Molecular Dynamics Study of the Electrical Double Layer at Silver Chloride−Electrolyte Interfaces

Molecular Dynamics Study of the Electrical Double Layer at Silver Chloride-ElectrolyteInterfaces

Piotr Zarzycki,* Sebastien Kerisit, and Kevin M. RossoChemical and Materials Sciences DiVision, Pacific Northwest National Laboratory, Richland, Washington

ReceiVed: December 15, 2009; ReVised Manuscript ReceiVed: March 3, 2010

Molecular dynamics simulations of the electrical double layer at AgCl-aqueous electrolyte (KCl) interfacesare presented, accompanied by a new force field and properties of bulk AgCl computed using planewavedensity functional theory. Long dynamics simulations were performed to estimate ion adsorption free energiesat the AgCl surface. The simulations demonstrate the formation of a bilayer hydration sheet composed of twosublayers of water molecules interconnected by hydrogen bonds. Potassium ions prefer to form an inner-sphere complex, whereas chloride ions prefer outer-sphere complexes. The adsorbed ion-water layers forma relatively rigid structure within the range of ionic strength considered, which confirms the applicability ofthe Helmholtz model in a high concentration regime. Profiles of the charge density, electric field, andelectrostatic potential across the simulation cell revealed that oscillations of water molecules govern thesequantities. The electrostatic potential generated only by the electrolyte ions was used to study the quasi-Nernstian response of the silver chloride surface to the variation in the ionic strength.

1. Introduction

If a hydrophilic surface is immersed in aqueous electrolytesolution, it develops surface charge which is accompanied by aspecific distribution of ions in the adjacent electrolyte phase.This specific ion distribution is known as an electrical doublelayer (EDL).1-8 The formation of the EDL consists of a netorientation of water dipoles and layers of electrolyte ionscompensating the surface charge.1 Because of the chargeseparation, a potential difference is developed across theinterface, generating a strong interfacial electric field (on theorder of 1010 V/m).1,2 In principle, we can distinguish twoextreme cases of EDL systems based on electrode polarizablility:polarizable electrodes (typically metal/electrolyte interfaces) andnonpolarizable electrodes (e.g., silver halide-electrolyte or somemetal (hydr)oxides-electrolyte interfaces). Both systems differin the magnitude and time dependence of the electrode responseto changes in the bulk electrolyte composition. Most molecularmodeling studies of such systems reported so far have beenconcerned with metal-electrolyte interfaces.2,3,6-8 However,other electrified interfaces (especially for the metal hydr(oxides))have also attracted attention.9-11

In this study we investigate some fundamental properties ofthe EDL formed at the silver chloride-electrolyte interface,where the electrolyte phase is a KCl aqueous solution. This studyis inspired in part by recent surface potential measurements usingsingle-crystal AgCl (SC-AgCl) electrodes, which were foundto behave significantly differently from traditional Ag|AgClelectrodes.12,13 Both electrodes are examples of almost perfectnonpolarizable ones, exhibiting fast and stable response tochanges in the bulk concentration of Cl- ions. For this reason,the Ag|AgCl electrode has been one of the most frequently usedreference electrodes in electrochemical and biomedical measure-ments. The surface potential at the silver chloride-electrolyteinterface is believed to obey the Nernst equation with respect

to the activity of potential determining ions (PDI, in this caseCl- or Ag+ ions).12-14 Nernstian behavior is also expectedbecause the Ag|AgCl reference electrode yields a Nernstianslope.15 The observed linear dependence of surface potentialwith respect to the PDI can be expressed in a form of the quasi-Nernstian potential:12,13

where kB is the Boltzmann constant, T is a temperature, n )1/ln(10), e is the elementary charge, pCl ) -log[Cl-], andpClPZP ) -log[Cl-]pzc is the pCl value when ψ0 ) 0 (the pointof zero potential, PZP). The factor R describes the deviationfrom an exact Nernstian response (for which R ) 1). The quasi-Nernstian equation is frequently used for describing metal(hydr)oxide electrodes,16 and it was adopted for AgCl by Kallayet al.12,13 A physical interpretation of quasi-Nernstian (R < 1)behavior of the AgCl electrode lies in numerous microscopicsurface phenomena (e.g., formation of the EDL, dissolution/growth processes, and electron transfer events). These processesresult in a dependence of the surface composition on the pClvalue (R ) 1 - (kBT)/(ne)f(surface)).13,17 Similarly, the recentpotential measurements using a SC-AgCl electrode confirmeda linear electrode response, but with 12-16% lower magnitudethan the exact Nernstian response (i.e., R ∈ (0.84, 0.88)).12,13

In this study, molecular modeling is used to gain insightinto the formation of the EDL at the AgCl(100) surface incontact with KCl electrolyte. In particular, we focus on theelectrostatic properties: the distribution of ionic charges andwater molecules, the electrostatic field and potential, and thedistribution of water dipole moments. To test for a quasi-Nernstian response, simulations with different electrolyteconcentration were performed.

2. Theory and Computation

2.1. Molecular Modeling. Several computer simulationstudies of solid-aqueous phase interfaces have been reported,2-8

* Corresponding author. Address: Piotr Zarzycki, Pacific NorthwestNational Laboratory, P.O. Box 999, MSIN K8-96, Richland, WA 99352.E-mail: [email protected].

