Correlation
between
electrochemical
impedance
measurements
and
corrosion
rate
of
magnesium
investigated
by
real-time
hydrogen
measurement
and
optical
imaging
M.
Curioni
a,*
,
F.
Scenini
a,
T.
Monetta
b,
F.
Bellucci
b aCorrosionandProtectionCentre,TheUniversityofManchester,ManchesterM139PL,UnitedKingdom
b
UniversityofNaples“FedericoII”,DepartmentofChemicalEngineering,MaterialsandIndustrialProduction,80125Naples,Italy
ARTICLE INFO Articlehistory:
Received31October2014
Receivedinrevisedform6March2015 Accepted9March2015
Availableonline11March2015 Keywords:
magnesium corrosion
electrochemicalimpedancespectroscopy hydrogencollection
ABSTRACT
Thecorrosionbehaviourofmagnesiuminchloride-containingaqueousenvironmentwasinvestigatedby potentiodynamicpolarizationandelectrochemicalimpedancespectroscopy(EIS)performed simulta-neouslywithreal-timehydrogenevolutionmeasurementsandopticalimagingofthecorrodingsurface. Thepotentiodynamicinvestigationrevealedsubstantialdeviationsfromlinearityincloseproximityof thecorrosionpotential.In particular,differencesin theslope ofthecurrent/potential curveswere observedforsmallpolarizationsaboveorbelowthecorrosionpotential.Theseobservations,suggestthat theusualmethodbasedontheuseoftheStern–Gearyequationtoconvertavalueofresistanceintoa value of corrosioncurrent is inadequate. Nonetheless, avery good correlation betweenvalues of resistancesestimatedbyEISandcorrosioncurrentsobtainedfromreal-timehydrogenmeasurementwas found.Real-timehydrogenmeasurementalsoenabled, forthefirsttime,directmeasurementofan ‘apparent’Stern–Geary coefficientfor magnesium. In order to rationalizethe complex behaviours experimentallyobserved,anelectricalmodelforthecorrodingmagnesiumsurfaceispresented.
ã2015TheAuthors.PublishedbyElsevierLtd.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).
1.Introduction
Theelectrochemicalbehaviourofmagnesiumisrelevantfora varietyofapplicationsincludinglightweightstructures,whereit determinesthecorrosionresistance[1–3],batteriesandsacrificial anodeswhereitdeterminesefficiency[4–7],andsurgicalimplants, where it determines the rate at which theimplant disappears withinthehumanbody [8,9].Theelectrochemicalbehaviourof magnesium in aqueous environment, however, is relatively complexcompared tootherlight metals suchasaluminium or titanium.Similartomagnesium,aluminiumandtitaniumhavea largedrivingforceforoxideformationbut,unlikemagnesium,the formationofaprotectiveoxide/hydroxidelayerhinderscorrosion. MgandMg-alloyshavealargethermodynamicdrivingforcefor oxideformation,sincetheequilibriumpotential formagnesium oxidationis2.37Vvs.SHE,but magnesiumoxide/hydroxideis relatively soluble in near-neutral and acidic environment, and relativelyinsolubleinalkalineenvironment[10].Duringcorrosion,
theincreaseinpHassociatedwithhydrogenevolutionstabilizesto someextenttheoxide/hydroxidefilm.
Inadditiontothebehaviouroftheoxide,magnesiumexhibits thesocalled‘negativedifferenceeffect’(NDE).Insimpleterms,the NDErelatestotheincreaseinhydrogenevolutionexperimentally observed duringanodic polarization and it is contrary towhat wouldbepredictedbyelectrochemicaltheory.Thefirst interpre-tationoftheNDE[11–13]assumesthatunipolarmagnesiumions aregeneratedduringanodicpolarization.Oncedetachedfromthe metalelectrode,theunipolarmagnesiumionsoxidizefurtherand reducewater,producinghydrogengasandhydroxideions.Thus, theNDEisconsideredtheconsequenceoftheincreasedoxidation rateofmagnesiumduringanodicpolarizationthatresultsin an increasein hydrogenevolutionrate. Thisargumentis indirectly supportedbytheobservationthat,foravalueofappliedanodic charge,thehydrogenevolvedandthemetaloxidizedareinexcess tothose predictedby Faraday's lawassumingthat magnesium oxidizesinasinglesteptoMg2+.Thesecondinterpretationofthe
NDE does not require assuming the existence of unipolar magnesium, and attributes the NDE to an increased cathodic activity of the magnesium surface during anodic polarization. Basedthereportedresultsfromvariousindependentapproaches andonownwork[14–20],theAuthors'viewisthattheincreasein *Correspondingauthor.
