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The Journalof Chemical Physics ARTICLE scitation.org/journal/jcp

Effects of surface charge and cluster sizeon the electrochemical dissolution of platinumnanoparticles using COMB3 and continuumelectrolyte models

Cite as: J. Chem. Phys. 152, 064102 (2020); doi: 10.1063/1.5131720Submitted: 15 October 2019 • Accepted: 20 January 2020 •Published Online: 10 February 2020

James M. Goff,1,a) Susan B. Sinnott,2 and Ismaila Dabo1

AFFILIATIONS1Department of Materials Science and Engineering, Materials Research Institute, Penn State Institutes of Energyand the Environment, The Pennsylvania State University, University Park, Pennsylvania 16802, USA

2Department of Materials Science, Materials Research Institute and Engineering, Department of Chemistry, The PennsylvaniaState University, University Park, Pennsylvania 16802, USA

Note: This paper is part of the JCP Special Topic on Interfacial Structure and Dynamics for Electrochemical Energy Storage.a)Author to whom correspondence should be addressed: [email protected]

ABSTRACTWe study the site-dependent dissolution of platinum nanoparticles under electrochemical conditions to assess their thermodynamic stabilityas a function of shape and size using empirical molecular dynamics and electronic-structure models. The third-generation charge optimizedmany-body potential is employed to determine the validity of uniform spherical representations of the nanoparticles in predicting dissolutionpotentials (the Kelvin model). To understand the early stages of catalyst dissolution, implicit solvation techniques based on the self-consistentcontinuum solvation method are applied. It is demonstrated that interfacial charge and polarization can shift the dissolution energies byamounts on the order of 0.74 eV depending on the surface site and nanoparticle shape, leading to the unexpected preferential removal ofplatinum cations from highly coordinated sites in some cases.

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I. INTRODUCTION

Fuel cells are attractive technological options that could elim-inate up to 70% of the carbon dioxide emitted during the life-cycle of personal transportation vehicles compared to internalcombustion engines.1 Although considerable progress has beenachieved in reducing the cost of the membrane-electrode assembly,the performance of fuel cells is still constrained by slow sweep-ing rates and reduced voltage windows to prevent the prema-ture degradation of the catalytic components.1 In order to predictthe durability of catalytic electrodes in aqueous media, we applyvoltage-dependent quantum–continuum methods with empiricalreactive molecular dynamics potentials to understand the electro-chemical corrosion of platinum nanoparticles under an appliedvoltage.

The goal of this work is to advance models of catalyst disso-lution by accounting for the polarization of the catalytic surfacewithin the electrical double layer and the effects of size andmorphol-ogy on local surface oxidation. In a widely used model proposed byDarling and Meyers, the standard reduction potentials of platinumnanoparticles are shifted from those of bulk platinum by a chem-ical potential ��Pt, calculated from the Kelvin equation assumingspherical geometries,2

��Pt = (γM)�(ρR). (1)Here, ��Pt is a function of the molecular weight M and density ρof platinum, the uniform surface tension γ, and the radius R of thenanocluster. This simple model has been successful in predicting theinitial rates of dissolution and equilibrium Pt concentrations as afunction of voltage. Yet, as mentioned in Ref. 2, this model does not

J. Chem. Phys. 152, 064102 (2020); doi: 10.1063/1.5131720 152, 064102-1

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include the effects of site-dependent dissolution and the interactionsof the surface atoms with the electrochemical double layer.

Ex situ electrochemical techniques have been used to character-ize the durability of nanostructured platinum electrodes.3 Studies ofcolloidal catalysts have also been carried out using transmission elec-tron microscopy, showing a curvature-dependent dissolution of thenanoparticles.4 The durability of nanoparticle electrodes depends ona multitude of factors, including the applied potential, nature of thesolvent, and chemical potential of the solvated ions. In the case ofnanoparticle-based electrodes used in proton exchange membranefuel cells, the degradation is highly size-dependent; results from Yuet al. indicate that cycling smaller nanoparticles with sizes around2.2-3.5 nm can cause the precipitation of platinum inside the mem-brane and are prone to coalescence in the electrode compared tolarger nanoparticles, 5-11.3 nm.5

Several theoretical approaches have been used to investigatecatalysts for the oxygen reduction reaction (ORR) and hydrogenevolution reaction (HER). Many of these involve calculating sur-face energies and applying Wulff constructions to predict mor-phology; others with explicitly simulated nanoparticles providesite-dependent adsorption behavior and substrate effects.6,7 First-principles studies germane to this work investigate potential-dependent oxidation and alloy behavior.8 Applied potential empiri-cal molecular dynamics simulations have been developed with thethird-generation charge optimized many-body (COMB3) poten-tials, allowing for large-scale atomistic simulations of solvatedelectrodes.9

Charge accumulation and polarization effects can influencethe stability of electrochemical systems to a large extent. Usingquantum–continuum embedding methods, voltage-dependent dis-solution trends can be predicted in the presence of a dielectricmedium for particles of a couple nanometers in diameter. Tomodel nanoparticles with larger sizes and varied shapes, we employreactive charge-dynamic potentials, namely, the third generation ofcharge optimized many-body (COMB3) potentials, to systematicallyexamine electrochemical dissolution trends as a function of shapeand size with a focus on assessing the validity of the Kelvin theory in

predicting curvature-dependent local chemical potentials. This workalso serves as a benchmark for dissolution energetics calculationswith COMB3 potentials.

