Onthethicknessofthedoublelayerinionicliquids

AntonRuzanova,MeeriLembinenb,PelleJakovitsc,SatishN.Sriramac,IuliiaV.Voroshylovad,e,M.NatáliaD.S.Cordeirod,CarlosM.Pereirae,JanRossmeislf,andVladislavB.Ivaništševa*

Inthisstudy,weexaminedthethicknessoftheelectricaldoublelayer(EDL)inionicliquidsusingdensityfunctionaltheory(DFT)calculations and molecular dynamics (MD) simulations. We focused on the BF4− anion adsorption from 1-ethyl-3-methylimidazoliumtetrafluoroborate(EMImBF4)ionicliquidontheAu(111)surface.AtbothDFTandMDlevels,weevaluatedthecapacitance–potentialdependencefortheHelmholtzmodelof the interface.UsingMDsimulations,wealsoexploredamorerealistic,multilayerEDLmodelaccountingfortheionlayering.ConcurrentanalysisoftheDFTandMDresultsprovidesagroundforthinkingwhethertheelectricaldoublelayerinionicliquidsisone-ormulti-ionic-layerthick.

IntroductionSince their rediscovery in the 1990s, the so-called room

temperatureionicliquids(RTILs)havebeenstudiedassolventswith a unique combination of diverse physicochemicalproperties,1–3 that make them captivating from fundamentalandapplicationpointsofview.4–9Withinthefollowingdecades,electrode | RTIL interfaces have attracted considerableattention. Currently, the electrical double layer (EDL) at theelectrode | RTILinterfacesisinfocusofresearchonenhancingperformance of energy storage and transformation insupercapacitors,10,11actuators,8,12batteries,2,13andsolarcells.14

Significant progress in understanding of the interfacialprocessesoccurring intheEDLhasbeenmaderecentlyatthetheoretical level,15–20 by computationalmodelling,21–27 and inexperimentalmeasurements.28–43Nevertheless, someauthorsarguewhethertheEDLinRTILsisone-ormulti-ionic-layerthick.On the one hand, by vibrational Stark shifts and capacitancemeasurements, Baldelli concluded that the EDL in RTILs iseffectivelyone-ionic-layerthickduetoasinglelayerofcounter-ions.32,33 On the other hand, other authors considered amultilayer structure for interpretation of electrochemicalimpedance data.34,36 In theory, an account for the innermostlayerofcounter-ionsiscrucialinmodifiedPoisson–Boltzmann,mean spherical approximation, and Landau–Ginzburg-typecontinuum models.17–19,44,45 Molecular dynamics (MD)simulations,26,46–48 atomic force microscopy,49 and X-rayspectroscopy50–52studieshaveascertainedthattheEDLinRTILsindeed consists of alternating layers of anions and cations.

Accordingtothesestudies,intheinnermostlayer,thecounter-ions are in direct contact with the surface, templating thesubsequentlayers.UponcloserexaminationofMDsimulationsresults,itappearsthattheEDLstructurechangesfrommulti-tomonolayeruponvariationofthesurfacecharge.25,27Overall,itmay be assumed that the innermost layer largely determinestheinterfacialproperties,yettheextentremainsunclear.53

HowthickistheEDLinRTILsanddoestheinnermostlayerdominate in the overall potential-dependent multilayer EDL?We endeavoured to investigate the subject as the answer tothesequestionsisessentialfordevelopmentofenergystoragedevices,especiallysupercapacitorsandbatteries.1,2

Wefocusedontheadsorption†ofBF4−anionsfrom1-ethyl-

3-methylimidazolium tetrafluoroborate (EMImBF4) ionic liquidon the Au(111) surface using density functional theory (DFT)calculations and MD simulations. First, we examined thedifferencesintheDFTandMDrepresentationoftheHelmholtzmodel of the Au(111) | BF4

− interface. Next, in comparison totheHelmholtzmodel,weexploredamorerealistic,multilayerAu(111) | EMImBF4interfaceaccountingfortheionlayering.

Tothebestofourknowledge,onlyValenciaetal.,54–56Klaveretal.,57andPlögeretal.58conductedsimilarDFTcalculationstostudy the adsorption of RTILs on uncharged lithium, gold,aluminium,andcopper surfaces.Differently, in this study,weinvestigatedtheadsorptionofBF4

−onchargedAu(111)surface.The interfaces between imidazolium tetrafluoroborate

RTILs and single crystal Au(111), Cd(0001), Bi(111) as well aspolycrystalline gold and platinum surfaces were previouslystudied using cyclic voltammetry and electrical impedancespectroscopytechniques.36–40,43,59–63Themeasuredcapacitancedependenceonpotentialiswidelyagreedtobedeterminedbythe adsorption of anions/cations, implying accumulation ofioniccounterchargenearthechargedmetalsurface.Forsomeions,theformationoftheorderedadlayersatsingle-crystalgoldfaces was observed by in situ scanning tunnellingmicroscopy.43,64–67Basedonthesefindings,weassumedthatanorderedlayerofBF4

−describestheAu(111) | EMImBF4interfaceatanodicpotentials.

