A perfect match: Silver deposition is one of the fastest electrochemical reactions, even though the Ag+ ion loses more than 5 eV solvation energy in the process. This phenomenon, an example of the enigma of metal deposition, was investigated by a combination of MD simulations, DFT, and specially developed theory. At the surface, the Ag+ ion experiences a strong interaction with the sp band of silver, which catalyzes the reaction.Fil: Pinto, Leandro M. C.. Universidade Estadual Paulista Julio de Mesquita Filho. Facultad de Filosofia E Ciencias-campus de Marilia; Brasil. Universitat Ulm; AlemaniaFil: Spohr, Eckhard. Universitat Duisburg - Essen; AlemaniaFil: Quaino, Paola Monica. Universidad Nacional del Litoral. Facultad de Ingeniería Química. Programa de Electroquímica Aplicada E Ingeniería Electroquímica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe; ArgentinaFil: Santos, Elizabeth del Carmen. Universitat Ulm; Alemania. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Instituto de Física "Enrique Gaviola"; ArgentinaFil: Schmickler, Wolfgang. Institute Of Theoretical Chemistry; Alemania. Universitat Ulm; Alemani

Pinto, Leandro M. C.

Quaino, Paola Monica

Santos, Elizabeth del Carmen

Schmickler, Wolfgang

Spohr, Eckhard

Angewandte Chemie International Edition

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Supporting Information Wiley-VCH 201369451 Weinheim, GermanyWhy Silver Deposition is so Fast: Solving the Enigma of MetalDeposition**Leandro M. C. Pinto, Eckhard Spohr, Paola Quaino, Elizabeth Santos, andWolfgang Schmickler*anie_201301998_sm_miscellaneous_information.pdfSupporting InformationMolecular dynamics simulationsPurely classical molecular dynamics were performed using the LAMMPS code[1]. The system consisted of a Ag(100) slab modeled by three layers (4.09 A˚ thick-ness), an ensemble of 470 water molecules, and the Ag+ ion initially located inthe bulk of the water. Periodic boundary conditions were used only in the xy–directions. The dimensions of the box were 23.14 × 23.14 × 32.09 A˚3. The correc-tion for the electrostatic long–range interactions was done by using a pppm/cgsolver. The temperature was set to 300 K using the NVT canonical ensemble.The following interactions were used: the parameters for the interaction be-tween the water molecules with the silver surface have been taken from a previ-ous work [2]; the interactions between the water molecules in the bulk and be-tween the silver ion with the water were specified by well–established Lennard–Jones potentials. For the water, we used the SPC/E model and the correspondingparameters for the oxygen and hydrogen have been taken from Yoshida et al. [3].The parameters for Ag+/O interaction have been taken from Spezia et al. [4].The Weighted Histogram Analysis Method (WHAM) code developed by Gross-field [5] was used to obtain the potential of mean force from a series of umbrellasampling simulations. A total of 40 umbrella samplings were performed. First wecarried out an equilibration run of 500 ps and then each sample ran for 200 ps,with a time step of 2.0 fs.Figure 1: Snapshot of a Ag+ ion positioned in the potential minimum near thesurface. Left panel: side view; right panel: top view without the metal atoms.Figure 1 show a snapshot from the molecular dynamics calculations for thecase where the ion is at the minimum of the potential of mean force. As can beseen from the two views presented, at this position it is surrounded by a stablesolvation cage.1Technicalities of the DFT CalculationsAll quantum chemical calculations were performed using the DACAPO code [6],which utilizes an iterative scheme to solve the Kohn–Sham equations of densityfunctional theory self–consistently. A plane-wave basis set is used to expand theelectronic wave functions, and the inner electrons were represented by ultrasoftpseudopotentials [7], which allows the use of a low energy cut–off for the plane–wave basis set. An energy cut–off of 400 eV, dictated by the pseudopotential ofthe metal, was used in all calculations. The electron–electron exchange and cor-relation interactions were treated with the generalized gradient approximation(GGA) in the version of Perdew, Burke and Ernzerhof [8]. The Brillouin–zone in-tegration was performed using a 8× 8× 1 k–points Monkhorst–Pack grid [9] cor-responding to the (1× 1) surface unit cell. The surfaces were modeled by a (2× 2)supercell