ψ0 ) RkBT

ne(pCl - pClPZP) R ) ne

kBT

dψ0

dpCl(1)

J. Phys. Chem. C 2010, 114, 8905–8916 8905

10.1021/jp9118666 2010 American Chemical SocietyPublished on Web 04/23/2010

with most focused on metal-aqueous phase interfaces.2,3,7 Evenwhen using relatively efficient molecular dynamics methods,simulations of the EDL have certain limitations. One is arestriction to relatively high ion concentration; another is anecessity of performing long simulations to obtain a well-equilibrated interfacial charge distribution (due to long ion orsurface residence times).2 Furthermore, in many cases ap-proximations used to construct the simulations prevent quantita-tive agreement with the experiment. For instance, all polarization-induced phenomena are missing in simulations employing rigidnonpolarizable water models. Despite having many shortcom-ings, classical EDL modeling can still provide remarkable insightinto the formation and structure of the EDL.2 More detaileddiscussion of EDL simulation methods can be found in recentreviews.2,3

Because H+ ions are also potential determining ions for metal(hydr)oxides, a molecular dynamics simulation of this interfaceis rather difficult. In the simplest case, hydrogen ions are treatedas a chemical entity (e.g., the hydronium ion H3O+ or Zundelcomplex H5O2

+).18 In more advanced studies, dissociable orpolarizable water models have been used.9

In the case of the AgCl-electrolyte interface, the ionscommon to the bulk crystal (Ag+ or Cl-) are the potentialdetermining ions.12-13 However, to the best of our knowledge,there are no force fields specifically optimized for describinginteractions in both the bulk and at the surface of AgCl. Wetherefore started our investigation by developing such a forcefield, accomplished by reoptimizing an existing force field forNaCl19 (see below).

2.2. Surface Potential, Charge Density, and Electric Field.The charge density is an observable key required to predict theelectric field and electrostatic potential across the computationalcell. The perturbation or inhomogenization of the bulk electro-lyte composition due to the presence of an electrified interfaceis revealed by almost any property, particularly in the densityprofiles, which are the two-dimensional counterparts of theRDFs. This ordering effect induced by the interface is mani-fested by the layering of the water molecules and a specificpeak sequence in the electrolyte ion density profiles.2

The electric field E across the simulation cell is obtained fromthe Poisson-Boltzmann equation by integration of the chargedensity σ2,3

where σ0 is the permittivity of free space, z is the distance fromthe surface, and � is the integral variable (distance from thesurface). The electrostatic surface potential ψ is obtained bydouble integration of the charge density profile:2

By the surface potential (ψ0), we mean the electrostatic potentialformed at the solvated silver chloride surface, which causes thespecific distribution of the ions in the adjfacent electrolyte phase:

where z0 defines the interface boundary (surface region). Asnapshot of the molecular model used in this study with a

graphical explanation of the z-parameter is shown in Figure 1.The concept of a well-defined surface with a finite surfacepotential and charge arises from phenomenological models ofthe EDL. These models usually picture the EDL as parallelcondensers connected in series.1

3. Results and Discussion

3.1. Force-Field Parametrization. To establish a force fieldfor bulk silver chloride, we started by reoptimizing thePettit-Rossky force field (PR-FF)19 developed for sodiumchloride in SPC/E water. The PR-FF is one of the mostfrequently used force fields for the NaCl-water interface (see,for instance, ref 20). Because both AgCl and NaCl crystallizein the same crystal structure (cF8, Fm3mj , #225), the PR-FF isan ideal starting point. In addition, the unit cell constant of AgClis only 1.5% (0.08 Å) smaller than that for NaCl.21 Integer pointcharges ( 1 were assigned to the ions (Ag+, Cl-), and Columbicinteractions were treated by the Ewald summation method.Dispersive interactions between ions in the bulk AgCl phaseare described by the three-parameter Buckingham potential[V(r) ) A exp(-r/F) - C/r6].

In the reoptimization procedure, the interaction parameters(A, F, C) were kept unchanged for chloride-chloride interactionsand were modified for silver-silver interactions. For silver-chloride interactions we used Lorentz-Berthelot mixing rules.We varied A and C parameters until the experimental cellconstant was reproduced (a ) 5.548 Å).21 For each ion we keptthe same effective radius (F ) 0.317 Å) and found optimal Aand C parameters by minimizing the two-dimensional errorfunction δ(A,C) ) |a(A,C) - aexp|. Reoptimization of the forcefield was performed using the code METADISE.22

The next step was to establish interaction parameters for Ag+/water and Ag+/(K+,Cl-) ion interactions, starting again fromthe Pettitt and Rosky19 force field for NaCl/SPC/E waterinteractions. Tailoring of force field parameters (σOAg, σHAg, εOAg,εHAg) for the Ag+/SPC/E water interactions was based on twotypes of molecular dynamics simulations. The first step was

E(z) ) 1ε0∫0

zσ(�) d� (2)

ψ(z) ) -∫0

zE(�) d� ) - 1

ε0∫ ∫0

zσ(�) d� (3)

ψ0 ) limzfz0

ψ(z) (4)

Figure 1. Simulation model: cubic box of crystal AgCl (25 Å × 25Å × 25 Å) immersed in SPC/E water (1080 H2O molecules, density 1g/cm3). Electrolyte ions are introduced by replacing water molecules.Molecular dynamics simulations are carried out in the NVT ensemblewith the Nose-Hoover thermostat.