E-mailaddress:michele.curioni@manchester.ac.uk(M. Curioni).
http://dx.doi.org/10.1016/j.electacta.2015.03.050
0013-4686/ã2015TheAuthors.PublishedbyElsevierLtd.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/). ContentslistsavailableatScienceDirect
Electrochimica
Acta
therateofhydrogenevolutionduringanodicpolarizationisdueto an increase in the cathodic activity of the regions that have undergone corrosion. Thus, by anodic polarization, corrosion propagatesfasterthanatthefreecorrosionpotential,generating regionswithenhancedcathodicactivity.Thepropagationofsuch cathodicallyactiveregionsisresponsiblefortheobservedincrease inhydrogen evolutionduringanodic polarization.Regardlessof themechanism,sincetheoxidationofamagnesiumatomresults inthegenerationofanhydrogenmolecule,thecorrosionrateof magnesiumcanbeestimatedbythehydrogencollectionmethod
[15,16,18,19,21–24].
Regardless of the exact nature of the NDE, the correlation betweenthedataobtainedbyelectrochemicalmeasurementand corrosion rate requires attention, since the electrochemical response of magnesium is more complex than that observed onmostothermetals.Specifically,thebehaviourofmagnesium deviatessubstantiallyfromTafel-typekineticduetothepresence ofanoxide/hydroxidelayer[25]whichcontrolsthecorrosionrate and dueto the propagation of the cathodically active regions during anodic polarization [15,17–19,21,26]. Asa consequence, extrapolation of the corrosion rates from potentiodynamic polarizationcurves is questionable. For similar reasons, values ofresistanceestimatedbyEISmustbeusedwithcaution,since theuseoftheStern–Gearyrelationshipisnot,strictlyspeaking, correct.
Whereas the cathodic Tafel coefficient is generally easily obtained[21,23],thedeterminationoftheanodicTafelcoefficient isnottrivial.Thisarisesfromthefactthatamagnesiumelectrode can sustain very high anodic current with minimal anodic polarization.Suchhighcurrentsareaccompaniedbysubstantial hydrogen evolution and local alkalinisation, producing a large Ohmicdropinproximityoftheelectrodesurface.Evenassuming thattheanodicreactionfollowsTafelbehaviour,itisdifficultto estimatetheanodicTafelcoefficientfrompolarizationcurvesnot correctedfortheIRdrop.However,reliablecorrection oftheIR dropisnoteasy,sincethesolutionresistance(stronglyaffectedby thepresenceofhydrogenbubbles)inproximityoftheelectrodeis mostlikelydependentontheappliedpotential[17].Generally,a well-defined and reliable linear anodic region in the Evans diagramsisnotreadilyobserved.Inadditiontotheaboveissues, duringimpedance measurement, aninductive behaviourat the low-frequency end of the impedance spectrum is generally observed [11,21,27,28]. The physical interpretation of inductive behaviourassociatedtoelectrochemicalprocessesisnon-trivial, andthatisprobablythereasonwhythisinductive behaviouris oftenneglected.
Apart from these ‘electrical’ complications, there are issues relatedtothe practicalitiesduringcorrosion testingthat might contributetosignificantvariationsinthefinalresult.Thefirstissue arises from the fact that magnesium corrosion results in alkalinisation of the environment and consequent decrease in the aggressiveness of the environment if the experiment is performedinafixedvolumeofelectrolyte.Consideringthatboth hydrogenmeasurementwiththetraditionalmethodofobserving visuallytheamountofhydrogencollectedinagraduatedcylinder initially filled with electrolyte and weight loss measurements requirerelativelylongtimes(atleasthours),itismostlikelythat significantdifferencesintheenvironmentdevelopduringthetest. Asaresult,thedataobtainedfordifferentvolumesofelectrolytes andpossiblydifferentgeometriesofthecorrosioncellmightnotbe directlycomparable.
Inadditiontotheabove,itiswellknownthatduringtheearly stages of corrosion the appearance of a magnesium electrode changessubstantiallyfromsilverytodarkascorrosionproceeds
[15,17–19,21,26]. It has been shown that such variation in
appearance results in a significant difference in the cathodic
potentiodynamicresponse,butdoesnotproduceanequallylarge variation inthe anodicpotentiodynamicresponse [17]. Forthis reason, the surface conditions prior to polarization initiation should be reported otherwise it is difficult to considered comparable the result presented in works investigating the corrosion rate on magnesium by potentiodynamic polarization
[22,26,29,30].Thepotentialatwhichthepolarizationisinitiated
also has a substantial effect on the estimated corrosion rate. Specifically,consideringthatmagnesiumismorepassiveathigh pH,when thepolarizationisinitiated wellbelowthecorrosion potential,alkalinisationinproximityoftheelectrodeoccursand thecorrosion rate frompotentiodynamicpolarizationis signi fi-cantly underestimated [17]. On the other hand, simultaneous measurement of the cathodic potentiodynamic polarization response and hydrogen evolution, indicated that extrapolation ofthelinearpartofthecathodicpolarizationcurvetotheopen circuitpotentialprovides arelativelyaccurateestimation ofthe corrosion current, provided that the cathodic potentiodynamic polarizationisinitiatedatthecorrosionpotential[17,31].
