and Na+ . The surface potential ΦDH shows a reversal at pH=7, slightly shifted compared to the results for low salt concentration c0 = 0.01 M in Figure 8. As a result we obtain two partial alterations in the ordering of |ΦDH | for low pH and another three alterations around 20


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pH=7. Figures 9C-F show ΦDH (solid lines) and its magnitude |ΦDH | (broken lines) for constant pH as function of the salt concentration. For the anions in Figures 9C and E the reversed Hofmeister series is seen throughout, |ΦDH (NaF)| > |ΦDH (NaCl)| > |ΦDH (NaI)|. Figure 9D displays a partial alteration of the Hofmeister series for the cations at low pH=3 in dependence of the salt concentration, caused by the surface charge reversal for CsCl. The ordering is direct at low salt concentrations, then Cs+ and Na+ exchange their positions, followed by Cs+ and Li+ . Figure 9F shows the series reversal at high pH=7 in dependence of the concentration. Here, the series displays a full reversal from direct at small salt concentrations, with two partial alterations at intermediate, to reversed at large salt concentrations.

Hofmeister State Diagram for Cations We summarize the results for the ordering of the magnitude of the effective surface potential |ΦDH | for the cations in a Hofmeister state diagram in dependence of pH and the salt concentration in Figure 10. For intermediate pH values the phase diagram features an extended region corresponding to the direct series where |ΦDH (LiCl)| > |ΦDH (NaCl)| > |ΦDH (CsCl)| (white). For high pH we obtain the reversed series where |ΦDH (CsCl)| > |ΦDH (NaCl)| > |ΦDH (LiCl)| (black), for very low pH and in between the direct and indirect series regions two partially altered series are encountered (light and dark gray). Our scheme of ordering the ions in terms of the magnitude of the effective DH surface potential classifies the cations according to their efficiency in stabilizing charged particles or surfaces against precipitation. The dashed lines in Figure 10 correspond to lines of instability on which the long-ranged repulsion vanishes because of an exact cancellation between the bare and the adsorbed surface charges. This happens for NaCl on the blue dashed line and for CsCl on the gray dashed line. At high pH, the pH dependent reversal of the Hofmeister series can be understood in terms 21


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of the reversed cationic affinities to the protonated and deprotonated carboxylic groups: The small Li+ ions has higher affinity than Cs+ to the charged carboxylate group, which dominates at high pH. As a consequence the effective surface charge is at high pH smaller for LiCl than for CsCl and therefore CsCl stabilizes surfaces at high pH more than LiCl does. At smaller pH this trend is opposite, Cs+ binds strongest to the neutral carboxyl group, thus reducing the surface charge and giving rise to the smallest stabilization. The additional Hofmeister series alterations we see at low pH have to do with a reversal of the effective surface charge due to the proliferating adsorption of Cs+ (and for high salt concentration also Na+ ) ions to the predominantly neutral surface, as shown in Figures 8 and 9B. Partial series alterations occur in the vicinity of the two instability lines (dashed lines in Figure 10) on which the negative bare surface charge due to deprotonated surface groups is canceled by a balance of specific cation/anion adsorption and repulsion. As discussed in the previous section, for the anions there are series reversals only at very low pH since the ordering of binding affinity remains unchanged as the surface carboxyl groups deprotonate. The corresponding state diagram is therefore rather featureless and not shown.

Conclusion A central mechanism underlying ion specific effects is ion binding to charged surface groups. 59 Here, we investigate specific ion binding to carboxylic groups in their protonated neutral form and their deprotonated charged form and the resulting pH dependence of the ionspecific interaction between surfaces. Our solvent-explicit MD simulations reveal that the surface affinity of cations strongly depends on whether the carboxyl group is dissociated or not. In our modeling approach, we connect the microscopic ion adsorption behavior to the macroscopic effective surface charge using modified Poisson-Boltzmann theory as a function of pH.