8906 J. Phys. Chem. C, Vol. 114, No. 19, 2010 Zarzycki et al.

reoptimization of the A and C parameters using nonperiodic 0K temperature dynamics of the Ag(H2O)4

+ complex until anaverage AgO distance agreed with those predicted by Martinezet al.23 (MP2 study, r ) 2.433 Å) and until the hydration energywas maximized (∆H ) -208 kJ/mol in 0 K dynamicsminimization). The second step consisted of 1 ns NVT (normalvolume-temperature) dynamics of the Ag+ ion in the bulk of255 SPC/E water molecules periodically replicated in threedimensions. The SHAKE algorithm was used to maintain theinternal water geometry.24 System properties predicted by thebulk dynamics are the following: an average AgO distance equalto 2.3 Å (by the position of the first peak in RDF), a hydrationenergy equal to ∆H ) -432.2 kJ/mol, and the coordinationnumber equal to 5.8. The new force field predictions agreereasonably well with experimental data; the experimentalaverage AgO distance was reported in the range of 2.32-2.43Å, and the experimental hydration enthalpy is reported to be-475.3 kJ/mol.25 Force-field parameters are presented in Table1. All molecular dynamics simulations presented in this paperwere obtained using the code DL_POLY.26

3.2. Silver Chloride from First Principles. Force-fieldreoptimization was assisted by planewave density functionaltheory calculations to estimate errors associated with theempirical potential approach. We used Vanderbilt ultrasoftpseudopotentials27 with an electron correlation described bythe Perdew-Burke-Ernzerhof functional (PBE).28 We per-formed convergence tests with respect to the energy cutoffand k-points sampling. Convergence up to 0.0001 Å (cellparameter) was obtained using a kinetic energy cutoff equalto 900 eV and a k-point mesh resolution defined by 10k-points (grid 6 × 6 × 6).

Cell parameters were optimized simultaneously with atomiccoordinates without symmetry restrictions using the Broyden-

Fletcher-Goldfarb-Shanno (BFGS) method.29 All calculationswere performed using the code CASTEP.30 The predicted cellparameter is in an excellent agreement with experiment, onlyslightly overestimating cell constant by 0.65% (a ) 5.583 Å,exp. 5.548 Å).21 Previously reported calculations employed thelocal density approximation (LDA) and underestimated the cellparameter by 2.5% (a ) 5.41 Å)31 and by 3.4% (a ) 5.36 Å).32

After optimization, the elastic modulus and dielectric con-stants were calculated to compare with experimental data.Because of the fact that the local density and generalizedgradient approximations (here, PBE) typically do not correctlydescribe the band structure of an isolator and in general predictsmall band gaps,33 we do not present the band structure. Moreaccurate results with nonlocal exchange and a many-bodyquasiparticle approximation33 will be presented in future work.Predictions from the planewave calculations were compared withthose from molecular mechanics using the new force field ascalculated with the METADISE code.22 The response to anisotropic compression (bulk modulus) was better described inthe planewave approach (85% of the experimental value), thanin the molecular mechanics calculations (76%). We note thatthe planewave results are also much closer to the experimentalvalue than previous planewave calculations. Our calculationsunderestimate the bulk modulus by 15%, whereas Nunes et al.31

overestimate it by 21% (K ) 62) and Kirchhoff et al.32 by 30%(K ) 66.8).

Young’s modulus is overestimated in both the classical andthe quantum approaches. However, deeper insight into thetendency of a material to be elastically deformed is providedby the elastic tensor, which captures anisotropy. For the presentcase of a cubic crystal, we expect to have only three differentsymmetry elements (c11, c12, and c44). Molecular mechanicsestimation of c11 is much more accurate than those from theplanewave approach (METADISE 96% of experimental value,CASTEP 73%). However, the molecular mechanics predictionsof other tensor elements artificially decrease the anisotropy(c12 ) c44) with a high relative error. On the contrary, theplanewave DFT estimation of c12 and c14 was accurate (97%and 91% of experimental values). Kirchhoff et al.32 reported amuch less accurate estimation of the elastic tensor elements:c11 ) 98 GPa (over by 29%), c12 ) 42 GPa (over by 7.5%),and c44 ) 1.3 GPa (under by 81%).

The dielectric constant, ε, consists of real and imaginary parts(ε ) εr + iεi). The planewave DFT calculations provideestimation for both parts as a function of wavelength, whereasthe molecular mechanics approach gives only static ε (zero-frequency value). In general, Im(ε) increases with the energycutoff and number of k-points. For a chosen energy cutoff andk-point mesh, Re(ε) + Im(ε) at high frequency gives excellentagreement with the experiment (99%). Both classical andquantum approaches provide a similar estimation of the staticdielectric constant (40% of the reported experimental value).

TABLE 2: Bulk AgCl Properties: Comparison of Molecular Mechanics and Planewave DFT Calculations with Experiment

property experiment CASTEP METADISE (FF)

cell [Å] 5.54821 5.583 5.548bulk modulus, K [GPa] (0 K) 51.334 43.73 33.24Young’s modulus, E 19.90 25.05 47.08

Elastic Tensor Constants, at 0 K [GPa], (exp. ref 34)c11 75.90 55.62 72.57c12 39.08 37.79 13.57c44 6.894 6.245 13.57dielectric constant, ε 11.2035a high frequency: 11.08 (Im(ε) + Re(ε)), 7.85 (|ε|) (Re(ε) ) 5.83,

Im(ε) ) 5.25)3.19 (static)

11.1535b static: 4.43

TABLE 1: Force Field Parameters (Dispersive Forces)

Lennard-Jones parameters of ion interactions with SPC/E-water

ion (X) σOX [Å] σHX [Å] εHX ) εOX [eV]

K+, ref 19 3.16 1.75 0.005679Cl-, ref 19 3.55 2.14 0.015604Ag+ 2.676 2.52 0.005617

Lennard-Jones parameters of K+ with bulk and surface ioninteractions

σ [Å] ε [eV]

K+/Cl- 3.541 0.01316K+/Ag+ 2.667 0.00473

Buckingham potential parameters for AgCl

pair A [eV] F [Å] C [eV ·Å6]

Ag+-Ag+ 288.6 0.3170 69.3100Ag+-Cl- 1885.7 0.3170 71.1440Cl--Cl- 3482.7745 0.3170 73.0259

EDL at AgCl-Electrolyte Interfaces J. Phys. Chem. C, Vol. 114, No. 19, 2010 8907

Experimental values were reported without information aboutthe frequency of measurement,35 which limits a direct compari-son, but comparisons are nonetheless provided in Table 2.