InterfacemodelsandcomputationalmethodsInterfacemodels

AsaroughapproximationofapositivelychargedelectrodeimmersedintoanEMImBF4ionicliquid,weconstructedasetofAu(111) | BF4

− interface configurations representing theHelmholtz model. In this model, the surface charge iscompensatedbyalayerofcounter-ionsatanaveragedistanced from the metal surface. This model represents a simpleparallelplatecapacitor.

IntheDFTcalculations,thecoverage(θ)rangedfrom1/20to1/2ofBF4

−anionspersurfacegoldatomintheunitcellofvariablesize.ThreelayersofgoldatomsintotalformedtheslabrepresentingtheAu(111)surface.Fig.1ashowsAu(111) | BF4

−interfacemodel atθ = 1/3.Only the first upperAu layerwasallowedtorelax,whilethetwobottomlayerswerekeptfixedintheir bulk positions. As a starting guess for the electronicstructure,avaryingnumberofBF4

•radicalswereplacedontheneutral Au(111) surface. The charge of the radicalsspontaneously decreased during relaxation, turning the BF4

•radicals into BF4

− ions. Consequently, the interface becamepolarised,andtheelectricfieldsetupbetweenthechargedgoldsurfaceandadsorbedions. WithintheHelmholtzmodelframework,welookedonlyattheadsorptionofanionsontheAu(111)surface,intheabsenceof cations. This divide-and-conquer approach is a reasonablefirststeptowardsmorecomplexmodels.AccordingtoRef.53,the currentmodel is the simplest “1D” representation of theEDLinRTILs.RecentMDsimulationsresultsrevealthattheEDLstructure can indeedbe reduced to “1D” at a certain surfacechargewhenamonolayerofcounter-ionsatachargedsurfaceis formed.27,68 Thus, we thoughtfully utilised the Helmholtzmodelnotonlytotestitslimitsbutalsotoverifytheconceptofthemonolayerformation.

In theMD simulationsof theHelmholtzmodel, a variablenumberofBF4

− anions (from1 to112)wereput into contactwithafixedAu(111)slab.Thecellsizewas4.04×4.00nm2andconsistedof224goldatoms.Eachanionhadatotalchargeof−e/√2,andeachgoldatomhadafixedpointchargerequiredtocompensatetheoverallioniccharge.Thestudiedrangeofthesurfacechargedensityvariedfrom1to80µC/m2correspondingtothecoverageof1/2.

In the more realistic MD simulations, the initialconfigurationswereconstructedusingthePACKMOLpackage,69

byinserting288cationsand288anionsofEMImBF4atrandompositionsbetweentwogoldenslabstoformthefinalsimulationcell,with dimensions of 2.98 nm × 2.95 nm × 11.36 nm. ThegoldenslabofAu(111)wassetupusing480goldatomswiththehelpofatomicsimulationenvironment(ASE).70Thegoldenslabswerefixedinpositionsduringallsimulations.Thepolarisationwasrealisedbyapplyinganelectricfieldinthez-directionofthesimulation cell. According to our preliminary tests, thisapproachisequivalenttotheassigningofpointcharges(as inthe case of the Helmholtz model), but it is computationallymoreefficient.

Densityfunctionaltheorycalculations

AllDFTcalculationswereperformedwiththeASEinterfaceusing the revised Perdew–Burke–Ernzerhof (RPBE) exchange-correlation functional and projector augmented wave (PAW)methodasimplementedinthereal-spacegridcodeGPAW.70–72AvanderWaals(vdW)correctionproposedbyTkachenkoandScheffler was applied on top of the RPBE functional.73Wavefunctions,potentials,andelectrondensitieswererepresentedongridswithaspacingofapproximately0.16Å.Brillouin-zoneintegrationswereperformedusingana×b×1Monkhorst–Packk-pointsamplinggrid,whereaandbequalled2or4dependingonthesizeofthesurfacelatticecell.Moleculeswerecomputedin a large non-periodic cell while the surface lattice cell wasrepeatedperiodicallyinthesurfaceplanetocreateaninfinitemetalslab.Theenergyconvergenceonk-pointsandh-spacingwas tested on the modelled slabs. Dipole correction wasemployedintheperpendiculardirectiontotheslabtodecoupletwo adjacent images electrostatically. The structuraloptimisationswereperformedwithaconvergencecriterionof0.05eV/Åforatomicforces.