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The ion-specific pH-dependent repulsion between carboxylated surfaces shows a reversal of the cation ordering at intermediate pH, similar to experimental results for silica surfaces, 10 which is rationalized by the different cation affinities for the uncharged and charged carboxylic groups. The global Hofmeister state diagram for the cations in terms of the magnitude of the effective surface potential features direct, reversed and altered series dependent on pH and salt concentration. Hofmeister series reversals result from two mechanisms: Surface charge reversal and reversed cationic affinities for the protonated and deprotonated carboxyl groups. Our mechanism for the binding of small cations like Li+ to the charged carboxylate groups seems to be different from previous results in solution, 36 where Li+ has been found to form a solvent-separated ion pair. The reason for this could have to do the with the influence the surface has on the ion-pairing properties, but more detailed studies should follow in the future. Also, the present methodology should be applied to other deprotonable groups as well in order to establish the generality of the pH-dependent series reversal at acidic surfaces. Finally, experimental studies on carboxylated surface along the lines of Ref. 10 would be desirable in order to enable direct comparison with the present predictions.

Supporting Information Available The fitting functions for the surface-ion PMFs, water density and orientation profiles obtained by MD simulations and tables containing all fitting parameters are listed in the supporting information. This material is available free of charge via the internet at http://pubs.acs.org.

Acknowledgments We thank U. Sivan for enjoyable discussions. We acknowledge financial support from the Alexander von Humboldt foundation, the DFG via the SFB 1078 and the German-Israeli Foundation for Scientific Research and Development (GIF) in the project ”Ion specific in23


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teractions between functionalized surfaces”.

References (1) Hofmeister, F. Zur Lehre von der Wirkung der Salze (About the science of the effect of salt). Arch Exp Pathol Phar 1888, 24, 247–260. (2) Traube, J. The attraction pressure. J. Phys. Chem. 1910, 14, 452–470. (3) Robertson, T. Contributions to the theory of the mode of action of inorganic salts upon proteins in solution. J. Biol. Chem. 1911, 9, 303–326. (4) Boström, M.; Tavares, F.; Finet, S.; Skouri-Panet, F.; Tardieu, A.; Ninham, B. Why forces between proteins follow different Hofmeister series for pH above and below pI. Biophys. Chem. 2005, 117, 217–224. (5) Kim, H.; Tuite, E.; Norden, B.; Ninham, B. Co-ion dependence of DNA nuclease activity suggests hydrophobic cavitation as a potential source of activation energy. Eur. Phys. J. E 2001, 4, 411–417. (6) Zhang, Y.; Cremer, P. S. The inverse and direct Hofmeister series for lysozyme. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 15249–15253. (7) Dishon, M.; Zohar, O.; Sivan, U. From Repulsion to Attraction and Back to Repulsion: The Effect of NaCl, KCl, and CsCl on the Force between Silica Surfaces in Aqueous Solution. Langmuir 2009, 25, 2831–2836. (8) Flores, S. C.; Kherb, J.; Cremer, P. S. Direct and Reverse Hofmeister Effects on Interfacial Water Structure. J. Phys. Chem. C 2012, 116, 14408–14413. (9) Flores, S. C.; Kherb, J.; Konelick, N.; Chen, X.; Cremer, P. S. The Effects of Hofmeister Cations at Negatively Charged Hydrophilic Surfaces. J. Phys. Chem. C 2012, 116, 5730–5734. 24


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(10) Morag, J.; Dishon, M.; Sivan, U. The Governing Role of Surface Hydration in Ion Specific Adsorption to Silica: An AFM-Based Account of the Hofmeister Universality and its Reversal. Langmuir 2013, 29, 6317–6322. (11) Lyklema, J. Simple Hofmeister series. Chem. Phys. Lett. 2009, 467, 217 – 222. (12) Lyklema, J. Lyotropic sequences in colloid stability revisited. Advances in Colloid and Interface Science 2003, 100-102, 1 – 12. (13) Dumont, F.; Warlus, J.; Watillon, A. Influence of the point of zero charge of titaniumdioxide hydrosols on the ionic adsorption sequences. J. Colloid Interface Sci. 1990, 138, 543–554. (14) Ries-Kautt, M.; Ducruix, A. Relative effectiveness of various ions on the solubility and crystal growth of lysozyme. J. Biol. Chem. 1989, 264, 745–748. (15) Carbonnaux, C.; Ries-Kautt, M.; Ducruix, A. Relative Effectiveness of Various Anions on the Solubility of Acidic Hypoderma-Lineatum Collagenase at pH 7.2. Protein Sci. 1995, 4, 2123–2128. (16) Finet, S.; Skouri-Panet, F.; Casselyn, M.; Bonnet, F.; Tardieu, A. The Hofmeister effect as seen by SAXS in protein solutions. Current Opinion in Colloid & Interface Science 2004, 9, 112 – 116. (17) Kunz, W. Specific Ion Effects, 1st ed.; Wiley & Sons: Chichester, 2007. (18) Baldwin, R. How Hofmeister ion interactions affect protein stability. Biophys. J. 1996, 71, 2056–2063. (19) Jungwirth, P.; Tobias, D. Molecular structure of salt solutions: A new view of the interface with implications for heterogeneous atmospheric chemistry. J. Phys. Chem. B 2001, 105, 10468–10472.