with four metal layers and eight layers of vacuum. Dipole correctionwas used to avoid slab–slab interactions [10]. The first two layers were allowedto relax, while the bottom two layers were fixed at the calculated nearest-neighbordistance. The optimized surfaces (pre-relaxed) in the absence of the Ag atom wereused as input data to carry out the calculations to study the approach of the silveratom to the metal electrode. For each system, we performed a series of calcula-tions for a single silver atom adsorbed on a four-fold hollow site, and varied itsseparation from the surface. The pre-relaxed surface was kept fixed while theAg atom was allowed to relax in the xy-coordinates during these calculations. Ateach position we calculated the adsorption energy, and the DOS projected ontothe 5s orbital of silver.The energy to detach an atom from the kink site position and to move it to theterrace was obtained from the nudged elastic band method [11]. To perform thiscalculation the surface was modeled by a (4 × 4) supercell with four layers. Thetop layer was used to create the defect. All other parameters are the same as forthe DFT calculations.Interaction of the silver 5s orbital with the silver Ag(100) surface.In order to understand the details of the interaction between the silver ion and thesilver surface, we have calculated the density of states (DOS) of the Ag atom’s 5sorbital as it approaches the surface (see Fig. 2). Over the range shown in the fig-ures, the atom is not spin-polarized. At larger distances the DOS is centered atthe Fermi level and is half-filled, as is to be expected. However, even at a distanceof 3.5 A˚ it is substantially broadened and exhibits a tail extending to lower ener-gies caused by the interaction with the sp band. At a distance of 2.5 A˚ the DOShas already become very broad, and largely follows the sp band. The DOS of theadsorbed atom is very similar to the sp band, and shows the same peak near -5.6eV with respect to the Fermi level. These densities of states show no visible inter-2–5 00.00.20.40.6energy / eVDOS / eVï1Ag at Ag(100)3.5 Å2.5 Åadsorbedsp bandd band1.5 2.0 2.5 3.0 3.5 4.00246distance / Å|V|2  / eV2d band couplingsp band coupling-2.5 2.5Figure 2: Left: Electronic density of states of a Ag atom at various distances fromthe Ag(100) surface; the Fermi level has been taken as the energy zero. Right:Coupling constants with the silver d and the sp bands.action with the silver d band, which lies well below the Fermi level. From theseDOS we evaluated the coupling constants, or rather their square |V |2, of the 5sorbital with the sp and with the d band of silver (see Fig. 2). The coupling to thed band is very small, but the interaction with the sp band is very strong and longranged.Interaction with the d bandAs noted in the main text, the 5s orbital of the silver atom interacts only veryweakly with the d band of silver. However, the 4d orbital of the silver atom inter-acts with the silver d band, and there is some interest in studying this interaction.Figure 3 shows the density of states of a silver atom approaching a Ag(100) sur-face. When the atom is at a distance of 3 A˚, its DOS is substantially broadened,and has roughly a Lorentzian shape. As expected, its center lies well below theFermi level. When the atom is adsorbed, its d orbital merges with the d band ofthe substrate. Since all of the DOS lies well below the Fermi level, there is nosizable contribution of the d orbital to the adsorption bond.Calculation of the free energy surfaceWe consider only the 5s valence orbital of silver, which bonds to the silver surface.The problem is therefore equivalent to the adsorption of hydrogen on metals, forwhich we have developed our own theory [13]. The electronic part of the problem3–10 –8 –6 –4 –2 00.00.51.0energy / eVDOS / eV-1density of states of Ag 4d orbital at 3 Åadsorbedd band of AgFigure 3: Density of states of a silver atom above a Ag(100) surface at a distanceof 3 A˚ and in the adsorbed state.is the same, but the treatment of the solvent is different. To make this supplementself-contained, we briefly state the Hamiltonian. We denote with the index a thesilver 5s orbital, by a its energy, and by na the corresponding number operator;the metal states are labeled k and thus have energies k and number operatorsnk. The reaction takes place so close to the surface that spin polarization plays norole. We