The presented first principles calculations seem to be the mostaccurate planewave results for silver chloride presented so far,based on a comparison to experimental data. By comparingquantum and molecular mechanics results, we showed that someproperties of the bulk phase are accounted for only in thequantum calculations (i.e., elastic anisotropy, dielectric con-stants). However, both approaches show similar trends inpredicted properties. One of the most striking limitations in themolecular mechanics approach comes from the simplifiedtreatment of the short-range forces (the Buckingham potential)and the spherical symmetry of two-body interactions.

3.3. Simulation Results. 3.3.1. Free Energy Calculations.Before simulating the EDL at the AgCl/KCl interface, weperformed free energy calculations for ion-water and ion-ioninteractions in the aqueous phase in the absence of the electrifiedinterface. In addition, we performed surface adsorption freeenergy calculations for ions at the AgCl(100) surface in contactwith the aqueous electrolyte phase. The free energies ofion-water and ion-ion interactions in the aqueous phase areshown in Figure 2A; as the reaction coordinate, we choose theion-water center of mass and ion-ion distances (separationrange determined from radial distribution functions, RDFs,Figure 2B). The potential of mean force (PMF) plots wereconstructed from 100 independent simulations, each performedin the NVT ensemble with the time interval of 0.001 ps andduration of 1 ns (255 SPC/E water molecules and ions). ThePMF plots are shifted with respect to the first minimum (firstRDF maximum), that is to say that the energy was scaled bysetting zero at the first minimum. As shown in Figure 2, all

ion-water and ion-ion free energy profiles possess at least twodistinct minima (which correspond to the peaks in the RDFplots). For ion-water interactions, the global minimum corre-sponds to the first shell ion-water distance, whereas for K+/Cl- interactions the minimum is located at higher separation(at 3.25 Å) due to partial screening of the ionic field by watermolecules of hydration. The energetic barrier between first(closer distance) and second minima (higher separation) in theion-water free energy profile is around 1 kcal/mol, and inthe ion-ion case the barrier is approximately 1.4 kcal/mol. Inthe case of water-ion interactions the energetic gain of transferfrom the second to the first minima equals 0.13 kcal/mol,whereas in the ion-ion case this transfer increases the systemenergy by almost the same amount. In summary, the ions arefound to prefer water in their first coordination shell andcounterions in the next coordination shell. This finding isconsistent with the general expectation from the electrolytetheories.25

K+ and Cl- ion adsorption free energy plots were constructedfrom 80 independent simulations with frozen ion-surfacedistances in the NVT ensemble (using the Nose-Hooverthermostat at 298 K). In this calculation, the system is composedpartly of the AgCl solid phase (25 Å × 25 Å × 25 Å; 500 Agand Cl centers) and 1080 SPC/E water molecules (see Figure1). A K+ or Cl- ion was inserted at a certain distance from thesurface with simultaneous removal of one (nearest) watermolecule (total system charge equals ( 1). The ion-surfacePMF plots are shown in Figures 3 and 4A.

As expected, a K+ ion in the first adsorption layer is foundto prefer to be located above Cl- sites at the AgCl surface.Surface diffusion of these ions is found to be almost negligible,that is, the K+ ion typically does not leave a given surface Cl-

Figure 2. Radial distribution functions, g(r), and the potential of mean force, W(r), for ion-water and ion-ion pairs in the absence of electrifiedinterfaces.


site in a 1 ns simulation. Ion mobility increases with distancefrom the surface, allowing the K+ ion to explore more surfaceCl- positions. The low mobility found when close to the surfacesuggests a long residence time for adsorbed K+ ions and anecessity of performing long simulations to correctly describethe formation of the EDL. The first minimum (3.2 Å) corre-sponds to the formation of an inner-sphere surface complex;here there are no intervening water molecules between the K+

ion and surface Cl- sites, and the calculated water exchangerate in the first coordination shell appears to be slower than forK+ in the bulk aqueous phase. The transition state between innerand outer-sphere surface complexes is located at a distance of4.28 Å, followed by the global outer-sphere minimum at 5.85Å and by a local minimum/plateau starting from z ) 4.95 Å.The plateau from 4.95 to 5.4 Å corresponds to increasing ion-surface distances that enable neighboring water molecules toadopt more energetically favorable orientations (0.61 kcal/moldecrease in free energy). However, this range of ion-surfaceseparation does not allow water molecules to penetrate the regionbetween the ion and the surface. The formation of a watermolecule interlayer starts at a distance of 5.4 Å. Here, the strongelectric field felt by the water molecules in the layer separatingthe ion from the surface restricts their orientation. Also, theformation of the outer-sphere complex yields a 0.23 kcal/molenergy gain (energetic difference between K-structures at 5.4and 5.85 Å). Calculated K+ adsorption free energies are 3.34kcal/mol (inner-sphere complex) and 0.61 kcal/mol (outer-spherecomplex); these are in the typical range for physisorption. Thissuggests that even inner-sphere adsorbed K+ is not specificallybonded to the surface, which agrees with related experimentalresults.12,13 Nevertheless, the relatively high energy gain associ-ated with transition from the outer- to inner-sphere complex(2.73 kcal/mol) suggests that K+ ions prefer the inner-spherecomplex configuration. Snapshots of surface complex configura-tions at each characteristic point are shown in Figure 3A.