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(20) Jungwirth, P.; Tobias, D. Ions at the air/water interface. J. Phys. Chem. B 2002, 106, 6361–6373. (21) Huang, D. M.; Cottin-Bizonne, C.; Ybert, C.; Bocquet, L. Aqueous electrolytes near hydrophobic surfaces: Dynamic effects of ion specificity and hydrodynamic slip. Langmuir 2008, 24, 1442–1450. (22) Horinek, D.; Herz, A.; Vrbka, L.; Sedlmeier, F.; Mamatkulov, S. I.; Netz, R. R. Specific ion adsorption at the air/water interface: The role of hydrophobic solvation. Chem. Phys. Lett. 2009, 479, 173–183. (23) Levin, Y.; Dos Santos, A. P.; Diehl, A. Ions at the Air-Water Interface: An End to a Hundred-Year-Old Mystery? Phys. Rev. Lett. 2009, 103, 257802. (24) Schwierz, N.; Horinek, D.; Netz, R. R. Anionic and Cationic Hofmeister Effects on Hydrophobic and Hydrophilic Surfaces. Langmuir 2013, 29, 2602 – 2614. (25) Horinek, D.; Netz, R. R. Specific Ion Adsorption at Hydrophobic Solid Surfaces. Phys. Rev. Lett. 2007, 99, 226104. (26) Schwierz, N.; Horinek, D.; Netz, R. R. Reversed Anionic Hofmeister Series: The Interplay of Surface Charge and Surface Polarity. Langmuir 2010, 26, 7370–7379. (27) Jungwirth, P.; Tobias, D. J. Specific Ion Effects at the Air/Water Interface. J. Chem. Rev. 2006, 106, 1259–1281. (28) Luo, G.; Malkova, S.; Yoon, J.; Schultz, D. G.; Lin, B.; Meron, M.; Benjamin, I.; Vanysek, P.; Schlossman, M. L. Ion Distributions near a Liquid-Liquid Interface. Science 2006, 311, 216–218. (29) Schwierz, N.; Netz, R. R. Effective Interaction between two Ion-Adsorbing Plates: Hofmeister Series and Salting-In/Salting-Out Phase Diagrams from a Global MeanField Analysis. Langmuir 2012, 28, 3881–3886. 26


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(30) Heyda, J.; Pokorna, J.; Vrbka, L.; Vacha, R.; Jagoda-Cwiklik, B.; Konvalinka, J.; Jungwirth, P.; Vondrasek, J. Ion specific effects of sodium and potassium on the catalytic activity of HIV-1 protease. Phys. Chem. Chem. Phys. 2009, 11, 7599–7604. (31) Dzubiella, J. Salt-specific stability and denaturation of a short salt-bridge-forming alpha-helix. J. Am. Chem. Soc. 2008, 130, 14000–14007. (32) Papastavrou, G.; Kuznetsov, V. Ion Adsorption on Modified Electrodes as Determined by Direct Force Measurements under Potentiostatic Control. J. Phys. Chem. C 2014, 118, 2673. (33) Uejio, J. S.; Schwartz, C. P.; Duffin, A. M.; Drisdell, W. S.; Cohen, R. C.; Saykally, R. J. Characterization of selective binding of alkali cations with carboxylate by x-ray absorption spectroscopy of liquid microjets. Proc. Natl. Acad. Sci. U. S. A. 2008, 105, 6809–6812. (34) Aziz, E. F.; Ottosson, N.; Eisebitt, S.; Eberhardt, W.; Jagoda-Cwiklik, B.; Vacha, R.; Jungwirth, P.; Winter, B. Cation-specific interactions with carboxylate in amino acid and acetate aqueous solutions: X-ray absorption and ab initio calculations. J. Phys. Chem. B 2008, 112, 12567–12570. (35) Vrbka, L.; Vondrasek, J.; Jagoda-Cwiklik, B.; Vacha, R.; Jungwirth, P. Quantification and rationalization of the higher affinity of sodium over potassium to protein surfaces. Proc. Natl. Acad. Sci. U. S. A. 2006, 103, 15440–15444. (36) Hess, B.; van der Vegt, N. F. A. Cation specific binding with protein surface charges. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 13296–13300. (37) Collins, K. Charge density-dependent strength of hydration and biological structure. Biophys. J. 1997, 72, 65–76.