can therefore write the electronic part of the Hamiltonian in the form:Hel = ana +∑kkck +∑k[Vkc+k ca + V∗k c+a ck](1)The last term effects electron exchange between the metal and the reactant; c+denotes a creation and c an annihilation operator. Of course, the 5s orbital cantake up two electrons.The solvent terms of our Hamiltonian are:Hsol =12∑νh¯ων(q2ν + p2ν) + (1− na)∑νh¯ωνgνqν (2)where ν labels the phonon modes, qν and pν are the dimensionless coordinateand momentum operators, and in the last term gν is the interaction constant ofthe charge with the mode ν; na is the occupation operator for the 5s orbital ofsilver. After transformation to a single generalized solvent coordinate q and nor-malization these terms are transformed to [12]:Hsol = λ(q2 + p2) + 2λq(1− na) (3)4where λ is the energy of reorganization familiar from Marcus theory. In electrontransfer theory, the solvent modes are divided into a slow (nuclear) part and afast (electronic) part. The energy of reorganization comprises only the slow part.The interaction with the fast part is [13]:Vf = (1− 〈na〉)λf (4)where λf is the interaction energy with the fast part. Note that the fast part cou-ples via the expectation value of the occupation operator na. The sum of the twoterms gives the free energy of solvation: λ+λf = ∆Gsolv. The division in two partsis given by the Pekar factor, which for water is practically 1/2. Therefore we haveset: λ = λf = ∆Gsolv/2. Our simulations give the free energy of solvation, andhence λ and λf as a function of the distance, and we have used these in the calcu-lation of the free energy surfaces. Thus the rough estimates for λ as a function ofthe distance that we employed in our previous works have been replaced by thevalues calculated from molecular dynamics. Finally, the electrode potential cou-ples to the charge on the reactant, and gives an extra term (1− 〈na〉)e0φ, where φis the potential difference between the potential in the solution and the metal.The electronic part of the Hamiltonian can be solved by Green’s function tech-niques familiar from Anderson-Newns theory. In particular, this gives a formalexpression for the density of states (DOS) of the silver atom’s 5s orbital in frontof the silver surface. We obtain the electronic parameters of our model by fittingthis expression to the DOS obtained from DFT.While the Anderson-Newns model gives a consistent description of the sys-tem, it suffers from the neglect of many-body terms. To compensate for this de-fect, we calculate the energy of the silver atom as a function of the distance bothfrom DFT and from our model. The difference ∆E is the error of our model foran occupation of 〈na〉 = 1, which is in equilibrium with a solvent configurationof q = 0. During the reaction the occupation changes from 0 to 1. We assume thatthe error in the electronic energy is proportional to the occupation of the valenceorbital: ∆E(q) = ∆E(q = 0) × 〈na〉. This linear interpolation is obviously correctfor the two limits 〈na〉 = 1 and 〈na〉 = 0.References[1] S. Plimpton, J. Comput. Phys. 1995, 117(1), 1–19.[2] S. Frank, C. Hartnig, A. Groβ, W. Schmickler, ChemPhysChem 2008, 9(10),1371–1374.[3] K. Yoshida, T. Yamaguchi, A. Kovalenko, F. Hirata, J. Phys. Chem. B 2002,106(19), 5042–4049.5[4] R. Spezia, C. Nicolas, P. Archirel, A. Boutin, J. Chem. Phys. 2004, 120(11),5261–5268.[5] A. Grossfield, “WHAM: an implementation of the weighted his-togram analysis method”, version 2.0.6, can be found underhttp://membrane.urmc.rochester.edu/content/wham.[6] B. Hammer, L. B. Hansen, J. K. Nørskov, Phys. Rev. B 1999, 59(11), 7413–7421.[7] D. Vanderbilt, Phys. Rev. B 1990, 41(11), 7892–7895.[8] J. P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 1996, 77(18), 3865–3868.[9] H. J. Monkhorst, J. D. Pack, Phys. Rev. B 1976, 13(12), 5188–5192.[10] L. Bengtsson, Phys. Rev. B 1999, 59(19), 12301–12304.[11] a) G. Henkelman, B. P. Uberuaga, H. Jo´nsson, J. Chem. Phys. 2000, 113(22),9901–9904; b) G. Henkelman, H. Jo´nsson, J. Chem. Phys. 2000, 113(22), 9978–9985.[12] W. Schmickler, E. Santos, Interfacial Electrochemistry, 2. ed., Springer, NewYork, 2010, p. 270.[13] E. Santos, A. Lundin, K. Po¨tting, P. Quaino, W. Schmickler, Phys. Rev. B 2009,79(23), 235436-1–235436-10.6

Why Silver Deposition is so Fast: Solving the Enigma of Metal Deposition