The counterpart adsorption free energy profile for Cl- at theAgCl surface is shown in Figure 4A. The first plateau on the

free energy plot corresponds to inner-sphere adsorption of Cl-

localized above a surface Ag+ site and can be considered as aninitial attachment step, such as in an electrodeposition process.However, the first local minimum with an energetic gain islocated at a distance of 4.4 Å from the surface and correspondsto specific Cl- adsorption (inner-sphere Cl- adsorption localizedabove a surface Cl- ion, snapshot b in Figure 4A). A deeperminimum (lower by 0.5 kcal/mol) is located at a distance of5.5 Å from the surface and corresponds to the first outer-sphereCl- surface complex (outer-sphere Cl-adsorption localized abovethe Ag+ surface ion, snapshot c in Figure 4A). The nextminimum at 7 Å is equally deep and corresponds to anotherouter-sphere complex (snapshot d in Figure 4A). Both outer-sphere minima are separated by an energy barrier of about 0.37kcal/mol, formed by a relatively rigid layer of water (see Figure4A,B). It is likely that at higher temperatures where waterordering is decreased, both minima would combine into onewide minimum. As was the case for K+, the calculated Cl-

surface mobility (diffusion parallel to the surface) increases withion-surface separation. At distances higher than 7 Å, theresidence time is lower than 0.4 ps. At distances higher than10 Å, the lateral motion of the chloride ion is no longerinfluenced by the presence of the surface. The outer-sphere Cl-

adsorption energy is much higher than for the K+ outer-spherecomplex, and for the inner-sphere complexes we observe theopposite trend. In summary, K+ ions prefer to form inner-spherecomplexes, whereas Cl- ions prefer to form outer-sphere com-plexes.

3.3.2. AgCl/(KCl, H2O) Interface Simulations. For simula-tions of the EDL formed at the silver chloride-electrolyteinterface we used the NVT ensemble with the Nose-Hooverthermostat (T ) 298 K). Simulations were run for 10 ns with a0.001 ps time step. We performed two types of simulations:one with the solid phase totally frozen and one with it partiallyfrozen (see Figure 1). Because of the fact that surface relaxationinduces an additional net-dipole moment37 and a subsequentresponse of the interfacial water molecules, we present results

Figure 3. Free energy profiles of K+ (A) ion adsorption onto the AgCl(100) surface. Snapshots of surface complex configurations are shown foreach of the characteristic points (a, b, c, d, e).


only for the totally frozen solid phase. This simplification allowsus to unambiguously define the EDL characteristics that arisein response to the geometrical AgCl surface. A similar approachis often used in EDL simulations for metal-electrolyteinterfaces.2-6

In Figure 5, calculated water density profiles (oxygen andhydrogen) are presented for simulations in the absence of K+

and Cl- ions, which are found to produce no effect on waterdensity with respect to the surface normal direction. As shownin Figure 5, initially random water molecules undergo a layeringtransformation upon contact with the surface (an ordering orpacking effect). In addition, the density profiles are highlysymmetric with respect to both AgCl-water interfaces presentin the simulation cell (Figure 5A); hence only half of thesimulation cell needs to be considered (Figure 5B,C). The F(z)/Fbulk profiles do not change for different electrolyte concentra-tions, which suggest that structure (ordering) is determined onlyby the presence of the AgCl surface. Similar observations werereported for the metal-electrolyte interface.2 The aqueous phaseis influenced by the presence of the interface up to approximately10 Å, similar to the ordering effect observed for the metal-waterinterface.2 In addition, this surface-induced ordering has beenobserved for both charged or uncharged surfaces.2-6 Eventhough density oscillations propagate up to 10 Å away fromthe surface, the modeled aqueous phase has a dimension of 55

Å, which guarantees that the water structure near either interfacewith AgCl is not perturbed by effects arising from the opposinginterface.

As shown in Figure 5B, we observe two distinct layers ofoxygen (peaks on FO(z)/Fbulk at 2.8 and 3.2 Å) in the range ofup to 4 Å from the surface, whereas only one layer was reportedin classical or quantum simulation studies of the metal-waterinterface.2 This can be interpreted as the splitting of the firstwater layer into two sublayers connected through the hydrogen-bond network. The presence of these two sublayers is consistentwith the popular, experimentally justified, highly structuredwater bilayer (sometimes referred to as an ice-like bilayer) modelproposed by Doering and Madey.38

Preferred orientations of water molecules at the AgCl surfaceare found to be more complex than those found at metal/waterinterfaces. Experimental studies of water orientation at the Ptsurface suggest that water tends to be located with the oxygenatom above the metal atom and hydrogen atoms pointed away(toward the bulk aqueous phase), whereas molecular dynamicsstudies suggest a flat (parallel to the surface) orientation of watermolecules adjacent to the surface.2 Simulations of water near ahard wall showed that water molecules exhibit a tendency topoint one hydrogen toward the surface.4,5 The orientation nearhydrophobic surfaces is governed by the loss of hydrogenbonding, whereas for hydrophilic surfaces it is governed by