To model and predict trends in the durability of platinumnanocatalysts, a description of the electrode–solution interface isneeded. When an electrode is brought into contact with the solutionphase, a group of solvent dipoles, adsorbed ions, and a diffuse ionlayer screen excess charge on the electrode surface.10 The arrange-ment of these solvent molecules and ions forms the electrochemicaldouble layer. The charge on the electrode surface can be determinedby the overall double-layer capacitance and the potential of zerocharge (PZC). While accounting for all contributions to the capac-itance would provide a more complete description of the interface,it can be convenient to adopt a single capacitive contribution thatis dominant in that particular voltage regime. For applied voltagesnear the potential of zero charge, the Gouy–Chapmanmodel, shownin Fig. 1(b), is often a reasonable approximation of the electrochemi-cal double layer. In the Gouy–Chapmanmodel, excess charge on theelectrode is screened by a distribution of ionic charge that followsa temperature- and potential-dependent Boltzmann law beyondsome exclusion distance from the electrode (the Poisson–Boltzmannmodel). In this work, the Gouy–Chapman model is adopted ratherthan the Helmholtz model, in which a plane of charge 3–5 Å fromthe electrode screens the excess charge, as depicted in Fig. 1(a). Thisplanar model is indeed not straightforward to apply to nanoparticlegeometries.

Some of the key difficulties in modeling the electrochemicalinterface involve the varied time and length scales of the differ-ent phenomena occurring at the interface. Charge transfer to theelectrode from redox processes can occur in times on the order ofattoseconds, while solution relaxations can occur in picoseconds.11Likewise, reactions at the surface occur on the angstrom scale,but diffuse layer equilibration, as schemed in Fig. 1, and diffusionlayer phenomena occur on length scales on the order of nanome-ters. Quantum–continuum models are an alternative to expensiveab initio molecular dynamics simulations or density functional the-ory (DFT) calculations involving explicit layers of the solvent. The

FIG. 1. (a) Schematic Helmholtz model of a platinum–solution interface. In a background dielectric caused by the water, the excess charge on the electrode is screenedcompletely by a Helmholtz layer which is approximately 3–5 Å away from the electrode surface. (b) Schematic Gouy–Chapman model for screening charges in a backgrounddielectric caused by water. The excess charge on the electrode surface is screened by a Poisson–Boltzmann distribution of charge. The screening length for this diffuse layerdepends on the temperature and the solution ions.

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https://scitation.org/journal/jcp


former method is difficult to employ still because of the size lim-ited by computational expense, among other issues. The latter canbe highly dependent on the orientation of the solvent molecules.We employ a quantum–continuummodel for this purpose, which isstill limited to length scales accessible with typical density functionaltheory calculations. We include calculations with reactive empiricalmolecular dynamics potentials for a two-fold purpose: to use den-sity functional theory to validate dissolution trends predicted withthe potentials and to extrapolate results to sizes difficult to accesswith quantum–continuum methods.

With these models, we predict trends in the early stages ofcorrosion for truncated octahedral, octahedral, cubic, and tetrahe-dral platinum nanoparticles. Dissolution energies are predicted as afunction of voltage using semilocal density functional theory calcu-lations with implicit solvation models of the electrochemical dou-ble layer. The resulting trends for smaller nanoparticles predictedwith density functional theory calculations are used to benchmarkgeneral trends predicted with COMB3 potentials. Once the trendsare verified, the COMB3 potentials are used to extrapolate dissolu-tion trends to sizes density functional theory calculations. Dissolu-tion energies are calculated spanning a broad range of sizes to pro-vide a site-specific assessment of the predictive ability of the Kelvinmodel.

II. COMPUTATIONAL METHODS

A. Nanoparticle shape constructionThe equilibrium cluster shape is dependent on the chemical

potential of the solvated ionic species. Bonnet and Marzari haveexamined the changes in nanoparticle shape upon proton adsorp-tion.12 Here, we resort to a simple model starting from surfaceenergies of undecorated slabs. To obtain the thermodynamic shapes(octahedra), we employ the Wulff construction, i.e., a constrainedminimization of the Gibbs free energy under constant volume. TheGibbs energy of the nanoparticle is given by

�G =�sγs�As, (2)

where the energy contributions from the surface energies γ run overevery surface s and �As is the change in the surface area of therespective surface. The Gibbs energy is minimized by variations inthe relative surface areas of the facets scaled by the respective sur-face energy. The surface energies of low index orientations are eval-uated using semilocal density functional theory. The equilibriumshapes are determined based on the surface energies using AtomisticSimulation Environment,13 as shown in Fig. 2.

The surface energies were calculated using the relationγ = Eslab − NEbulk with converged slab thicknesses following thecomputational protocol outlined in Ref. 14. It was found that avacuum layer of 7 Å on either side of slabs converged Fermi ener-gies to within 0.005 eV. Other calculation details are described inSec. II B. The surface energies in vacuum and in solvent are reportedin Table I and are compared to other values reported in the liter-ature. The surface energies are usually lowered in the presence ofa continuum dielectric with the exception of the (110) facet. All ofthe surface energies calculated and reported are for unreconstructed

FIG. 2. Wulff-construction Pt nanoparticle with a maximum diameter of 1.6 nm.The (100) facets are in yellow and the (111) facets in blue. The shape is calculatedusing the surface energies calculated in vacuum.

surfaces. Using the surface energies calculated in vacuum, the 201-atom (1.6 nm) truncated octahedral nanoparticle shape is predicted.Octahedral and cubic nanoparticles can be generated by shifts inthe (100) and (111) surface energies that reflect different redox con-ditions. Tetrahedral nanoparticles are obtained from cutting cubicnanoparticles along the (111) family of planes. The nonequilibriumtetrahedral nanoparticles are considered for high (111) facet ratioper mass and cubic nanoparticles due to the high activity reportedby Wang and co-workers.15

These structures are reported for our classical moleculardynamics in Fig. 3. The truncated octahedra used for empiricalmolecular dynamics simulations are built with the surface ener-gies calculated from first principles; these have the same qualitativetrends as the surface energies predicted using the COMB3 potentials.Similar ratios between the respective surface energies yield similarWulff constructions.

B. Self-consistent continuum solvationTo consider electrostatic energy contributions to the nanopar-

ticle systems, we begin with the Poisson equation for a system in

TABLE I. The first two rows are the surface energies calculated from first principlesin vacuum and in continuum solvent environments. The next two rows are the sur-face energies reported in the literature using density functional theory and moleculardynamics potentials.16 The final row gives experimental surface energies.