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(38) Scott, W. R. P.; Hunenberger, P. H.; Tironi, I. G.; Mark, A. E.; Billeter, S. R.; Fennen, J.; Torda, A. E.; Huber, T.; Kruger, P.; van Gunsteren, W. F. The GROMOS Biomolecular Simulation Program Package. J. Phys. Chem. A 1999, 103, 3596–3607. (39) Horinek, D.; Mamatkulov, S. I.; Netz, R. R. Rational design of ion force fields based on thermodynamic solvation properties. J. Chem. Phys. 2009, 130, 124507. (40) Fyta, M.; Kalcher, I.; Dzubiella, J.; Vrbka, L.; Netz, R. R. Ionic force field optimization based on single-ion and ion-pair solvation properties. J. Chem. Phys. 2010, 132 . (41) Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. A smooth particle mesh Ewald method. J. Chem. Phys. 1995, 103, 8577–8593. (42) Torrie, G. M.; Valleau, J. P. Nonphysical sampling distributions in Monte Carlo freeenergy estimation: Umbrella sampling. J. Comput. Phys. 1977, 23, 187 – 199. (43) Kumar, S.; Rosenberg, J. M.; Bouzida, D.; Swendsen, R. H.; Kollman, P. A. Multidimensional Free-Energy Calculations Using the Weighted Histogram Analysis Method. J. Comput. Chem. 1995, 16, 1339–1350. (44) Van Der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J. C. GROMACS: Fast, flexible, and free. J. Comput. Chem. 2005, 26, 1701 – 1718. (45) Collie, C. H.; Hasted, J. B.; Ritson, D. M. The Dielectric Properties of Water and Heavy Water. Proceedings of the Physical Society 1948, 60, 145160. (46) Chorny, I.; Dill, K. A.; Jacobson, M. P. Surfaces Affect Ion Pairing. The Journal of Physical Chemistry B 2005, 109, 2405624060. (47) Sedlmeier, F.; Netz, R. R. The spontaneous curvature of the water-hydrophobe interface. The Journal of Chemical Physics 2012, 137, 135102.

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(48) Netz, R. Electrostatistics of counter-ions at and between planar charged walls: From Poisson-Boltzmann to the strong-coupling theory. The European Physical Journal E 2001, 5, 557574. (49) Parsegian, V. A.; Gingell, D. On the Electrostatic Interaction across a Salt Solution between Two Bodies Bearing Unequal Charges. Biophys. J. 1972, 12, 1192 – 1204. (50) Haynes, H. W. M. Handbook of Chemistry and Physics, 95th ed.; CRC Press/Taylor and Francis, 2014-2015. (51) Bikerman, J. Structure and capacity of electrical double layer. Philos. Mag. 1942, 33, 384–397. (52) Borukhov, I.; Andelman, D.; Orland, H. Adsorption of large ions from an electrolyte solution: a modified Poisson-Boltzmann equation. Electrochim. Acta 2000, 46, 221– 229. (53) Boroudjerdi, H.; Kim, Y.-W.; Naji, A.; Netz, R.; Schlagberger, X.; Serr, A. Statics and dynamics of strongly charged soft matter. Phys. Rep. 2005, 416, 129 – 199. (54) Caspers, J.; Goormaghtigh, E.; Ferreira, J.; Brasseur, R.; Vandenbranden, M.; Ruysschaert, J.-M. Acido-basic properties of lipophilic substances: A surface potential approach. Journal of Colloid and Interface Science 1983, 91, 546 – 551. (55) Evans, D.; Wennerström, H. The Colloidal Domain: Where Physics, Chemistry, Biology and Technology Meet, 2nd ed.; Wiley-VCH, 1999. (56) Bonthuis, D. J.; Netz, R. R. Beyond the Continuum: How Molecular Solvent Structure Affects Electrostatics and Hydrodynamics at Solid-Electrolyte Interfaces. J. Phys. Chem. B 2013, 117, 11397–11413. (57) Garcia-Celma, J. J.; Hatahet, L.; Kunz, W.; Fendler, K. Specific Anion and Cation