Figure 4. Adsorption free energy profile for chloride ion (A) with configuration snapshots (a-e) shown for characteristic structures. The localminima for the outer (c, d) sphere complexes are perturbed by the water structure; for comparison, water density profiles are repeated in panel B.


formation of a surface water hydrogen network, distinct fromthe structure of bulk water.5 In the case of the Ag(111)-waterinterface, the hydrogen-bond network of bulk water was reportedto be strongly disrupted in the near-surface water layers, withwater dipole orientation depending on the potential applied tothe electrode.7 As shown by Schweighofer et al.,7 the oxygenredistribution induced by a high electrode potential results intheformationofabilayer (ice-type)structureat theAg(111)-waterinterface. Highly structured water was also reported for thehydroxylated and nonhydroxylated rutile surface by Pedota al.;10

they observed near-zero diffusivity and infinite viscosity of thefirst hydration layer of water molecules. The presence of therutile (110) surface was found to affect water moleculediffusivity and viscosity up to about 15 Å from the surface.10

In our case, interfacial water molecules in the first sublayerlocated above surface chloride ions point one hydrogen atomtoward the surface, with another laying parallel to the surface.There are also a certain number of water molecules above theAg+ surface site with hydrogen atoms pointed toward neighbor-ing Cl- sites. Both orientations give rise to the slope on theleft-hand side of the first FH(z)/Fbulk peak (profile from 1.5 to2.3 Å, Figure 5C). All hydrogen atoms lying parallel to thesurface in the same layer as oxygen atoms (at 2.3 Å, Figure5B) give rise to the subtle peak in the hydrogen density profiles.

Hydrogen atoms of water molecules in the first layer pointedtoward the bulk aqueous phase (2.3 Å, Figure 5B) and those ofthe second water layer pointed toward the surface (3.2 Å, Figure5B) produce the large peak in the hydrogen density profile at2.8 Å. This proves that both sublayers of interfacial watermolecules are interconnected by a hydrogen-bond network. Thewide peak in the hydrogen density profile covers both of thefirst hydrogen peaks in FO(z)/Fbulk (Figure 5A).

Hence the structure of water at the AgCl(100) surface exhibitsthree layers, with the first two very close to each other. Inaddition, we observe a single peak in the hydrogen densityprofile (at 2.8 Å) with a subtle structure at 2.3 Å. This isconsistent with the applicability of the Doering-Madey bilayermodel38 for the silver chloride-electrolyte interface. Similarly,two sublayers of water within the first hydration layer wereobserved on hydrophilic silica5 and for the Ag-water interfaceat higher electrode potentials.7 In our case the specific positiveor negative charge pattern on the AgCl surface and inclusionof the short-range repulsive interactions between water hydrogenatoms and surface sites are responsible for generating the bilayerhydration sheet of water at z < 4 Å.

Additional insight into water orientation at the surface isprovided by the distribution of molecular dipole moments atdifferent distances from the surface (Figure 6). To investigatedipole orientations, the interfacial region was divided into 10compartments having widths of 0.3 Å. The results are presentedalong with the density profile following the methodology ofSpohr.2 The distribution of dipole moments changes frombimodal (region 1, Figure 6) to bell-shaped (regions 2, 3; Figure6) to bimodal again (region 4) and then to a more uniformdistribution at higher distances (regions 6-10, Figure 6). Thebimodal orientation at the near-surface slope of the oxygendensity peak corresponds to two opposing orientations, one withhydrogen atoms pointed toward the surface and another towardthe bulk aqueous phase. The flat, parallel to the surface ori-entation of dipole moments dominates in region 3; that is, inthe minimum between both peaks on F(z).

Calculated ion density profiles are shown in Figure 7. Thepeak position of the K+ and Cl- density profiles does not changewithin the considered range of concentration, which confirmsthe expectation of the Helmholtz character of the EDL at highionic strength, and the applicability of the parallel-planecapacitor model. The Helmholtz model assumes that surfacecharge is exactly compensated by the layer of ions at a constantdistance (about 4 Å) from the geometrical electrode-electrolyteinterface.1

The analysis based on the density profiles alone would suggestthat the K+ and Cl- ions form outer-sphere complexes; that is,they are always separated from the surface by at least one waterlayer (i.e., the oxygen peak is closer to the surface than the K+

peak). However, from the PMF calculations we know that K+

potassium ions in the first peak are not separated from thesurface by water molecules and form an inner-sphere complex(Figure 3). Further, the formation of inner-sphere complexesdoes not imply specific adsorption (low adsorption energy,Figure 3), which is expected for the metal-electrolyte interfaceonly for larger halide ions.2 In addition, a lack of specificadsorption at SC-AgCl electrodes was recently confirmedexperimentally by Preoeanin et al.13 Their surface potentialmeasurements13 showed that pClPZP does not depend on the ionicstrength and that the surface potential is practically independentof electrolyte type (based on the electrolyte series: LiNO3,NaNO3, CsNO3, Mg(NO3)2, La(NO3)3). Collectively, these

Figure 5. Water density profiles. In panel A, a schematic picture ofthe system with the oscillation of oxygen density profiles near thesurface is shown. Simulation results are presented for the AgCl-waterinterface in the absence of electrolyte ions because the presence of theelectrolyte does not affect water density profiles. In panels B and Cthe density profiles in the near interface region are shown for wateroxygen and hydrogen, respectively.


observations can be interpreted as consistent with a picture ofnonspecific ion accumulation at the AgCl-electrolyte interface.