γ (J/m2) Pt (100) Pt (110) Pt (111)

PBE (vacuum) 1.87 1.93 1.49PBE (solvent) 1.16 2.27 0.41PBE (vacuum)14 1.81 1.85 1.49COMB316 2.22 2.38 1.71Expt.17 2.73 2.91 2.35

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FIG. 3. Per-site chemical potential shift[Eq. (12) without electrochemical poten-tial contributions from electrons or ions]at 0 K, as calculated with COMB3for energy minimized structures. Thetwo columns on the left correspond to2.8 nm, 3.2 nm, and 3.6 nm truncatedoctahedra, the third column correspondsto tetrahedral nanoparticles with edge-lengths of 3.5 nm, 4.5 nm, and 5.6 nm,and the right-most column correspondsto cubic nanoparticles with edge-lengthsof 2.4 nm, 3.2 nm, and 4.0 nm, respec-tively, in the order of increasing indexon the right. The dissociation energiesfor all nanoparticles and facets are onthe same scale for comparison acrossshapes.

vacuum. The electrostatic potential ϕ (r) is given by its solution fora given charge density ρ (r),

∇2ϕ (r) = 4πρ (r). (3)In the presence of a spatially varying dielectric, � (r), as in ourcontinuum model, we obtain the generalized Poisson equation,

∇ ⋅ � (r)∇ϕ (r) = 4πρ (r), (4)where the solution now yields the electrostatic potential of the chargedistribution in the presence of the dielectric. The cavity that deter-mines the spatial dependence of the dielectric function is defined bya cavity function, s(r) through the following relation:

�(r) =��

1, if ρ(r) > ρmaxs(r) = exp(t(ln ρ(r))), if ρmin < ρ(r) < ρmax�bulk, if ρ(r) < ρmin,

(5)

where the dielectric constant is equal to that of bulk water,�bulk = 78, if the electronic density is less than the minimum cutoffand 1 if it is greater than the maximum cutoff with a smooth transi-tion in between defined by the exponential of the switching function.The switching function, t, is given by

t(ρ(r)) = ln(�bulk)2π �2π (ln(ρmax) − ρ(r))� ln(ρmax) − ln(ρmin)

− sin�2π (ln(ρmax) − ρ(r))� ln(ρmax) − ln(ρmin)��. (6)The originally fitted values of ρmin = 0.005 a.u. and ρmax = 0.0001 a.u.were used to define the cavity regions of both the dielectric and thecounter-charge distribution.

Up to this point, only the electrostatic contributions from thesolvent have been accounted for in the form of the dielectric, �(r).To account for solution ions that form the counter-charges in theelectrochemical double layer, another charge distribution is added.When including the contributions from solution ion distributionsand dielectrics, we obtain the generalized Poisson equation withcounter-charges present,

∇ ⋅ � (r)∇ϕ (r) = 4π�ρ (r) + ρcc (r)�, (7)where the counter-charge distribution is given by ρcc (r) and thespecific form of this charge distribution depends on the double-layer model. A Helmholtz model has commonly been used forcounter-charge representations of the double-layer in similar stud-ies.18 In practice, this model is often implemented as a Gaus-sian of a certain width positioned 3–5 Å away from the electrodesurface as pictured in the schematic in Fig. 1(a). While this canbe a powerful approximation for planar slab models, it is diffi-cult to systematically assign Helmholtz models above nanoparticlefacets. In this work, a Poisson–Boltzmann distribution of counter-charges is assumed. This is a function of the electrostatic poten-tial and can contour to the shape of the cluster. For this distri-bution, ρcc (r) takes the form of the Poisson–Boltzmann distri-bution now referred to by ρPB (r), given by the following chargedensity:

ρPB (r) = γ (r) eNA�ic○i e−βzieϕ(r). (8)

Here, β = 1/(kBT), c○i is the concentration of ion i in the bulksolution, γ(r) is the complimentary cavity function defined byγ(r) = 1 − s(r) from Eq. (5), and zi is the charge of ion i in thesolution. The complimentary cavity function defines the region theelectrolyte can occupy; the implicit ions should not enter the bulkregion of the nanoparticle.

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This results in the free energy functional in the presence ofa dielectric and counter-charge distribution from Nattino et al.19given by

F[ϕ, ρtot] = � − �(r)8π �∇ϕ(r)�2 + ρPB(r)ϕ(r) + ρtot(r)ϕ(r)−�

i�i�ci(r) − T�s(ci(r))dr, (9)

where �(r) is the dielectric function following the form in Eq. (5)and ρtot is the total charge density from the solute ion cores andthe electrons. The fourth term in Eq. (9) gives the chemical workcontribution for ion i in solution based on its chemical potential,�i, and concentration change from the solution bulk, �ci(r). Thefinal term accounts for entropy contributions from the electrolytewhere the change in electrolyte entropy density �s(ci(r)) is the elec-trolyte entropy density change from that in the bulk solution anddepends on the spatially dependent ion density in solution. Fromthis functional, assuming ideal mixing and that counter-charges canbe represented as point charges, it can be shown that the functionalsimplifies as19

FPB[ϕ, ρtot] = � − �(r)8π �∇ϕ(r)�2 + ρtot(r)ϕ(r)+1β�i c

○i (1 − γ(r))e−βziϕ(r) dr. (10)

The functional in Eq. (10) is minimized for a given nanoparticle sys-tem, providing the energy for the Gouy–Chapman model in Fig. 1.Single, monovalent ions were used to represent the electrolyte witha bulk solution concentration of 5.0M for both positive and negativespecies unless otherwise specified.

The Gibbs solvation energies are obtained by adding non-electrostatic terms that account for the cavitation energy, repulsionfrom short-range interactions, and dispersion from van der Waalsforces,

�Gsol = �Ges + γS + αS + βV , (11)where �Ges is the electrostatic contribution, S is the quantum sur-face, and V is the quantum volume. The experimental surface ten-sion of the solvent, γ, determines the cavitation energy from thequantum surface, and the parameters α and β capture the repul-sion and dispersion contributions. The α and β parameters are fitto best reproduce the experimental solvation energies of moleculardata sets. The parameters used in this work are those reported in thework of Andreussi, 2012: γ = 72 dyn/cm (water), α = −22 dyn/cm,and β = −0.35 GPa. From the Gibbs energy in Eq. (12), thechemical potential shifts are calculated under the assumption thatcontributions from pressure and thermal vibrations are negligibleunder standard conditions.