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ElectrochemistryDOI: 10.1002/anie.201301998Why Silver Deposition is so Fast: Solving the Enigma of MetalDeposition**Leandro M. C. Pinto, Eckhard Spohr, Paola Quaino, Elizabeth Santos, andWolfgang Schmickler*The international Ampere, which was the accepted unit ofcurrent until 1948, was defined as that unvarying current thatwould deposit 0.001118000 g of silver from a solution of silvernitrate in water. Silver deposition was chosen to define thestandard because it is fast and reproducible, and because itsequilibrium potential is far from the hydrogen or oxygenevolution regions. In fact, the elementary deposition step:Ag+ + eÐAg is so fast that its rate constant has not yet beendetermined. Faraday could have saved a lot of time if he hadstudied silver deposition instead of the sluggish evolution ofgases.At a first glance it is surprising that silver deposition is sofast: The energy of hydration of the silver ion is about 5.15 eV,and it would be expected to lose a large part of its solvationshell when it approaches the electrode surface, so that thecorresponding energy of activation should be a sizablefraction of its solvation energy: somewhere between 1–3 eV.The same argument holds for the deposition of all commonmetal ions. Univalent ions typically have solvation energies ofthe order of 5 eV, divalent ions of 20 eV, and for trivalent ionsthe situation is even worse. To some extent, the electrostaticimage interaction of the ion with the metal should aid theapproach to the surface, but at distances at which thesolvation shell breaks up the image energy is much smallerthan the solvation energy. So how do these ions ever comeclose enough to the electrode surface to become dischargedand incorporated into the metal? This problem has been aptlynamed the “enigma of metal deposition”.[1]Because of its interesting properties, we have performeda theoretical investigation of silver deposition as a prototypefor the deposition of monovalent ions; in the following wepresent on our results, which are based on a combination ofmolecular dynamics, density functional (DFT) calculations,and a theory developed in our own group. First we shalldiscuss, how the solvated silver ion approaches the silverelectrode, then we present the electronic interaction of thesilver 5s orbital with the silver electrode, and finally we shalluse these results to calculate the free energy surface for thedeposition. All technical details are provided in the Support-ing Information.Experimentally, the mechanism of silver dissolution anddeposition was elucidated in the 1950s by Gerischer,[3] whoshowed that the first and rate-determining step in thedissolution is the detachment of a silver atom from a kinksite onto a terrace. The subsequent dissolution, namelyAg(terrace)!Ag+ + e is so fast that it is in equilibrium.A central question in the deposition or the adsorption ofions from solution is: What happens to the solvation sheath asthe ion approaches the surface? Does it have to overcome anenergy barrier to shed its solvation shell before it isdeposited? The first article to investigate this problem waspublished by Pecina et al. ,[4] who studied the adsorption of aniodide ion on Pt(100). The relevant quantity is the potential ofmean force (PMF) for the ion to move from the interior of thesolution towards the surface. This potential was calculated byumbrella sampling techniques based on a classical moleculardynamics simulation employing a suitable force field. For theI ion, the potential of mean force rises rapidly as it movesfrom the bulk of the aqueous solution towards the surface,reaching a value of about 1.35 eV (see Figure 1). Thus, this ionloses about half its solvation energy (about 2.5 eV), as wouldbe expected from simple geometric considerations.However, the situation for the Ag+ ion is completelydifferent: Here the potential stays almost constant as the ionmoves towards the surface, and even reaches a shallowminimum near 2.9 . A closer investigation shows that in thisposition the silver ion is surrounded by a stable sheath ofwater molecules providing a very effective solvation cage (seethe Supporting Information). We stress that this potentialincludes only the interaction with the water, not with theelectrode. Thus, in this configuration the role of the electrodeis indirect: it helps to fix the water molecules in the optimumposition to form the solvation sheath.