As shown in Figure 7A,B, the first layer of K+ ions start tobe formed at a distance of 2.8 Å from the surface, and this isfollowed by a layer of Cl- ions compensating the positive chargeassociated with the K+ ion layer. The first maximum in the K+

density profile is around 3.2 Å and corresponds to inner-spherecomplex formation (see PMF plot, Figure 3); the second smallpeak at 5.9 Å corresponds to the outer-sphere complex. At thedistance of 3.7 Å (end of first K+ peak), Cl- ions start toaccumulate at the surface. The global maximum of FCl(z)/Fbulk

is located at approximately 7 Å and corresponds to outer-spherecomplex formation (see PMF plot, Figure 4A). There is alsothe subtle structure on the left-hand side of the main peak inthe FCl(z)/Fbulk plot (small peaks at 4.4 and 5.5 Å, Figure 7C).The first small peak at 4.4 Å corresponds to specific Cl-

adsorption; the next one at 5.5 Å is much higher and correspondsto the outer-sphere complex (see Figure 4A).

As shown in Figure 7B,C, fluctuations in the ion densityprofiles are relatively large compared to fluctuations in the waterdensity profiles. These would also be responsible for a largeerror in short simulations. This is another reason why in theMD study of EDL, long time simulations have to be performed.

Because the solid phase is kept frozen, the electrostaticpotential inside the AgCl and at the geometric surface boundaryis zero (mutual compensation of Cl- and Ag+ ions). The surfacepotential is generated by the accumulated ions and the orientedwater molecules at the interface, and it is formed somewherebetween the crystal surface and ion layers (in the innerHelmholtz plane). As previously reported, water molecules havea tremendous impact on the charge, potential, and fielddistribution.3 In this study we include only the monopole

Figure 6. Orientational distribution of the molecular water dipole moments at the AgCl surface. The angle, θ, between the water dipole momentand the surface normal is analyzed for each water molecule whose oxygen atom is within the considered compartment. The interfacial region isdivided into 10 compartments, with each one having a width equal to 0.3 Å.


contribution of water molecules to the electrostatic propertiesacross the interface. Although Phillpott and Glosi3 showed thatfor the metal-electrolyte interface, dipole and quadrupole effectsare also important. However, the inclusion of just the monopolecontributions is a very common approach.2

In Figure 8 the charge density (F(z)), electric field (E(z),) andelectrostatic potential (ψ(z)) across the computational cell areshown. For simplicity of analysis we combined both interfacesinto one picture with the periodic boundary as marked (Figure8A-C). The charge density and electrostatic potential aresymmetric with respect to the boundary, whereas the electricfield is asymmetric. The structure in electrostatic propertiesdisappears at z > 15 Å. The total charge density (Figure 8A,D)and electric field (Figure 8B,E) are not very sensitive to theionic strength, and only small differences can be observed inψ(z) (Figure 8C,F). The characteristic points (structure) in σ,E, and ψ roughly correspond to each other.

The similarities in water density profiles and the structure ofinterfacial electrostatic properties, as well as the weak depen-dence of these properties on the electrolyte concentration,suggest that compensation for the presence of electrolyte arisesprimarily from the response of water monopoles. Water mono-pole contributions compensate the ionic contributions, whichresults in similar distance profiles for the AgCl-water andAgCl-electrolyte interfaces. In Figure 9A, both contributionsand their sum are shown, whereas in Figure 9B, ψ(z) for theAgCl-water and AgCl-electrolyte interfaces are compared. Asexpected, the characteristic oscillatory behavior of electrostaticproperties is a manifestation of the water monopoles; the ioniccontributions provide smooth monotonic behavior. Moreover,similarities between the electrostatic potential for pure waterand electrolyte solution (Figure 9B) can be seen to be aconsequence of the compensating effect (Figure 9A). In the case

of 0.3 mol/dm3 KCl solution, the ions generate the negativepotential across the cell (about -2.8 V at the cell boundary).Accounting for water monopoles shifts this value up to +0.12V. Although the ψ(z) profiles for the AgCl/H2O and AgCl/H2O+ KCl interfaces are similar, the presence of ions is manifestedby a shift in ψ(z) near the surface (oscillation regions). Theelectrostatic potential across the AgCl-water cell shows higherfluctuations at larger distances from the surface (see Figure 9A).By considering only electrolyte ions (Figures 9A and 10), weobtain the correct dependence of Ψ on the ionic strength,exhibiting near exponential decay with distance. However, it issteeper than that in the Gouy-Chapman model (ψ(z) ) ψ0

exp(-κz)) (Figure 10A). To determine the surface potential (ψ0),we need to define the surface plane (z0) where this potential isformed (see eq 4). The slope of ψ0(pCl) has a physically justifiedvalue (i.e., ∈(0;1), see Figure 10A,B) only for a narrow rangeof z0 (3.15-3.36 Å). The slope, R, for the Ag|AgCl electrode,as well as for many metallic electrodes, is 1 (i.e., the Nernstresponse).12-14 Metal (hydr)oxides give a lower magnitude inpotential response to the variation in PDI con-centration, with slopes typically between 0.6 and 0.9 (i.e., thequasi-Nernst response).1639 Measurements using SC-AgCl elec-trodes showed that R behaves similar to that for the metal oxides,that is, it has a value in the range from 0.82 to 0.88.12,13 Fromour simulations we conclude that this R range is observed onlyfor potentials formed in a plane 3.3 Å from the surface. Thecorresponding pClPZP is about 1.5 and is much lower thanexperimentally observed (e.g., the IEP of AgCl suspensions isabout 5.2).12,13 This experimental pClPZP value corresponds topotentials generated in the plane at z0 ) 3.18 Å, with anunphysical slope of 0.09.