There are numerous parameter sets and cavity representationsfor implicit solvation models with varied levels of rigor.20–22 Someof these models use solute and solvent specific dispersion contribu-tions, as in the work of Sundararaman and Goddard.23 Others useelement specific parameters defining the cavity, omitting the vol-ume terms for slab models entirely, such as in the work of Huanget al., to reproduce the PZC of a Pt (111) surface under certain ionadsorption conditions. In the self-consistent continuum solvation

(SCCS) model employed in this work, the ρmin and ρmax values are fitto reproduce experimental solvation energies of molecular datasets.The area and volume terms, and therefore the dispersion contribu-tions, were parameterized with molecular datasets. The applicabil-ity to metal clusters may not be optimal for this reason, and theapplicability to slab systems is limited due to size inconsistenciesintroduced by the volume term. The result is that the PZCs, capac-itances, and solvation energies calculated with this model may notbe well-compared to those from experiment; however, this model isused to predict trends in these properties as a function of nanopar-ticle shape and size as it relates to catalyst stability. The SCCSmodel adopted in this work has these deficiencies, but it will pro-vide general trends in shape and size for the driving forces fordissolution for the Ptn → Ptn−1 + Pt2+ dissolution mechanisms inthe presence of environmental effects. To reproduce experimentaltrends in PZC values and capacitances, it may be better to adoptother more rigorous models for the dispersion or fit cavity param-eters to reproduce experimental PZCs. The PZC for nanoparticlesis highly shape and size-dependent; it is best considered with ionadsorbates.24 Dissolution mechanisms in the presence of adsorbatesor oxide layers are not considered in this work, but shape-/size-dependent dissolution calculations in the presence of adsorbatesand oxide layers would be beneficial for the understanding of plat-inum nanocatalyst corrosion in a broader range of electrochemicalconditions.

The change in chemical potential of Pt for neutral nanopar-ticles without electrochemical double-layer contributions, ��○Pt, isdefined as

��○Pt = (En−1 + �Pt2+ + 2�e−) − En (12)and is given as the energy of a partially dissolved nanoparticle, En−1,plus the electrochemical potential of the dissolved platinum ion insolution, �Pt2+ , and the chemical potential of the electrons, �e− , minusthe energy of the pristine nanoparticle in the implicit solution, En.For neutral calculations in vacuum, the electrochemical potential isreplaced with the bulk energy of platinum and the chemical poten-tial of the electrons is not included. The standard electrochemicalpotential of the platinum ion is calculated under standard conditionsassuming an ideal solution. The chemical potential reference of neu-tral platinum comes from a DFT calculation of bulk platinum in theFCC phase, �FCCPt ; this is also used in the calculation of the standardelectrochemical potential of platinum ions, �○Pt2+ = �FCCPt + 2eϕPt�Pt2+ .In this work, we assume an ideal solution under standard condi-tions with standard reduction potentials from NIST.25 The standardreduction potential for bulk platinum, ϕPt�Pt2+ , is 1.2 V vs SHE, andthe applied voltages are calculated on the absolute hydrogen elec-trode scale with a shift of 4.44 V. The chemical potentials in Eq. (12)are transformed to voltage-dependent chemical potentials byapplying Legendre transform, −QΦ, for a constant potential formof the chemical potential,

��Pt(Φ) = (En−1 + �Pt2+ + 2�e− −Qn−1Φ) − (En −QnΦ), (13)where Qn−1 and Qn are the charges on the partially dissolvednanoparticle and the pristine nanoparticle at potential Φ, respec-tively. The charges are determined using an electrical double-layercapacitance model with the net intrinsic capacitance for the entire

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nanoparticle calculated on systems with applied charge. The chargeterms are applied to account for the changes in charge on eachnanoparticle to maintain a constant potential. The charge of ananoparticle is given by Q = C(Φ − Φpzc), where Φ is the appliedpotential, and the potential of zero charge, Φpzc, is calculated fromfirst principles for a given nanoparticle shape from Φpzc = −�F/e, asin Ref. 18. The diffuse double-layer capacitance C = dQ�dΦ usedto calculate this charge is determined by an expansion of the sys-tem energy with respect to charge. Electrons are added or removedfrom the nanoparticle system with the Poisson–Boltzmann counter-charges in Eq. (8), and the capacitance is determined by a quadraticfit of the resulting energies.26 This is the capacitance calculated basedon the model in Fig. 1(b).

Electronic-structure calculations were performed using theQuantum Espresso package with the Environ module.19,27,28 Planewave basis sets were used with kinetic energy cutoffs of 800 eVand charge density cutoffs of 6500 eV. Ultrasoft pseudopoten-tials were used from Materials Cloud library within generalized-gradient approximations.29,30 A smearing of 0.4 eV was usedwith the Marzari–Vanderbilt formalism on the electronic occu-pations.31 Binding energies were converged to 10 meV/atom andthe forces to 0.003 eV/Å unless otherwise specified. The vacuumlength was set to twice the maximum diameter of the nanoparti-cle to ensure convergence of the self-consistent Poisson–Boltzmanncountercharges.