[*] L. M. C. Pinto, Dr. E. Santos, Prof. W. SchmicklerInstitute of Theoretical Chemistry, Ulm University89069 Ulm (Germany)E-mail: wolfgang.schmickler@uni-ulm.deL. M. C. PintoFaculdade de CiÞncias, Univ Estadual Paulista, UNESP17.033-360 Bauru-SP (Brazil)Prof. E. SpohrUniversitt Duisburg-Essen, Lehrstuhl fr Theoretische Chemie45134 Essen (Germany)Dr. P. QuainoPRELINE, Universidad Nacional del LitoralSanta Fe (Argentina)Dr. E. SantosFaculdad de Matemtica, Astronoma y FsicaIFEG-CONICET, Universidad Nacional de CrdobaCrdoba (Argentina)[**] Financial support by the Deutsche Forschungsgemeinschaft (Schm344/34-1,2, and FOR 1376), and by an exchange agreement betweenthe DFG and CONICET are gratefully acknowledged. E. Santos,P.Q., and W.S. thank CONICET for continued support. E. Santosacknowledges PIP-CONICET 112-2010001-00411 for support. Agenerous grant of computing time from the Baden-Wrttemberggrid is gratefully acknowledged.Supporting information for this article is available on the WWWunder http://dx.doi.org/10.1002/anie.201301998.AngewandteChemie7883Angew. Chem. Int. Ed. 2013, 52, 7883 –7885  2013 Wiley-VCH Verlag GmbH & Co. KGaA, WeinheimExactly the same effect had been observed before byPecina and Schmickler for the Zn+ ion,[5] the PMF of which isalso shown in Figure 1. Similarly, Eck and Spohr[6] observed intheir simulations that Li+ ions have a stable configurationvery close to a mercury electrode.The more strongly solvated divalent Zn2+ ion also showsa minimum in the PMF, but at a larger distance from thesurface, where its two primary solvation sheaths are stillintact. At shorter distances, where it has to shed its secondarysheath, its potential starts to rise steeply. Cu+ and Cu2+, whichwe have also investigated, behave very similarly to zinc. Forreasons of clarity we have not included these data in theFigure.Thus, in the cases investigated here or in the literature,small univalent metal ions can get very close to the electrodesurface without losing solvation energy. In contrast, thepotential of mean force of bigger anions or of divalent ionsrises steeply as they approach the surface. The small univalentmetal ions fit neatly into the water structure at the surface,while the larger anions do not.To study the electronic interaction of the Ag5s orbitalwith a silver surface, we have investigated the energy ofa silver atom near a Ag(100) surface as a function of thedistance. The atom adsorbs at a hollow site at a distance of1.88  measured from the center of the top layer of Ag(100)atoms, with an energy of adsorption of 2.46 eV with respectto the vacuum. To understand the details of the interaction,we have calculated the density of states (DOS) of the 5sorbital for the Ag atom as it approaches the surface; thecorresponding plot is shown in the Supporting Information.From these DOS we evaluated the coupling constants, orrather their square jV j 2, of the 5s orbital with the sp and withthe d band of silver (see the Supporting Information). Thecoupling to the d band is very small, but the interaction withthe sp band is very strong and long-range, and reaches a valueof about 7 eV2 close to the surface where the deposition takesplace. To give a comparison, hydrogen adsorption on Pt isimmeasurably fast, and is catalyzed by the interaction of theH1s orbitals with the Ptd band. But even in the adsorbedstate, the coupling jV j 2 of hydrogen with the d band is onlyabout 3.9 eV2.[7] We shall show below that this strong andlong-range interaction is one of the factors that make silverdeposition and dissolution so fast.The experimental results by Gerischer[3] show that therate-determining step in the dissolution is the detachment ofa silver atom from a kink site onto the terrace. This occurswithout electron transfer, and can be evaluated by standardDFT. According to our calculations, on the Ag(100) surfacethe energy of a silver atom adsorbed on the terrace is DE =0.28 eV higher than for the kink site; the energy of activationfor the detachment from the kink is DE† = 0.57 eV. Gerischerobtained the corresponding Gibbs free energies, and hisvalues are for a polycrystalline surface, namely DG = 0.45 eV,and DG† = 0.58 eV. The agreement in the activation energiesis very satisfying, the small difference in the reaction energycan easily be explained by the difference in the surfacestructure and by the entropy term, which is missing in ourcalculations. For more information about the diffusion ofsilver atoms on a silver surface see Refs. [10,11] andreferences therein.With the information from the calculations presentedabove, we are able to calculate the free energy surface for thedeposition/dissolution of silver in aqueous solutions. Ourcalculations are based on our own theory, which combinesideas of the Marcus[8] and Hush[9] theories with those of theAnderson–Newns model.