ThestartinggeometryforEMIm+–BF4−ionicpairandlattice

parameters for EMImBF4 crystal were taken from supportinginformation in Refs. 74–76 and optimisedwith RPBE+vdW. Thedissociation energy −344 kJ/mol for EMIm+–BF4

− ionic pairagrees with the post-Hartree–Fock results.74,77 The energy ofEMImBF4 crystal dissociation into single ions is 161 kJ/mollower. It is in reasonable agreementwith the experimentallydetermined value for EMImBF4 liquid evaporation (135–149kJ/mol at 298 K).78,79 EMImBF4 crystal structure optimisationwasperformedonAmazonEC2publiccloud,‡usingtheDesktoptoCloudMigration(D2CM)tool.80,81

The binding energy of BF4− in the modelled systems was

expressed relative to the potential energy of BF4− in vacuum,

andcorrectedbytheBF4•adiabaticelectronaffinity(EA):82

Esurf(BF4−) =

[E(N,n) − E(N,0) − nE(BF4−) − nEA(BF4

•)]/n, (1)

wherenandNarethenumbersofionsandsurfacemetalatomsin the simulated cell, andE(N,0) andE(N,n) are the potentialenergiesofthebareAu(111)surfaceandthechargedAu(111)surfacewithn BF4

− species in the cell. The adiabatic electronaffinity of BF4

• calculated with RPBE+vdW in this work (634kJ/mol)agreeswellwiththevalueof649kJ/mol,calculatedbyGutsevetal.atCCSD(T)83leveloftheory.

Figure1. a)Au(111) |BF4− interfacemodel at surface coverageθ =1/3.b)BF4

−reorients and spontaneously dissociates at the same coverage. Only the upper,relaxedlayerofgoldisshown.

TheE(BF4−)canbedirectlyrelatedtotheMadelungenergy

ofBF4−intheEMImBF4crystal(Ecr)whichmaybeconsideredas

anapproximationtotheelectrochemicalpotentialoftheanionin the RTIL. The formation energy of a vacancy in EMImBF4crystalisexpressedasfollows:84

Ecr(BF4−) = E(EMImBF4) − E(BF4

−) − E(EMIm+), (2)

where E(EMImBF4) is the potential energy of the EMImBF4crystal, and E(EMIm+) is the potential energy of EMIm+ invacuum.Onceananionleavesthecrystal,itcanbedeionisedtoBF4

•andthencanadsorbontheAu(111)surface.For the Au(111) | BF4

− interface, the integral free energychangepersurfacemetalatom(ΔGint)wasdefinedas

85–87

ΔGint ≈ [nEsurf(BF4−) − nEcr(BF4

−)]/N. (3)

Inthisform,theintegralfreeenergychangeservesasameasureoftheBF4

−affinitytowardsthesurfacecomparedtotheaffinitytowardstheEMImBF4crystal.Itwascalculatedusingthevaluesconsistent with the forces presented in the models andneglectingthecontributionofentropytermsnon-presentedinthemodels.Thisshouldbeasufficientlyreliableestimateoftheinterfacialfreeenergy,asonthetransitionfromarealRTILtoan interface the ions remain in glass-like phase. Thus, theentropyterm(TΔS)shouldbemuchsmallerthantheenthalpychange (ΔH), determined by strong Coulomb interaction inRTILs.

Theintegralcapacitancewasdeterminedinfourwaysfromthe integral free energy, work function, ionic charges, andinterfacialdipolemoment.

Firstly,usingtheclassicalrelation:

CG = 2∆Gint/∆U 2, (4)

whereΔGint isequaltotheenergystoredinanidealcapacitorwhich,inourcase,issetupbyBF4

−ionsandthecounterchargeon the metal surface. Here, ∆U = U − Upzc is the electrodepotentialcalculatedfromtheworkfunction(U=We/e),andUpzcisthepotentialofzerocharge(PZC).Heree istheelementaryelectronic charge. TheUpzc was set to be equal to calculatedworkfunctionoftheAu(111)surface(5.08eV),whichisslightlylowerthantheexperimentalvalueof5.26eV.88

Secondly, taking into account that each anion brings achargeofqtothesurface:

Cθ = q·e/A·θ/∆U, (5)

whereAistheareaoftheunitcell,andtheioniccharge(q)wasobtained by the density derived electrostatic and chemical(DDEC)method.89,90

Thirdly,usingtheinterfacialdipolemoment(µ):

Cµ = q·e·ɛ0/µ, (6)

whereɛ0isthepermittivityofvacuum.Finally,assumingthatthesystemisaparallelplatecapacitor

CH = ɛɛ0/d, (7)

whereɛisthehigh-frequencydielectricconstantof2.0(typicalfor RTILs 91), and d is the distance from the position of the

nearestlayerofAunucleitothelayerofBnuclei.Eq.7isderivedbasedontheHelmholtzmodelassumptions.

Moleculardynamicssimulations

AllMD simulations were carried out using the GROMACS2016.1simulationpackage92andNaRIBaSscriptingframework93at temperatures of 300 K. The parameters of Lennard-JonespotentialforgoldreportedbyHeinzetal.wereutilised.94OPLS-AAforcefieldwasusedforEMImBF4.

95For the initial relaxation of EMImBF4, all systems were

subjectedtothesteepestdescentminimisation.Then,the20nsequilibrationrun,followedbythe2nsofsystempolarisation,were performed. Finally, a production run of 10 ns wasaccomplished.