C. Classical molecular dynamicsThe COMB3 potential32 comprises the following primary

terms:

ECOMB3(rN , qN) = Uself(qN) + UCoul(rN , qN)+Upolar(rN , qN) + Ushort(rN , qN)+UvdW(rN) + Ucorr(rN), (14)

where qN = (q1, q2, . . ., qN) is an array of the charges of all atomsin the system, rN = (r1, r2, . . ., rN) is an array of the positions of allatoms in the system, Uself is the self-energy coming from an expan-sion of the system energy with respect to charge of an atom, Upolar isa polarization term including atomic polarizabilities as well as dipoleinteractions, UCoul is a Coulombic interaction term including a cut-off function, Ushort is a bonding term similar to a Tersoff potentialbut including charge and angular terms, and Ucorr is an angular cor-rection term.32 An electronegativity equalization QEq-based chargescheme is used to equilibrate the charges.33,34

Molecular simulations were carried out using the LAMMPSsimulation package with the newly developed Pt-O-H potentialsdeveloped by Antony and co-workers.16,35 For dissociation energycalculations with COMB3, the energies were calculated at 0 Kfrom conjugate gradient minimization with a quadratic line searchmethod. Here, charge equilibration was performed at every min-imization step. The cells were constructed with vacuum spacing2–3 times the length of the nanoparticles so that the separationbetween any two atoms across periodic images was larger than theCoulombic interaction cutoff for two atoms with the Wolf sum-mation (22.5 Å).36 The platinum reference energy used for thesesimulations is from a minimization of bulk face-centered platinum

at 0 K. Dissolution was tested from each individual atom plotted inFig. 3.

III. RESULTS AND DISCUSSIONInitially, the Pt chemical potential shifts of nanoparticles were

calculated from Eq. (12) without contributions from the appliednanoparticle voltage or the chemical potential of electrons. Thechemical potential shifts from neutral, pristine nanoparticles fol-low the coordination of the site. For all sites tested, the chemicalpotential shift is positive, as seen in Table II. This is always the casefor solvated nanoparticles including the electrochemical potential ofthe electrons. When the dissociation is considered in vacuum with-out electrochemical potential of electrons, electrochemical potentialof platinum ions, or the electrochemical double-layer, the chemi-cal potential shift is negative and the dissociation is favorable. Thistrend is also demonstrated in Table II. The dissolution of largernanoparticles is less favorable and the chemical potential shift fromsites on the 201-atom truncated octahedron is systematically largerthan that at similar sites on the 79-atom truncated octahedron. Forneutral nanoparticles, the implicit solvation stabilizes the partiallydissolved structures. For the truncated octahedra, tetrahedron, andoctahedron, the solvated chemical potential shift was higher. Thetrends in the neutral chemical potential shifts remain the same;lower coordination leads to lower shifts. Including solvent effectsand the chemical potential of the electrons in the nanoparticle leadsto large changes in the stability of partially dissociated nanoparticles,and these results highlight the importance of accounting for theseeffects.

The largest nanoparticles simulated with implicit solvent are1.6 nm in diameter. This is in the lower-end of experimental sizeranges for certain electrode preparations.37 Experimental studieshave shown increased stability in ORR applications, specifically byincreasing the nanoparticle size range to 3–5 nm.38 Furthermore, themass activity of platinum nanoparticle catalysts can be optimized byincreasing the size to around 2.2 nm.15,39 While electronic-structurecalculations provide dissolution trends under an applied potential,classical molecular dynamics makes nanoparticle sizes such as thesemore accessible. The stability of larger nanoparticles is assessed byconsidering dissociation in vacuum [Eq. (12)]. This is done for larger2.8 nm atom truncated octahedral nanoparticles as well as othershapes and sizes shown in Fig. 3.

The relative stability of the truncated octahedral nanoparticlesis a trend carried across both levels of theory. In Fig. 3, the chem-ical potential shift is given for the same shapes of nanoparticlescalculated with semilocal DFT but with increasing size. The quali-tative trends in the vacuum chemical potential shifts for semilocalDFT are the same as those calculated with COMB3, but the shiftsin COMB3 are systematically higher. For example, ��○Pt for the cor-ner site of the smallest COMB3 tetrahedron is −1.36 eV, whereasgradient-corrected calculations predicts−0.97 eV for amuch smallernanoparticle. For truncated octahedra in COMB3, all of the siteshave positive chemical potential shifts predicting that dissolution isnot favorable from any site. The ��○Pt for the corner site on a 79-atom truncated octahedron is −0.12 eV, and in COMB3, the cornersite of the smallest truncated octahedron gives 0.15 eV. Contrary toresults with semilocal DFT, the chemical potential shifts are positive

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TABLE II. Shift in the chemical potential ��○Pt for nanoparticles of different shapes in the implicit solvent and in vacuum.The chemical potential shift is obtained for edges, corners, and facets of nanoparticles with the respective relaxed structuregiven above and the dissolution sites highlighted. The values calculated in vacuum do not include the contributions fromthe electrochemical potential of electrons, platinum ions, or the electrochemical double-layer. The geometry of the smalltruncated octahedron and tetrahedron is assumed; the octahedral and 201-atom truncated octahedral nanoparticles are theWulff constructions for the respective sizes.

Cluster structure Dissolution site

201-atom truncated octahedron (Wulff)

Corner (111) Edge (100)��○Pt (eV) (vacuum) 0.13 1.11 0.48 0.16��○Pt (eV) (solvent) 0.98 1.99 1.32 1.0279-atom truncated octahedron

Corner Face Edge��○Pt (eV) (vacuum) −0.12 0.53 0.29��○Pt (eV) (solvent) 0.81 1.44 1.2185-atom octahedron (Wulff)

Corner Face Edge��○Pt (eV) (vacuum) −0.54 0.69 0.78��○Pt (eV) (solvent) 0.56 1.79 1.8856-atom tetrahedron

Corner Face (middle) Face (corner) Edge��○Pt (eV) (vacuum) −0.97 0.68 0.34 0.68��○Pt (eV) (solvent) 0.24 1.86 1.47 1.84

for all truncated octahedral nanoparticles. For a given nanoparticle,COMB3 predicts the correct trends of the sites’ relative energy, butit may not predict favorable dissolution as semilocal DFT does. Thepronounced instability of the cubic nanoparticles in vacuum for the

COMB3 simulation is also shown in the semilocal DFT calculations;dissociation from the majority of sites tested resulted in reconstruc-tion for a 63-atom cubic nanoparticle. Edge-sites on cubic nanopar-ticles become less stable with size, and the stability of the center sites

FIG. 4. (a) Chemical potential shift associated with dissolution from the corner sites on Wulff-construction nanoparticles. The coefficient of determination for the linear fit (theKelvin equation) is 0.97 with a local surface energy of γsite = 0.0431 J/m2. (b) The chemical potential shift is associated with dissolution from the (100) facet. The relativelyhigh and low values for the third and sixth points correspond to Pt atoms removed from the center of a (100) facet and a site near the edge. The respective sites and relativedissolution energies are shown in the colormaps above the plots.