[12,13] Detailed information is pro-vided in the Supporting Information. Here, we briefly discussthe concept of the solvent coordinate, which plays a centralrole in electron-transfer theory. In the deposition of a silverion, the initial state is a fully solvated ion sitting in theminimum of the PMF curve in Figure 1. The final state is anatom deposited on the terrace, which interacts only weaklywith the solvent. For the reaction to occur, the solventconfiguration must fluctuate and assume an intermediateconfiguration in which an electron transfer happens and theion is discharged. The configurations of the solvent canconveniently be described by the solvent coordinate intro-duced by Hush. In our representation it is normalized in sucha way that a solvent coordinate q describes a solventconfiguration that would be in equilibrium with a reactantof charge q.[14] Thus, during silver deposition the solventcoordinate passes from 1 to 0.As the solvent fluctuates, the occupation of the valenceorbital changes and assumes fractional values. From DFT wecan obtain the energy of neutral atom as a function of thedistance and, with some tricks,[2,15] that of ions with integralcharges. We compare these energies with those obtained fromour model and correct for the many-body terms missing in theAnderson–Newns theory (for details, see Ref. [2] and theSupporting Information). We can then calculate the freeenergy surface for the reaction as a function of the position ofthe reactant and the solvent coordinate q.Figure 2 shows the surface for the deposition/dissolutionof a Ag+ ion. Our theory allows calculations for a specifiedelectrode potential, and this surface is for the case where theion in the bulk of the solution is in equilibrium with the kinksite, which defines the equilibrium potential for the overallreaction. As the energy of the atom adsorbed on the terrace ishigher than that of a kink atom, the deposition is uphill byFigure 1. Potentials of mean force (PMF) for the approach of ions tomove from the bulk of an aqueous solution towards an electrodesurface: Ag+ towards a Ag(100), Zn+ and Zn2+ towards Zn(0001), andI towards Pt(100). The potential refers only to the interaction of theions with the solvent. The data for Zn deposition were taken fromRef. [5], those for the iodide ion from Ref. [4]..AngewandteCommunications7884 www.angewandte.org  2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Angew. Chem. Int. Ed. 2013, 52, 7883 –78850.28 eV. The free energy at large distances and q =1corresponds to the Ag+ ion. There is a local minimumcentered near q =1 and d = 2.3 , which is induced by theminimum in the PMF observed in Figure 1; the interactionwith the silver electrode has shifted the minimum closer to thesurface. At q = 0 and short distances the surface exhibitsa shallow minimum for the deposited atom. The saddle pointfor the deposition is close to the minimum for the depositedatom. This is in line with the idea expressed by Gileadi;[1] thatis, it is the ion that transfers through the larger part of thedouble layer. The energy of activation for the deposition isabout 0.39 eV; for the reverse direction, the dissolution, it is0.11 eV. The saddle point is so close to the surface because theion does not lose solvation energy during its approach. Itsposition at a solvent coordinate near q =0.18, that is, closeto the final state, is due to the fact that the reaction is uphill,and is in line with the expectations of Marcus theory. Asmentioned above, the energy of activation for the detachmentof a silver atom from a kink site is 0.57 eV and thus higherthan that for silver dissolution, in agreement with the findingsof Gerischer.