A coupling constant for a V-rescale thermostat, usedthroughout all calculations to maintain constant thetemperature, was 0.5 ps.96 Due to the slab-like geometry ofstudiedsystems,theperiodicboundaryconditionswereappliedonly in x and y directions. The Verlet leapfrog algorithmwasusedtointegratetheequationsofmotion,withatimestepof1 fs.97 The short-range non-bonded Coulomb and Lennard-Jones interactions were computed with a 1.45 nm cut-offdistance. The same cut-off distance was used for the short-range neighbour list. The corrections for the Coulombinteractions beyond the cut-off were performed using theparticlemeshEwaldmethodwithinterpolationorderof6and0.1nmspacingofthegridpointsinthereciprocalspace.98The3dc Ewald geometry was used, i.e. the force and potentialcorrections were applied in the z-dimension to produce apseudo-2D summation. The short-range interaction listswereupdated every 40 steps, using a grid-based method. Thedielectric constant was chosen to be 2.0. Constraints wereenforced on all bond lengths using the LINCS algorithm.99Trajectorydatawerewrittenatevery5psand lateranalysedusing GROMACS inbuilt tools and our codes, whenever therespectiveanalysistoolwasunavailableinGROMACS.

Theintegralcapacitancewasdeterminedusingthevaluesofthecalculatedelectrostaticpotentialdrop(U)andthesurfacechargedensity:

C = s/∆U (8)

wheres denotesthesurfacechargedensityand∆U=U−UpzcobtainedbyintegratingthePoisson’sequation(seeRef.100fordetails).Thescreeningoftheexternal fieldbythegoldatomswascharacterisedbyaneffectivepositionoftheimageplane.Thepositionwasfixedat0.135nmfromthenearestlayerofAunuclei,whichisslightlyfurtherthanhalfanAu(111)interlayerspacing(0.118nm).ThispositionvaluewastakenfromRef.101,athighersurfacecharges.

Table1.Fordifferentsurfacecoverage(θ)thevaluesoftheadsorptionenergy(Eads/kJmol−1)wereevaluatedfromtheresultsofcalculationsusingRPBEandvdW-DF functionals, ionic charges (q / e) were obtained using DDEC method,89,90whereasthedistance(d/Å)wascalculatedfromthepositionofthenearestlayerofAunucleitothelayerofBnuclei.

Adsorbate θ−Eads/kJmol−1

−q/e d/Å

BF4− 1/3 237 0.41 2.94

BF4− 1/4 268 0.41 2.99

BF4− 1/6 281 0.49 3.01

BF4− 1/12 301 0.62 3.11

BF4− 1/20 308 0.67 3.13

F•(BF3) 1/3 248 0.36 F• 1/3 221 0.34 F• 1/4 213 0.34 F• 1/6 224 0.37 F• 1/12 225 0.38 F• 1/20 232 0.39

Resultsanddiscussion

ModelAu(111) | BF4−interface

To obtain a qualitative comparison of the preferredorientationofasingleBF4

−ion,theusualadsorptionsitesonthesurfacewereconsidered:FCCandHCPhollow,bridgeandtopsites. At 1/20 coverage, the FCC and HCP hollow sites werefoundtobethemoststableadsorptionsiteswithanegligibleenergy difference. At the same time, the translationalmovementofBF4

−fromanFCCtoanHCPhollowsiterequiresovercominganenergybarrierof11kJ/mol.Uptocoverageof1/3,theorientationofanionwiththreefluorineatomspointingtowards the surface is the most favourable. At highercoverages,there-orientationofanionscanhappenduringthegeometryoptimisation.

Fig.2demonstratesthedependenceoftheintegralenergy(Gint)ofBF4

−anionsontherelativeelectrodepotentialsquared(∆U2). A linear dependence is seen, which means that themodelled Au(111) | BF4

− interface behaves as a parallel platecapacitor. Yet, the results also indicate a strong potentialdependenceontheorientationofBF4

−ions.Asitfollowsfromthe calculations, the formation of the √3×√3 ordered adlayer(Fig. 1a, θ = 1/3) occurs at 4.6 V relative to the PZC (Fig. 2,Table2).However,theformationofthe√3×√3adlayerwithhalfoftheanionsflippedanddissociated(Fig.1b)cantakeplaceataconsiderablylowerpotentialof3.5V(Fig.3).

AsitcanbeseeninFig.3,atθ=1/3,thephysicaladsorptionenergy difference between the undissociated and thedissociated structures is relatively small (11 kJ/mol), yet thepotentialdifferenceispronounced(1.1V).Ontheonehand,thepotentialisdirectlyrelatedtotheinterfacialdipolemoment,ina direction perpendicular to the surface, which is apparentlydeterminedbytheorientationofspecies(BF4

−,F−,BF3).Ontheother hand, the adsorption energy results from the lateralrepulsion among the species, which is less sensitive to theirorientation.