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remain constant. General trends with the tetrahedral nanoparticlesalso follow those with DFT, and the chemical potential shifts followthe coordination of sites.

These general trends in shape and size are extrapolated forcomparison with the Kelvin equation2 for the chemical potentialshift with size. Figure 4 indicates that chemical potential shifts fromnearly symmetrically equivalent sites on nanoparticles are inverselyproportional to the nanoparticle radius R. This is consistent with theKelvin equation. However, when comparing different sites on the(100) facets, the chemical potential shift can vary beyond the Kelvinequation, as demonstrated in the right inset in Fig. 4. For similarsites across nanoparticle sizes where the Kelvin equation is valid, alocal surface tension can be defined for the site, γsite. This can beobtained from fitting the Kelvin equation and reflects the local forceson the site. For the corner sites, this is 0.0431 J/m2 from COMB3simulations, which is comparable to the average value used in Ref. 2,0.0237 J/m2. Local surface tensions fit with COMB3 simu-lations could help develop site-dependent kinetic dissolutionmodels.

These results are in contrast with those calculated using (13)in Fig. 5, indicating a negative potential-dependent chemical poten-tial shift over a wide potential window. The dissolution of the sitefrom the less coordinated (100) facet was the lowest over the sta-bility window of water. Dissolution from the (100) facet and thecorner sites is negative in the potential window of water, and othersrequire significant amounts of overpotential. The favorable dissolu-tion of the (100) facet over the corner site is a direct result of theintrinsic electrochemical quantities obtained from the implicit sol-vent model. Similar calculations of other nanoparticle shapes arereported in the supplementary material. Complementary classical

FIG. 5. Voltage-dependent chemical potential shift, ��Pt , from the various sitestested in Table II. The electrochemical potential of electrons is subtracted offto show the magnitude of the energy change due to capacitive terms alone inEq. (13). The thermodynamic stability of a given site is determined by its positionrelative to the black line which is the coupled chemical potential of the dissolvedplatinum and electrons in the electrode. The stability window of water is highlightedby the dotted blue lines. It can be seen that the most favorable dissolution site inoxidizing conditions of water is from the small (100) facet. Counter-ion concentra-tions used for these simulations were set to 1.0M. The nanoparticles show the fullyrelaxed structures with the dissolution site highlighted.

FIG. 6. Voltage-dependent chemical potential shift, ��Pt , from sites tested inTable II for the 79-atom truncated octahedron. Again, the electrochemical potentialof electrons is subtracted off. Contrary to the larger truncated octahedron in Fig. 5,the edge site exhibits favorable dissolution near the upper end of the potentialwindow of water.

molecular dynamics simulations of a nanoparticle in real time arereported in the supplementary material (Fig. 6).

Molecular dynamics simulations of explicitly solvated nanopar-ticles were also carried out under the Berendsen NPT barostat(see supplementary material) for 1 ns to test for dissolution. Themechanisms involving the dissociation of water or oxidation of thesurface may have a larger barrier than expected when using COMB3potentials. However, the qualitative trends extracted from the sim-ulations are useful in describing local charge transfer and solventinteractions, indicating which sites are more prone to dissolution.Positive charge accumulates near nanoparticle edges and corners;there is more specific adsorption of water molecules along thesesites.

To consider size dependence for truncated octahedra, thesmaller nanoparticles are predicted to dissolve at lower potentialscompared to large octahedra. The chemical potential shifts are sys-tematically lower for the smaller truncated octahedron, but thecurvature of ��Pt(Φ) matches qualitatively. This indicates that theintrinsic capacitance and potential of zero charge associated witha site are similar with increasing size. These results show noveltrends in the dissolution of Pt nanoparticles from different sitesand highlight the sensitivity of driving forces for dissolution tovoltage.

IV. CONCLUSIONThe chemical potential shift of platinum dissolution tends to

follow the coordination of the dissolution site, and generally, smallerclusters were predicted to dissolve more readily. These quantitieswere demonstrated to be highly dependent on the applied poten-tial. The correction from capacitive contributions to the energyis nearly 0.74 eV per site over the voltage range shown. In somecases, inclusion of the polarized surface and electrochemical dou-ble layer predicted dissolution of highly coordinated sites over lesscoordinated ones, especially at high overpotentials. Calculations for

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voltage-dependent chemical potential shifts predicted dissolution ofsmaller nanoparticles at lower overpotentials compared to largernanoparticles.

Changes in local chemical potentials were presented for plat-inum nanoparticles as a function of shape and size. It was shownthat the Kelvin equation is a good descriptor for the chemical poten-tial shift of a nanoparticle from bulk platinum but only for average orequivalent local configurations (e.g., symmetrically equivalent sites).The shape-dependent changes in chemical potentials predicted withCOMB3 potentials reflect qualitative trends from semilocal DFTcalculations. Predictions from COMB3 yield slightly overestimatedpotentials but capture the same trends as quantum simulations.

In future refined models, the effects of the electrochemicaldouble layer should also be considered as they can lead to dra-matic changes in the thermodynamic driving forces for dissolution.The Kelvin equation can be used for an average chemical poten-tial shift from the bulk, but site-specific dissolution energies can bepredicted using reactive molecular dynamics potentials to accountfor local curvature. The coupled results from the different modelsdemonstrate the sensitivity of these systems to the applied poten-tial and particle size. Incorporating some of these effects can helpimprove models of nanocatalyst corrosion and dissolution in fuelcells.