[3]The central question of our investigation was: Why issilver deposition so fast, even though the ion loses more than5 eV of solvation energy in the process? The explanation liesin the combination of two effects: 1) Like several otherunivalent metal ions, the Ag+ ion can get very close to theelectrode surface without losing solvation energy. There iseven a minimum in the potential of mean force when the ion isin a position very close to the surface, where it has a firmsolvation shell stabilized by the electrode surface. In thisposition, the ion is close enough to the surface to experiencethe electronic interaction with the silver electrode; 2) Theinteraction of the silver 5s orbital with the sp band of silver isvery strong and long-range. This is understandable, as theapproaching reactant interacts with identical atoms on thesurface, which is energetically favorable. Furthermore, the 5sorbitals are large, which increases the overlap and extends therange of the interaction.We surmise that the deposition of small univalent metalcations is always fast. In the four cases investigated so far,namely Ag+, Zn+, Li+ Cu+, the ions can approach very closeto the surface without loss of solvation energy. Furthermore,the electronic overlap of a metal ion with metal atoms of thesame kind should always be favorable. So the deposition ofthese ions is not governed by d-band catalysis, but by sp-bandautocatalysis. The same holds for the reverse directions,namely metal dissolution. Therefore our findings imply thatcorrosion is much faster than expected from simple argu-ments.What about multivalent ions? Marcus theory suggests thattheir deposition or dissolution should involve a series of one-electron steps, as the reorganization energies for the simulta-neous transfer of two electrons are typically four times higher.Furthermore, these ions cannot get close to the surfacewithout losing their secondary solvation sheath, which costsenergy. For Zn2+ and Cu2+ we have already shown that thepotential of mean force rises steeply as the ion approaches thesurface (see Figure 1 and Ref. [5]), and we may conclude thatthe transfer indeed occurs in two steps. This suggests that thedeposition of multivalent ions occurs in a series of one-electron steps, and only in the last step the ion is depositedonto the electrode; mutatis mutandis this should hold also formetal dissolution.Received: March 9, 2013Published online: June 20, 2013.Keywords: corrosion · metal deposition ·theoretical electrochemistry[1] E. Gileadi, J. Electroanal. Chem. 2011, 660, 247 – 253.[2] E. Santos, P. Quaino, W. Schmickler, Phys. Chem. Chem. Phys.2012, 14, 11224 – 11233, and references therein.[3] H. Gerischer, Z. Elektrochem. 1958, 62, 256 – 264.[4] O. Pecina, W. Schmickler, E. Spohr, J. Electroanal. Chem. 1995,394, 29 – 34.[5] O. Pecina, W. Schmickler, Chem. Phys. 2000, 252, 349 – 357.[6] B. Eck, E. Spohr, Electrochim. Acta 1997, 42, 2779 – 2788.[7] E. Santos, A. Lundin, K. Pçtting, P. Quaino, W. Schmickler,Phys. Rev. B 2009, 79, 235436.[8] R. A. Marcus, J. Chem. Phys. 1956, 24, 966 – 978.[9] N. S. Hush, J. Chem. Phys. 1958, 28, 962 – 972.[10] B. D. Yu, M. Scheffler, Phys. Rev. Lett. 1996, 77, 1095 – 1098.[11] K. Pçtting, N. Luque, P. Quaino, H. Ibach, W. Schmickler,Electrochim. Acta 2009, 54, 4494 – 4500.[12] P. W. Anderson, Phys. Rev. 1961, 124, 41 – 53.[13] D. M. Newns, Phys. Rev. 1969, 178, 1123 – 1135.[14] W. Schmickler, E. Santos, Interfacial Electrochemistry, 2. ed.,Springer, New York, 2010, p. 270.[15] P. Quaino, N. B. Luque, R. Nazmutdinov, E. Santos, W.Schmickler, Angew. Chem. 2012, 124, 13171 – 13174; Angew.Chem. Int. Ed. 2012, 51, 12997 – 13000.[16] W. Schmickler, Electrochim. Acta 1996, 41, 2329 – 2338.Figure 2. Free energy surface for the deposition of silver as a functionof the distance from the electrode and the solvent coordinate q. Thecalculations have been performed for the equilibrium potential of theoverall reaction, that is, for equilibrium with a kink site. All energiesare in eV.AngewandteChemie7885Angew. Chem. Int. Ed. 2013, 52, 7883 –7885  2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.angewandte.org

English

A perfect match: Silver deposition is one of the fastest electrochemical reactions, even though the Ag+ ion loses more than 5 eV solvation energy in the process. This phenomenon, an example of the enigma of metal deposition, was investigated by a combination of MD simulations, DFT, and specially developed theory. At the surface, the Ag+ ion experiences a strong interaction with the sp band of silver, which catalyzes the reaction. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Why Silver Deposition is so Fast: Solving the Enigma of Metal Deposition

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