BF4−anodicoxidation

As follows from Table 1, the total ionic charge on BF4−

noticeably depends on the coverage, varying from −0.7e to−0.4e. Hence, due to the strong inter-ionic repulsion, −Eadsdecreaseswithincreasingθ (Fig.3).Oppositely,thechargeonF• is only slightly above −0.4e at all coverages.§ Thus, in theabsenceofstronginter-ionicrepulsion,Eads(F

•)weaklydependsonθ(Fig.3).

Figure2.Dependenceoftheintegralenergy(Gint)ofBF4−anions(●)ontherelative

electrodepotentialsquared(∆U2).Blankmarkers(○)indicateBF4−dissociationto

BF3+F•.Surfacecoverage(θ)islabelledwitharrows.Theslopecorrespondstothe

differentialcapacitancevalueof6µF/cm2.

Figure3.DependenceoftheBF4−(●)andF−(■)adsorptionenergies(Eads)onthe

surfacecoverage.Atahighcoverage,BF4−isoxidizedanddissociatesintoBF3and

F•(○).Relativeelectrodepotential(∆U)islabelledwitharrows.

Atθ ≥ 1/3,when aBF4− anion is flipped, it spontaneously

dissociates to BF3 and F• (Fig. 1b). Notably, that according to

Gutsevetal.83“BF4•has tobeconsideredratherasavander

Waals complex”. Accordingly, the observed dissociation is aconsequenceofBF4

−oxidationatanodicpolarisation:1)BF4−=

e−+BF4•;2)BF4

•=BF3+F•.TheformedfluorideF•canfurther

recombine to F2 and react with RTIL components, as wasobserved in work 102, or form a covalent bond with surfaceatoms,forinstance,formingMeFn,asdescribedinRef.

103.TheformedBF4

−canalsoformastableB2F7−complex.Usinginsitu

infrared spectroscopy technique, Romann et al.61 found thatcombination of BF3 with BF4

− anion happens if there are nobetterelectronpairdonors.Thecomplex formationshifts theequilibriumfurthertowardstheanionbreakdown.

Relativeelectrodepotentialandintegralcapacitance

DFTcalculationscapturetheoxidationprocessthatsetstheanodiclimitontheelectrochemicalwindowforEMImBF4.Dueto the simplicity of the Helmholtz model, the correspondingpotential remainsoverestimated.Table2shows thepotentialvalues at the Au(111) | BF4

− interface (MD/DFT) and thepolarisedAu(111) | EMImBF4 interface(MD).OnecanseethattheMDandDFTresultsareinagreementfortheAu(111) | BF4

−interfaceatθ<1/3.IntheMDsimulations,thespontaneousflipof anionshappens atθ = 2/5 leading to the formationof thesecondlayerofanionsandcrowding.Atsuchhighcoverages,inthe DFT calculations, BF4

− loses its charge and decomposes(Table1).Besides that,bothDFTandMDcomputationsshowthat the distance of closest approach of BF4

− to the surfacedecreases with the increase of coverage as well as surfacecharge,andpotential–thisisreflectedbytheslightgrowthoftheintegralcapacitanceshowninFig.4.

Fig. 4a shows the integral capacitance values calculatedaccordingtoEqs.4–7forthesystemswithallBF4

− ions inthesame orientation, i.e. characterised by the largest possible

interfacial dipole moment. The match between the Eqs. 4–7curves implies consistency in themechanism and energetics:the accumulation of ions happens via simple physicaladsorption, and the integral energy rises due to repulsionbetweencounter-ions.

The integral capacitance for themore complexmultilayerAu(111) | EMImBF4 interface shows the impact of the ioniclayering on the potential magnitude. In Fig 4b, at the samepotential value, the capacitance is higher for the multilayermodelthanfortheHelmholtzmodel.Atthesamecoverage(orsurface charge) the relative electrode potential values aresmallerforthemultilayermodelthanfortheHelmholtzmodel,asshowninTable2.Onlywhenthemonolayerofcounter-ionsofmaximaldensityisformed,thepotential,surfacecharge,andintegral capacitance are the same for both models. In oursimulations, this takes place at the coverage of 2/5 at 6.3 V.Abovethisvaluecrowdingofanionsoccurs.

The obtained capacitance values are in reasonableagreementwithexperimentalvaluesof5–10µF/cm2forhigh-frequency differential capacitance measured at gold singlecrystal (100) and (111) surfaces.28,29,40,43,64–66 However, theHelmholtz model capacitance increases with increasing therelative electrode potential, while themultilayer layermodelcapacitancedecreasesinthesamewayasinexperimentalwork104.

Table2.Relativeelectrodepotential(∆U)valuescalculatedfordifferentsurfacecoverageusingMDsimulationsofHelmholtz(MDH)andmultilayer(MDML)modelsincomparisontotheDFTdata.