SUPPLEMENTARY MATERIAL

The attached supplementary material includes an example sim-ulation of a platinum nanoparticle in explicit water. Along withthis simulation is a brief discussion on the implementation ofQEq charge equilibration in COMB3 and how this leads to exces-sive charge transfer to the solution. In addition to the moleculardynamics simulation, additional voltage-dependent chemical poten-tial shifts are given for tetrahedral and octahedral nanoparticles.

ACKNOWLEDGMENTSWe acknowledge financial support from the U.S. Department

of Energy, Office of Science, Basic Energy Sciences, CPIMS Pro-gram, under Award No. DE-SC0018646. We acknowledge supportand training provided by the Computational Materials Educationand Training (CoMET)NSF Research Traineeship (Grant No. DGE-1449785). Computations for this research were performed at thePennsylvania State University’s Institute for CyberScience AdvancedCyberInfrastructure (ICS-ACI).

REFERENCES1T. Yoshida and K. Kojima, “Toyota MIRAI fuel cell vehicle and progress towarda future hydrogen society,” Electrochem. Soc. Interface 24, 45–49 (2015).2R. M. Darling and J. P. Meyers, “Kinetic model of platinum dissolution inPEMFCs,” J. Electrochem. Soc. 150, A1523–A1527 (2003).3Y. Shao, G. Yin, and Y. Gao, “Understanding and approaches for the durabil-ity issues of Pt-based catalysts for PEM fuel cell,” J. Power Sources 171, 558–566(2007).4R. Narayanan and M. A. El-Sayed, “Effect of nanocatalysis in colloidal solu-tion on the tetrahedral and cubic nanoparticle SHAPE: Electron-transfer reac-tion catalyzed by platinum nanoparticles,” J. Phys. Chem. B 108, 5726–5733(2004).

5K. Yu, D. J. Groom, X. Wang, Z. Yang, M. Gummalla, S. C. Ball, D. J. Myers,and P. J. Ferreira, “Degradation mechanisms of platinum nanoparticle catalysts inproton exchange membrane fuel cells: The role of particle size,” Chem. Mater. 26,5540–5548 (2014).6P. C. Jennings, H. A. Aleksandrov, K. M. Neyman, and R. L. Johnston,“ADFT study of oxygen dissociation on platinum based nanoparticles,” Nanoscale6, 1153–1165 (2014).7G. N. Vayssilov, Y. Lykhach, A. Migani, T. Staudt, G. P. Petrova, N. Tsud,T. Skála, A. Bruix, F. Illas, K. C. Prince et al., “Support nanostructure boosts oxy-gen transfer to catalytically active platinum nanoparticles,” Nat. Mater. 10, 310(2011).8R. Jinnouchi, K. K. T. Suzuki, and Y. Morimoto, “DFT calculations on electro-oxidations and dissolutions of Pt and Pt–Au nanoparticles,” Catal. Today 262,100–109 (2016).9T. Liang, A. C. Antony, S. A. Akhade, M. J. Janik, and S. B. Sinnott, “Appliedpotentials in variable-charge reactive force fields for electrochemical systems,”J. Phys. Chem. A 122, 631–638 (2018).10D. C. Grahame, “The electrical double layer and the theory of electrocapillarity,”Chem. Rev. 41, 441–501 (1947).11A. Baskin and D. Prendergast, “Improving continuum models to define practi-cal limits for molecular models of electrified interfaces,” J. Electrochem. Soc. 164,E3438–E3447 (2017).12N. Bonnet and N. Marzari, “First-principles prediction of the equilibrium shapeof nanoparticles under realistic electrochemical conditions,” Phys. Rev. Lett. 110,086104 (2013).13A. H. Larsen, J. J. Mortensen, J. Blomqvist, I. E. Castelli, R. Christensen,M. Dułak, J. Friis, M. N. Groves, B. Hammer, C. Hargus et al., “The atomic simula-tion environment—A python library for working with atoms,” J. Phys.: Condens.Matter 29, 273002 (2017).14N. E. Singh-Miller and N. Marzari, “Surface energies, work functions, and sur-face relaxations of low-index metallic surfaces from first principles,” Phys. Rev. B80, 235407 (2009).15C. Wang, H. Daimon, T. Onodera, T. Koda, and S. Sun, “A general approachto the size- and shape-controlled synthesis of platinum nanoparticles andtheir catalytic reduction of oxygen,” Angew. Chem., Int. Ed. 47, 3588–3591(2008).16A. Antony, S. Akhade, Z. Lu, T. Liang, M. J. Janik, S. Phillpot, and S. B.Sinnott, “Charge optimized many body (COMB) potentials for Pt and Au,”J. Phys.: Condens. Matter 29, 225901 (2017).17R. Tran, Z. Xu, B. Radhakrishnan, D. Winston, W. Sun, K. A. Persson, and S.P. Ong, “Surface energies of elemental crystals,” Sci. Data 3, 160080 (2016).18N. Keilbart, Y. Okada, A. Feehan, S. Higai, and I. Dabo, “Quantum-continuumsimulation of the electrochemical response of pseudocapacitor electrodes underrealistic conditions,” Phys. Rev. B 95, 115423 (2017).19F. Nattino, M. Truscott, N. Marzari, and O. Andreussi, “Continuum modelsof the electrochemical diffuse layer in electronic-structure calculations,” J. Chem.Phys. 150, 041722 (2018).20K. Mathew and R. G. Hennig, “Implicit self-consistent description of electrolytein plane-wave density-functional theory,” arXiv:1601.03346 (2016).21M. Truscott and O. Andreussi, “Field-aware interfaces in continuum solvation,”J. Phys. Chem. B 123, 3513–3524 (2019).22S. Nishihara and M. Otani, “Hybrid solvation models for bulk, interface, andmembrane: Reference interaction site methods coupled with density functionaltheory,” Phys. Rev. B 96, 115429 (2017).23R. Sundararaman and W. A. Goddard III, “The charge-asymmetric nonlo-cally determined local-electric (CANDLE) solvation model,” J. Chem. Phys. 142,064107 (2015).24A. López-Cudero, J. Solla-Gullón, E. Herrero, A. Aldaz, and J. M. Feliu, “COelectrooxidation on carbon supported platinum nanoparticles: Effect of aggrega-tion,” J. Electroanal. Chem. 644, 117–126 (2010).25S. G. Bratsch, “Standard electrode potentials and temperature coefficients inwater at 298.15 K,” J. Phys. Chem. Ref. Data 18, 1–21 (1989).26S. E. Weitzner and I. Dabo, “Quantum–continuum simulation of underpoten-tial deposition at electrified metal–solution interfaces,” npj Comput. Mater. 3, 1(2017).