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Binding to Lipid Membranes Investigated on a Solid Supported Membrane. Langmuir 2007, 23, 10074–10080. (58) Melander, W.; Horvath, C. Salt Effects on Hydrophobic Interactions in Precipitation and Chromatography of Proteins: An Interpretation of the Lyotropic Series. Arch. Biochem. Biophys. 1977, 183, 200–215. (59) Lund, M.; Jungwirth, P.; Woodward, C. E. Ion Specific Protein Assembly and Hydrophobic Surface Forces. Phys. Rev. Lett. 2008, 100, 258105.

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Page 31 of 41

Figure 1: (A) Ionic concentration profiles ci (z)/c0 perpendicular to the carboxylic interface for LiCl, NaCl and CsCl solutions at bulk salt concentration c0 = 0.1 M and degree of dissociation ξ = 0.1 as follows from eqs 1 and 2. The Cl− concentration profile is shown for a NaCl solution and very similar for all different salts. (B) Corresponding electrostatic potential profiles Φ(z). The potential is negative since the negative surface charge due to deprotonation is not compensated by cation adsorption. (C) Simulation snapshot of the neutral carboxylic interface without ions. The solid vertical line indicates the mean position of the surface oxygen atoms at zO = 0 nm and the broken vertical line indicates the mean position of the carboxylic hydrogens at zH = 0.11 nm. Both positions follow from the normalized number density distributions ρ(z) of the carboxylic oxygen and hydrogen atoms shown in (D).

(A)

c /c 0

20

Li + Na+ Cs +Cl

10 0

)[V]

0 (B) -0.04 -0.08 [ = 0.1, c0= 0.1 M

-0.12 0

1

2 z [nm]

z 0 zH

3

(C)

ρ/ρ0 [1/nm]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

6 (D) 0 -2

H-atoms O-atoms

0

2 z [nm]

31

4


Langmuir

Figure 2: (A) Ionic density profiles ci (z)/cmax for NaCl at bulk salt concentration c0 = 1 M and deprotonation degree ξ = 0.5 using the unmodified approach (dotted lines, eq 1 and 2) and the modified approach (solid lines, eq 1, 7, 8). cmax is the density set by the density of close packed spheres. (B) pH as a function of the deprotonation degree ξ for three different NaCl concentrations using the unmodified Poisson-Boltzmann approach eqs 1 and 2. The non-monotonicity results from an unrealistically high ionic density close to the charged carboxylate groups as seen in (A). Note that the pH diverges as ξ goes to zero and to unity, see eq 14. (C) pH-ξ relation for a square-well potential eq 9 and three different cationic interaction strength V0+ using the unmodified Poisson-Boltzmann approach. (D) pH as a function of ξ for three different NaCl concentrations using the modified Fermionic Poisson Boltzmann approach. In this case the ionic concentrations do not exceed the physical limit set by the ionic volume and the pH dependence is monotonic.