θ DFT MDH MDML1/3 4.6V 5.3V 4.3V1/4 3.8V 4.1V 2.7V1/6 3.3V 2.9V 1.3V1/12 2.2V 1.7V 0.4V1/20 1.4V 1.1V 0.15V

Figure 4. a) Integral capacitance dependence on potential, calculated using the DFT data and Eqs. 4–7. b) Integral (CML andCH) and differential (Cdiff) capacitancedependenciesonpotentialcalculatedusingtheMDdata.Surfacecoveragevalues(θ)arelabelledwitharrows.Experimentaldata(Exp.)takenfromRef.104,whereAu|EMImBF4interfacewasstudiedusingelectrochemicalimpedancespectroscopy.

Anionicadlayersvsdensemonolayerofanions

Thepresentedresultscanbe interpretedthroughtheoriesdevelopedbyLothetal.,Bazant–Storee–KornyshevorYochelis,as well as molecular-level interpretations by Feng et al. andIvaništšev et al.18,20,21,27,105 According to Feng et al., themultilayer structure can be divided into layers with zero netcharge (except for the innermost layer) and characterised byalternatingdipolemomentsfromlayertolayer.21ThepresenceofthestructuredRTILabovetheinnermostlayerdecreasestheabsolutevalueofthepotentialdropacrosstheinterface.ThatiswhyinFig.4theintegralcapacitanceforthemultilayermodelishigherthanfortheHelmholtzmodel.AccordingtoIvaništševet al., the capacitances are equal at the potential of themonolayerformationwhenasinglemonolayerofcounterionscompletelycompensatesthesurfacecharge.27Thesepotentialsmanifest the transition from overscreening to crowdingregimes.18,27,106Atlowerabsolutepotentials,duetotheanion–cation correlation, there is an alternating layer of anions andcations;athigherabsolutepotentials,thesurfaceiscrowdedbythecounter-ions.

In the presented MD simulations, the potential of themonolayerformationwasfoundtobe6.3V(Fig.4b,thecrosspointofCHandCML),whichcorrespondstothecoverageof4/5or65µC/cm2 (accounting forpolarizabilityof ions).However,the DFT calculations demonstrated that at a comparablepotentialscaletheinterfacebecomesunstablealreadyat3.5V(θ = 1/3, Figs. 1b and 3). In a hypothetical DFT based MDsimulations of the multilayer model, the decompositionpotentialshouldbeevenlower,firstly,duetothedissociationoftheoxidisedBF4

−,and,secondly,duetotheioniclayering.Inexperiment,anodicelectrochemicalreactionsstartaround1.6VvsPZC.104

Notice, that from a geometrical point of view the BF4−

patternsatthecoveragehigherthan1/6completelyoccupytheinnermost layer, as the free spaceon the surface is stericallyhindered for larger cations. In the MD simulations of themultilayermodel,thiscoveragecorrespondsto1.3V(Table2).Thus,wesurmisethatsimilarstructureswerevisualizedbythescanning tunnelling microscopy in works 66,67, where theformation of ordered anionic adlayers was assigned to lowvoltagesoflessthan1VvsPZC.Westressthatinthiscase,theobservation of the anionic adlayers does not rule out theoverscreeningnor thepresenceof EMIm+ cationsnext to theinnermostlayer.Moreover,theaccumulationofanionsstartingfrom the coverage of 1/6 and ending with the monolayerformationat4/5requiresmarkedpotentialandsurfacechargeincrease. Consequently, 1) anionic adlayers and the densemonolayerofanionsaredifferentstructures,2)theadlayersarepartofthemultilayerEDL,and3)thecrowdingofanionsatlowpotentialvaluesisextremelyimprobable.

HelmholtzvsMultilayermodels

ComparisonoftheDFTandMDresultsprovidesagroundforresolvingwhether theEDL inRTILs isone-ormulti-ionic-layerthick. As expected, for theone-ionic-layer thick, according toHelmholtzmodel(Eq.7),thecapacitanceisalmostindependent

of the potential. For themultilayermodel, both integral anddifferential capacitancedecreaseswith increasing the relativeelectrodepotential(Fig.4b).ThesametendencywasshownforthedifferentialcapacitanceoftheAu|EMImBF4interfaceintheexperiment.104Also,previouscomputationsbyFengetal.21andHuetal.107showedthatwhilesomequalitativetrendsmightbecaptured by structural changes in the innermost layer, thesubsequent layers have an essential influence in defining thedependenceofcapacitanceonelectrodepotential.Allinall,themultilayerEDLinEMImBF4,asawhole,determinestheoverallpotential-dependentcapacitance.

IntheHelmholtzmodel,theEDLthicknessisdefinedasthedistance of closest approach on counter-ions to the surface.Only for thismodel, thepositionsof the ionicchargeand theionicmassplanescoincide.Thefirstonedefinesthepotentialdropinthecorrespondingparallelplatecapacitor.Thesecondappears due to steric effects. Both might be equal to thecounter-ionradiusunderanassumptionthatthesurfacechargeplane liesata surface-atom-radiusdistance thesurfaceplane(definedbythenucleipositions).