The distance range which generates experimentally observedR values corresponds to the right-hand side of the first K+ peak

Figure 7. Density profiles for the electrolyte ions (A) for both interfaces (c ) 0.97 mol/dm3). The effect of ionic strength on relative densityprofiles (F/Fbulk) for the K+ and Cl- ions are shown in panels B and C, respectively.


(FK(z) Figure 7) and the second solvent sublayer in the first waterhydration sheet (FO(z) Figure 5). This suggests that the surfacepotential is generated by some K+ ions accumulated in theposition of the second sublayer of the first hydration shell. Ifwater monopoles are neglected, water has only indirect effectson the surface potential by governing the ion distribution andtheir separation at the interface. Because of the fact that thevalues of R and pClPZP depend on the way in which thesimulation model was constructed, the discussed distances andpotential values have only a comparative meaning.

4. Conclusions

A new force field for bulk AgCl and for Ag+/SPC/E waterinteractions was obtained by minimizing discrepancies betweenexperimental and molecular mechanics or dynamics predictions.Accompanying first principles calculations were carried out forbulk AgCl to assess quantum effects missing in the classicalmechanics approach. We found good agreement between thecalculated properties (in both quantum and classical approaches)and the experiment, particularly in terms of trends, withrelatively small deviations. However, in the classical treatmentssome of the elastic anisotropy and dielectric properties are notcorrectly reproduced. Planewave DFT calculation results are

much closer to the experimental data than any other publishedso far using this approach. However, as expected with pure LDAor GGA approaches, the lack of exact exchange appears toprevent good agreement in terms of the band structure.

According to our molecular dynamics simulations, the waterhydration layer at the AgCl(100)-electrolyte interface is com-posed of two distinct sublayers interconnected by hydrogenbonds, consistent with the bilayer model already established foraqueous interfaces with other materials. Some of the watermolecules in the first sublayer point one hydrogen toward thesurface and another in the plane parallel to the surface, forminghydrogen bonds with other oxygen atoms in first layer. Otherfirst sublayer water molecules point one hydrogen towardoxygen atoms in the second sublayer, with the other pointedtoward oxygen atoms in the first layer or toward chloride ionsin the AgCl surface. The orientation of water molecules at theinterface was confirmed by analysis of water dipole momentdistributions. The bilayer water structure at the interface isrelatively rigid and resembles the ice-like structure observedpreviously for the Ag(111)-water interface at high electrodepotential and for the silica-water interface.5 The specific patternof ionic charges (Ag+, Cl-) at the surface and the water

Figure 8. Charge density (A), electric field (B), and electrostatic potential (C) across the simulation cell. Structural dependence on ionic strengthis shown in panels D, E, and F.


hydrogen bonding network are responsible for the constructionof this specific bilayer hydration sheet.

Electrolyte ion density profiles suggest outer-sphere complexformation, however the adsorption free energy profiles revealthat K+ ions preferentially form an inner-sphere complex at 3.2Å from the surface. An outer-sphere K+ surface complex isformed at a distance of 5 Å (from the PMF for K+/AgCl surfaceinteraction) but can be slightly shifted to 5.9 Å if a Cl- layer isformed between the two K+ peaks. Specific adsorption of Cl-

is formed at a distance of 4.4 Å, but for chloride, outer-spherecomplexes are preferred (having a large maximum at 7 Å).

If electrolyte ions and water monopoles are considered, theircontributions compensate each other to some extent, and thetotal surface potential remains similar to those generated at theAgCl/H2O interface. This results in a low sensitivity of elec-trostatic properties to the electrolyte concentration and makesthe surface potential analysis difficult. In a simplified picture,neglecting water contributions, the near-surface potential de-creases with increasing ionic strength, as expected theoretically.Although its slope and PZC value depend on the definition ofz0, reasonable values are obtained for z0 in the range 3.3-3.36Å (R ∈ (0.6; 1)). Our modeling predicts a lower PZC value

Figure 9. Electrostatic potential across the computational cell with ionic and water monopole contributions (A) (KCl 0.31 mol/dm3). In panel B,the electrostatic potential profile for AgCl/H2O and AgCl/(KCl + H2O) interfaces.

Figure 10. Panel A, the ionic contributions to the electrostatic potential (half computational cell) with the range of the distance z0 (surface definition)providing a physical range of ψ0 (pCl) slope (i.e., R ∈ (0, 1)). Panel B, the dependence of R and pClPZP on the surface definition z0 is shown.Nerstian response (R ) 1, Ag|AgCl) and the quasi-Nernstian response region with a slope typical for metal (hydr)oxides R ∈ (0.6, 1) and that forsingle-crystal AgCl electrodes R ∈ (0.82, 0.88) are shown.


than that used to analyze single-crystal AgCl measurements,12,13

falling roughly between the values for single-crystal AgCl andthe hypothetical point of zero charge for the Ag|AgCl electrode.

Acknowledgment. We thank Niri Govind (Pacific NorthwestNational Laboratory) for helpful discussions. We also thankSteven Parker for granting access to the METADISE code. Thiswork was supported by a grant from the U.S. Department ofEnergy, Office of Basic Energy Sciences, Geosciences Program.The research was performed using the Environmental MolecularSciences Laboratory located at Pacific Northwest NationalLaboratory, a national scientific user facility sponsored by theDepartment of Energy’s Office of Biological and EnvironmentalResearch.

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