(A) Density profiles for NaCl 7

0.4

Cl , modified PB

0.2

4 2

pH

6

c-/cmax

Na+-, unmodified PB Cl , unmodified PB Na+, modified PB -

8

c+/cmax

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 41

(B) Unmodified PB for NaCl

6

6

5

5

0 0

1

2 z

3

0

(C) Unmodified PB with square-well V0+=-10 + V0 =-15 V0+=-20

10

3

NaCl 0.001 M NaCl 0.1 M NaCl 1 M

2 0

0.2

6 c0=0.1 M

2 0.6

0.4

0.8

1

[

0

0.2

NaCl 0.001 M NaCl 0.1 M NaCl 1 M

2 0.4

0.6

[

32

(D) Modified PB for NaCl

18 14

4

4 3

c0 = 1.0 M

[

7


0.8

1

0

0.2

0.4

0.6

[

0.8

1

Page 33 of 41

Figure 3: (A) pH as a function of the deprotonation degree ξ for constant bulk salt concentration c0 = 0.1 M for different salt types using the modified Fermionic Poisson-Boltzmann approach. (B) pH as function of the salt concentration c0 for constant deprotonation degree ξ = 0.5. (C) Electrostatic potential at the surface hydrogen position Φ(zH ) as a function of ξ for constant bulk salt concentration c0 = 0.1 M and (D) as function of c0 for constant ξ = 0.5. The curves for the anions overlap since they affect the pH and the electrostatic potential only slightly.

12 8

9 8

4

c0 = 0.1 M

0 (C)

c0 = 0.1 M

7

(D)

-0.1

-0.2

-0.2

-0.4

-0.3

[ = 0.5

-0.6 0

0.2

pH

[ = 0.5 10

NaCl NaI LiCl CsCl

0.4

0. 6

0.8

1.0 0

[

33

0.2

0.4 0.6 c0 [Mol/l]

0.8


1

-0.4

) (zH)

pH

11

(B)

16 (A) NaF

) (zH)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Langmuir

Figure 4: Potential of mean force for anions and cations at the uncharged COOH-terminated SAM (A, B) and at the charged COO− -terminated SAM (C, D). For the charged surface the bare Coulomb interaction between the ion and the surface charge is subtracted. The origin z = 0 is defined by the mean position of surface oxygen atoms, see Figure 1 C and D.

FCl I-

(A)

3

Li + Na+ Cs +

(B)

8 5

1 3

-1

1

-3

0

0.2

0.4

0.6 0.8 z [nm]

1

0

0.2

0.4

0.6 0.8 z [nm]

1

-10

2 0

-3 1.2

-2

34

0

4

Charged COO--SAM

Charged COO--SAM

Uncharged COOH-SAM

Uncharged COOH-SAM

10

Li + Na+ Cs +

(D)

6

-1

-5 -7

FCl I-

(C)

7 V COO - [k B T]

5

V COOH [k B T]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 41

0

0.2

0.4

0.6 0.8 z [nm]


1

1.2

0

0.2 0.4 0.6 0.8 z [nm]

1

-20

1.2 1.4

Page 35 of 41

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Langmuir

Figure 5: Simulation snapshots of anions (upper row) and cations (lower row) at the uncharged COOH-terminated SAM. (A) F− , (B) Cl− and (C) I− snapshots at the position of the PMF minimum of F− (z = 0.15 nm). (D) Li+ , (E) Na+ , (F) Cs+ snapshots at the position of the minimum of Cs+ (z = 0.275 nm). Water molecules within 6 ˚ A of the ions are shown. The radii of the ions correspond to their Pauling radii. The simulation snapshots shown here are only a graphical illustration of one actual configuration. The ionic PMFs in Figure 4 result from sampling all possible configurations of the surface groups and water molecules.

Anions at COOH-SAM (A)

(B)

(C)

(E)

(F)

Cations at COOH-SAM (D)

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Langmuir

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Page 36 of 41

Figure 6: Simulation snapshots of anions (upper row) and cations (lower row) at the charged COO− -terminated SAM. (A) F− , (B) Cl− and (C) I− at the position z = 0.6 nm. (D) Li+ , (E) Na+ , (F) Cs+ at the position of the PMF minimum of Na+ (z = 0.025 nm). Water molecules within 6 ˚ A of the ion are shown. The radii of the ions correspond to their Pauling radii.

Anions at COO-SAM (A)

(B)

(C)

(E)

(F)

Cations at COO-SAM (D)

36


Page 37 of 41

Figure 7: Surface tension increment ∆γ obtained from thermodynamic integration as a function of the bulk salt concentration c0 for different anions (A) and for cations (B) at the uncharged COOH-terminated SAM and for anions (C) and for cations (D) at surface containing 10% charged COO− -groups (ξ = 0.1). The inset in (C) schematically illustrates protein unfolding driven by a negative ∆γ. All calculations are done using the modified PB approach (eq 1, 7 and 8). The dashed line in (A) accounts for non-ideal solution effects using eq 5 and the experimental values for the activity coefficient, 50 all other curves are obtained assuming ideal solution behavior.