Forthemultilayerstructure,theionicchargeandmassplanepositionsaredifferent.Theionicmassdensityispositiveatanydistance from the surface, while the sign of the ionic chargedensity(ρ)dependsontheexcessofanionsorcationsatagivendistance from the surface (z). The ionic chargeplaneposition(zion)isexpressedas:

zion = −∫ρ(z)zdz/s. (9)

zion value can be smaller than the counter-ion radii. On thecontrary, inthemultilayerstructure,any i-thlayer liesfurtherfromthesurfacethanoftheinnermostlayer.

Force–distancecurves,asthoseprovidedinworks49,108,canbe used to count the number of layers and to estimate thegeometrical thickness of the EDL. However, such thicknesswould be useless for calculating the EDL capacitance as thesurface charge–potential dependence is dictated by the ionicchargeplaneposition. To clarify thedifference letus simplifythemultilayerintoanionicbilayer.

Ionicbilayermodel

In the recent ionic-bilayer model, the multilayer waspresentedasabilayer–thecontact layerofcounter-ionsandthe subsequent layer of co-ions.109 It is a simplifiedrepresentation of the multilayer EDL. The integral anddifferentialcapacitancesofthismodelaregivenas:

C = ɛɛ0/(d – δλ/s), (10)

Cdiff = ɛɛ0/(d – δ(dλ/ds)), (11)

whereδ isthegeometricaldistancebetweenthefirstandthesecondlayers,ɛisthehigh-frequencydielectricconstant,andλistheco-ionchargedensityinthesecondlayerthatisequalinmagnitude,butoppositeinsigntothesurfacechargeexcessofthecounter-ionsinthefirstlayer.106

LetususethissimplemodeltoreflectthethicknessoftheEDL.Note,conditionλ=0meansthatthemodelsimplifiestotheHelmholtzmodel.Otherwise,bydefinition,theEDL inthe

ionic-bilayermodelistwo-layerwithaconstantwidthof(d+δ).Herewith,fortheintegralcapacitance,thedenominatorinEq.10 is smaller than d. That is why the integral capacitance ishigher in the simulationsof themultilayermodel thanof theHelmholtzmodel(Fig.4b).Forthedifferentialcapacitance,thedenominatorinEq.11mightbeequalto(d+δ)onlywhenthesurface charging relies solely on the exclusion of the co-ionsfrom the second layer to thebulk, i.e. dλ =−ds.Competitionwith the more traditional mechanism of charging, i.e.adsorption of counter-ions on the surface, ensures that theconditiondλ=−dsisnotsatisfied.Yet,thechangeintherateofthesecondlayerdestruction(dλ/ds→−1)causesthedecreaseofthecapacitancewithincreasingthepotentialafteramaximalco-ionchargedensityisaccumulatedinthesecondlayerwhendλ/ds=0.109FromFig.4bonecandeducethatthisoccursatanintersectionofCHandCdiffaround2.6V.Note,thecapacitancedecreases with increasing potential also at lower potentials.AccordingtoEq.11,thecapacitancepeak(notshowninFig.4b)appears at a potential when the accumulation of co-ions ismaximal (dλ/ds → d/δ), and the capacitance inevitablydecreases above this potential. Most important for ourdiscussion is that the geometric thickness of the ionic bilayermodelisunrelatedtoitscapacitancevspotentialdependence.

AssoonastherearetwoormorechargedlayersintheEDL,one shouldaccountat least for two layers in thegeometricalinterpretation of the potential-dependent capacitance. Theknowledgeof thePZCposition is essential. It allows forusingbothEqs.10and11byconvertingthedifferentialcapacitanceto the integral capacitance or surface charge–potentialdependence. In principle, one can estimate δ, λ, and dλ/dsvalues,amongwhichtheonlyδisageometricparameter.

Foraqualitativeexampleconsiderworks34,110,111,inwhichbasedonEq.7withɛ=8authorsconcludedthatdvaluesforthe same anion vary in monocationic and dicationic RTILs:dmono>ddi.ThesameauthorshighlightedthesimplicityoftheHelmholtz-typemodelsaswellastheneedforamoreadvancedtheory. From Eq. 10 a more expectable relation emerges:δmono<δdi,meaningthatthepositionofthedicationlayerliesfurtherfromthesurfacethanofthemonocationlayerwhilethepositionoftheanioniclayerremainsthesame.

Thegivenalternativeexplanationreliesonhypothesesthatcall fornewexperimental andcomputational studies.Amoredetailed analysis of published experimental results is alsodesirable.104,112Thegenerichypothesisisthattheionicchargeplanepositioncouldbeestimatedbyaccountingfortwoioniclayers, as in the ionic bilayer model.109 Substituting the one-ionic-layerthickfoundationoftheHelmholtzmodelshouldbeastepforwardamoregeneralmodeloftheEDLinRTILs.