J. Chem. Phys. 152, 064102 (2020); doi: 10.1063/1.5131720 152, 064102-9


https://scitation.org/journal/jcphttps://doi.org/10.1063/1.5131720#supplhttps://doi.org/10.1149/2.f03152ifhttps://doi.org/10.1149/1.1613669https://doi.org/10.1016/j.jpowsour.2007.07.004https://doi.org/10.1021/jp0493780https://doi.org/10.1021/cm501867chttps://doi.org/10.1039/c3nr04750dhttps://doi.org/10.1038/nmat2976https://doi.org/10.1016/j.cattod.2015.08.020https://doi.org/10.1021/acs.jpca.7b06064https://doi.org/10.1021/cr60130a002https://doi.org/10.1149/2.0461711jeshttps://doi.org/10.1103/physrevlett.110.086104https://doi.org/10.1088/1361-648X/aa680ehttps://doi.org/10.1088/1361-648X/aa680ehttps://doi.org/10.1103/physrevb.80.235407https://doi.org/10.1002/anie.200800073https://doi.org/10.1088/1361-648x/aa6d43https://doi.org/10.1038/sdata.2016.80https://doi.org/10.1103/physrevb.95.115423https://doi.org/10.1063/1.5054588https://doi.org/10.1063/1.5054588http://arxiv.org/abs/1601.03346https://doi.org/10.1021/acs.jpcb.9b01363https://doi.org/10.1103/physrevb.96.115429https://doi.org/10.1063/1.4907731https://doi.org/10.1016/j.jelechem.2009.06.016https://doi.org/10.1063/1.555839https://doi.org/10.1038/s41524-016-0004-9


27P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni,D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. D. Corso,S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougous-sis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello,S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero,A. P. Seitsonen, A. Smogunov, P. Umari, and R. M. Wentzcovitch, “QUAN-TUM ESPRESSO: A modular and open-source software project for quantumsimulations of materials,” J. Phys.: Condens. Matter 21, 395502 (2009).28O. Andreussi, I. Dabo, and N. Marzari, “Revised self-consistent continuumsolvation in electronic-structure calculations,” J. Chem. Phys. 136, 064102 (2012).29G. Prandini, A. Marrazzo, I. E. Castelli, N. Mounet, and N. Marzari, “Precisionand efficiency in solid-state pseudopotential calculations,” npj Comput. Mater. 4,72 (2018).30J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximationmade simple,” Phys. Rev. Lett. 77, 3865 (1996).31N.Marzari, D. Vanderbilt, A. De Vita, andM. Payne, “Thermal contraction anddisordering of the al (110) surface,” Phys. Rev. Lett. 82, 3296 (1999).32T. Liang, Y. K. Shin, Y.-T. Cheng, D. E. Yilmaz, K. G. Vishnu, O. Verners,C. Zou, S. R. Phillpot, S. B. Sinnott, and A. C. van Duin, “Reactive potentials foradvanced atomistic simulations,” Annu. Rev. Mater. Res. 43, 109–129 (2013).

33A. K. Rappe and W. A. Goddard III, “Charge equilibration for moleculardynamics simulations,” J. Phys. Chem. 95, 3358–3363 (1991).34W. J. Mortier, S. K. Ghosh, and S. Shankar, “Electronegativity-equalizationmethod for the calculation of atomic charges in molecules,” J. Am. Chem. Soc.108, 4315–4320 (1986).35A. C. Antony, T. Liang, and S. B. Sinnott, “Nanoscale structure and dynamics ofwater on Pt and Cu surfaces from MD simulations,” Langmuir 34, 11905–11911(2018).36D.Wolf, P. Keblinski, S. Phillpot, and J. Eggebrecht, “Exact method for the sim-ulation of Coulombic systems by spherically truncated, pairwise r−1 summation,”J. Chem. Phys. 110, 8254–8282 (1999).37Y. Shao-Horn, W. C. Sheng, S. Chen, P. J. Ferreira, E. F. Holby, and D. Morgan,“Instability of supported platinum nanoparticles in low-temperature fuel cells,”Top. Catal. 46, 285–305 (2007).38E. F. Holby, W. Sheng, Y. Shao-Horn, and D. Morgan, “Pt nanoparticle stabilityin PEM fuel cells: Influence of particle size distribution and crossover hydrogen,”Energy Environ. Sci. 2, 865–871 (2009).39M. Shao, A. Peles, and K. Shoemaker, “Electrocatalysis on platinum nanopar-ticles: Particle size effect on oxygen reduction reaction activity,” Nano Lett. 11,3714–3719 (2011).

J. Chem. Phys. 152, 064102 (2020); doi: 10.1063/1.5131720 152, 064102-10

https://scitation.org/journal/jcphttps://doi.org/10.1088/0953-8984/21/39/395502https://doi.org/10.1063/1.3676407https://doi.org/10.1038/s41524-018-0127-2https://doi.org/10.1103/physrevlett.77.3865https://doi.org/10.1103/physrevlett.82.3296https://doi.org/10.1146/annurev-matsci-071312-121610https://doi.org/10.1021/j100161a070https://doi.org/10.1021/ja00275a013https://doi.org/10.1021/acs.langmuir.8b02315https://doi.org/10.1063/1.478738https://doi.org/10.1007/s11244-007-9000-0https://doi.org/10.1039/b821622nhttps://doi.org/10.1021/nl2017459

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