0

(B) LiCl

2 (A) ∆γ [mN/m]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

0

(C)

2

NaCl CsCl

Δγ < 0

(D)

σ surf= -0.46 e/nm2 0

-10

-10

1

-2 -4 -6 0

0.2

-20

-20

NaCl NaI NaF

0 0.4 0.6 c0 [Mol/l]

0.8

0

0.2

0.4 0.6 c0 [Mol/l]

0.8

1

37

-30

σ surf= -0.46 e/nm2 0

0.2

0.4 0.6 c0 [Mol/l]


-30 0.8

0

0.2

0.4 0.6 c0 [Mol/l]

0.8

1

Langmuir

Figure 8: DH surface potential ΦDH and equivalent effective surface charge σDH in dependence of the pH for a small bulk salt concentration c0 = 0.01 M. The salt concentration was chosen to match the experimental condition in Ref. 10 All calculations are done using the modified PB approach (eq 1, 7 and 8).

0 c0 = 0.01 M

-0.04 2

-40

VDH[e/nm ]

0 ) DH [mV]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 41

-0.08 -80

-0.12 LiCl NaCl CsCl

-120 2

-0.16 -0.2 4

6

8

10

pH

38


Page 39 of 41

Figure 9: Long range DH surface potential ΦDH (solid lines) and its magnitude |ΦDH | (dotted lines) as a function of the pH for constant bulk salt concentration c0 = 0.5 M (A, B). ΦDH and |ΦDH | in dependence of the bulk salt concentration c0 for anions and constant pH=4 (C), cations and constant pH=3 (D), anions and constant pH=7 (E), cations and constant pH=7 (F). |ΦDH | determines the efficiency of different salts to stabilize solutes against precipitation. The arrows indicate partial alterations in the Hofmeister series at the intersection points of |ΦDH |. Open circles indicate instability points at which ΦDH = 0, corresponding to vanishing electrostatic repulsion. All calculations are done using the modified PB approach (eq 1, 7 and 8).

|)DH|, )DH [V]

0.2

(A)

(B)

0.2

0.1

0.1 LiCl NaCl CsCl

NaF NaCl NaI

0 -0.1 c0 = 0.5 M

-0.2

3

4

5

6

7

8

9

3

10

4

|)DH|, )DH [V]

0.08

5

0 -0.1 -0.2

c0 = 0.5 M 6

7

8

9

10

pH

pH

(C)

0.08

(D)

0.04

0.04

0

0

-0.04

0.1

-0.04 0

pH = 3

pH = 4

-0.08 |)DH|, )DH [V]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

(E)

(F)

-0.04 -0.08

0

-0.12

-0.1

pH = 7

pH = 7 0

0.2

0.4 0.6 c0 [Mol/l]

0.8

10

39

0.2

0.4 0.6 c0 [Mol/l]


0.8

-0.16 1

Langmuir

Figure 10: Hofmeister state diagram for LiCl, NaCl and CsCl in dependence of pH and bulk salt concentration c0 at surfaces containing carboxyl-groups. Salts are ordered according to their efficiency in stabilizing solutes against precipitation based on the magnitude of the effective surface charge |ΦDH |. We observe the direct Hofmeister series |ΦDH (LiCl)| > |ΦDH (NaCl)| > |ΦDH (CsCl)| (white), the reversed series |ΦDH (CsCl)| > |ΦDH (NaCl)| > |ΦDH (LiCl)| (black) and two partially altered series (gray). The dashed lines are instability lines for NaCl (blue) and CsCl (gray) on which |ΦDH | = 0 and thus the long ranged repulsion between two surfaces vanishes since the bare surface charge is exactly canceled by specific cation adsorption. All calculations are done using the modified PB approach (eq 1, 7 and 8).

10

Cations at carboxylic surface Cs>Na>Li

8 pH

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 41

Cs>Li>Na Li>Cs>Na

6

Li>Na>Cs

4

Li>Cs>Na 0

0.2

Cs>Li>Na 0.4 0.6 c0 [Mol/l]

40

0.8


1

Page 41 of 41

Langmuir

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Specific Ion Binding to Carboxylic Surface Groups and the pH

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