ConclusionsWehavestudiedtheadsorptionofBF4

−anionsfrom1-ethyl-3-methylimidazolium tetrafluoroborate (EMImBF4) on thechargedAu(111)surfaceusingDFTandMDcomputations.Thestudy represents a crucial piece of the scientific puzzle. Itaddressesthequestion:doestheinnermostlayerdominateinthe overall potential-dependent multilayer EDL? It also

illustrates how the relative electrode potential is set throughthe interfacial potential dropacross themodel interface, andhowitservesasameasuringtapeforadsorptionandoxidationofBF4

−anions.First,DFTcalculationsandMDsimulationsof the simplest

Helmholtz model of the Au(111) | BF4− interface give similar

results, once a surface change plane is accounted in theMDsimulations.Theagreementholdsuptohighanodicpotentials,whereintheDFTcalculationsBF4

−spontaneouslyoxidizes:BF4−

=e−+F•+BF3.TheHelmholtzcapacitanceisalmostindependentofthepotential.

Second, in theMD simulationsof themultilayermodel ofthepolarisedAu(111) | EMImBF4interface,thepotentialdropissignificantly reduced due to the ionic layers above theinnermost layer. For themultilayermodel, the capacitance isdependent on the potential, in-line with the experimentalresults.104

We conclude that the multilayer EDL in EMImBF4, as awhole, determines the overall potential-dependentcapacitance. Consequently, we suggest that the Helmholtzmodel(Eq.7)shouldbeusedwithgreatcautioninthecaseofRTILs,astheEDLinionicliquidsisapparentlymulti-ionic-layerthick. We recommend accounting for the multilayer EDLstructure when discussing properties of RTIL-based energystorageandtransformationdevices,especiallysupercapacitors.

ConflictsofinterestTherearenoconflictstodeclare.

Acknowledgements ThisworkwassupportedbytheEUthroughtheEuropeanRegional Development Fund under project TK141 “Advancedmaterialsandhigh-technologydevicesforenergyrecuperationsystems” (2020.4.01.15-0011), by the Estonian ResearchCouncil (institutional research grant No. IUT20-13), by theEstonianPersonalResearchProjectsPUT1107andPUT360,andby short-term scientific missions funded by COST actionsMP1303 and CM1206. This work was also supported byGraduate School of Functional materials and technologiesreceiving funding from the European Regional DevelopmentFundattheUniversityofTartu,Estonia.Thefinancialsupportfrom Fundaçãopara a Ciência e Tecnologia (FCT/MEC) funds,and co-financed by the EuropeanUnion (FEDER funds) underthe Partnership Agreement PT2020, through projectsPOCI/01/0145/FEDER/007265 with reference UID/QUI/50006/2013, and POCI/01/0145/FEDER/006980 withreference UID/QUI/UI0081/2013 (LAQV@REQUIMTE andCIQUP, respectively) and postdoctoral research grant SFRH/BPD/97918/2013isalsoacknowledged.Resultswereobtainedin part using the High-Performance Computing Center of theUniversity of Tartu, in part using the EPSRC funded ARCHIE-WeSt High-Performance Computer (www.archie-west.ac.uk,EPSRCgrantno.EP/K000586/1).

WethankEnnLustforinspirationaldiscussionsofthenewphenomena in RTILs at electrified interfaces. We firmlyacknowledge the contribution of Maxim V. Fedorov in theinterpretationof thepresentedresults.Lastbutnot least,weare grateful to Renat R.Nazmutdinov for his consultations inDFTcalculations.

Notesandreferences†Adsorption–isanincreaseintheconcentrationofasubstanceattheinterfaceofaliquidphaseduetotheoperationofsurfaceforces.Inthemostcasesstudied,thephysicaladsorptionofBF4

−arise due to Coulomb attraction of ions to the charged goldsurface.ThespecificadsorptionF•takesplaceonlywhenBF4

−anionoxidizes.‡AmazonEC2real-timecomputingresourceswereaccessedbyusingtheD2CMtool,designedtomigrateacompletesoftwareenvironment from a local desktop directly to the cloud.80,81D2CMtoolallowedustoscalecalculationson-demandwithoutqueues, which are common for traditional High-PerformanceComputationfacilities.Italsoenabledustodefinethefulllife-cycle of the calculations by specifying which input files andscriptstoinclude,whichcommandstoexecuteandwhichfilesto download when a calculation ends. Overall, it hassignificantly simplified the use of elastic cloud computingresourcesforperformingelectronicstructurecalculations.§ For comparison, in AuF3 molecule, the average calculatedchargeon fluorine is−0.35e.Additionalanalysis suggests thatAu–F in AuF3 is a polar covalent. At the modelled Au(111)surface, fluorine adsorbs preferably at the hollow site, i.e.coordinatingwiththreegoldatoms.Forthesakeofsimplicity,wedenotetheadsorbedfluorineasaradicalF•.

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