Recently, King et al. [21] have investigated in detail the correlation between impedance measurements and corrosion ratebycomplementingtheimpedancedatawithweightlossand hydrogenmeasurement. In order tofit theimpedance spectra, theyusedacircuitcomprisinganinductivepartandfoundgood correlation between the zero-frequency values of the total impedance and the corrosion rate measured by weight loss andhydrogenmeasurement(thetermzero-frequencyresistance denotesinthisworktheequivalentresistanceatzerofrequency of thecircuit usedfor thefitting of theexperimental data,i.e. calculatingtheequivalentresistanceofthecircuitconsideringall capacitorasopencircuitsandallinductorsasshort-circuits).In ordertoconvertthevalueofthezerofrequencyresistanceintoa corrosion rate,they usedanodic andcathodic Tafelcoefficient obtained from the literature. For the Tafel coefficients they selected, they found that it wasnecessary to account for the inductivebehaviourinordertoobtaincorrectvaluesofcorrosion rate.
Thepurposeofthepresentworkistoprovidefurtheradvances in the understanding of the relationship between the electro-chemicalresponseandthecorrosionphenomenaonthe magne-siumsurface.Inordertoevaluatetheelectricalresponsewithin potentialrangesrepresentativeofthoseprobedduringimpedance measurements, the potentiodynamic polarization behaviour in proximity of the free corrosion potential was investigated. Subsequently, a seriesofimpedance measurementwere under-taken during free corrosionwhilst monitoringin real time the amount of hydrogen evolved from thecorroding electrodes,to obtaininstantaneousvaluesofcorrosioncurrent.Asaresult,the correlation between the values of resistance obtained from impedance spectroscopy and the corrosion currents measured byhydrogenevolutioncouldbedisclosedbydirectmeasurements. Finally,amodelaccountingfortheDCandACelectricalresponseof acorrodingmagnesiumelectrodeispresented.
2.Experimental
Magnesiumelectrodeswereobtainedfromacastingotofpure magnesium (nominal composition 99.95wt.% Mg, composition measuredbyopticalemissionspectroscopy:Zn:0.003,Al:0.006, Si:0.005,Mn:0.006,Fe:0.003,Ca:0.005,Pb:0.001,Pr:0.010,Nd: 0.010,wt/wt%)andcutinto1cm2(forimpedancemeasurements)
or2cm2(forpotentiodynamicpolarizationmeasurements)
speci-mens.Themagnesiumspecimenswereconnectedtoacopperwire andembeddedinepoxyresin,suchasthecopperwasnotexposed to the test electrolyte. After polymerization of the resin, the electrodesweremechanicallypolishedwithsiliconcarbidepaper
of decreasingsize, up to4000 grit, in order toexpose a fresh magnesiumsurfacetotheelectrolyte.
In ordertomonitorthehydrogenevolutionin real-timeand obtainthetime-evolutionofthecorrosioncurrent,theapparatus schematicallyrepresentedinFig.1a,anddescribedindetailin[17] wasused.Aplasticcylinder,connectedbyaholdertotheplateofa laboratory balance, was completely submerged in the test electrolyte and used to collectthe hydrogen evolved fromthe corroding magnesium surface. The submerged cylinder was initiallyfilledwithelectrolyte.Progressively,thehydrogenevolved fromthemagnesiumelectrodereplacedtheelectrolytewithinthe submergedcylinder.Asaresultofthehydrostaticforceduetothe displacementoftheelectrolytewithinthesubmergedcontainer,a changein weightwas recorded by thebalance. Fromthe time evolution of the hydrostatic force, the time evolution of the amountofhydrogenevolvedcouldbecalculatedand,byFaraday's law,itwasconvertedtothetimeevolutionoftheelectricalcharge associatedtohydrogenevolution.Finally,byderivingthecharge with respect to the time, the time evolution of the corrosion currentwasobtained.Whentwoelectrodeswereused,thevalueof corrosioncurrentestimatedbyhydrogenevolutionwas normal-izedbytheareaofbothelectrodes.
Simultaneously to electrochemical and hydrogen evolution measurements,thesurfaceappearanceofthecorrodingelectrodes wasrecorded(Fig.1b)byusingacomputercontrolledmicroscope. In orderto evaluatethe areaof theelectrode surface that had undergonecorrosion,theacquiredimageswerebinarizedandthe area of the corroded regions computed with an in-house developedLabview program.Anexample ofa corrodedsurface and corresponding binary image is provided in Fig.1b and c respectively.
Potentiodynamicpolarizationswereperformedemployingthe usual3electrodescellconfigurationatasweeprateof1mVs1, withthemagnesiumspecimenasworkingelectrode,acommercial calomelelectrode asreferenceelectrode anda platinum foilas counterelectrode,byusinganIviumstatpotentiostat.Inorderto synchronize hydrogen measurement, image acquisition and potential-time history, the potential of the working electrode wasalsorecordedbyamultichannelanaloguetodigitalconverter (NI USB-6009), controlled by the same in-house developed Labviewprogramthatwasusedtocontroltherecordingofimages andweight.
Afterpreliminarytesting,itwasdecidedtoperformimpedance measurementbyusinga‘modified'two-electrodecellcon figura-tion.In practice,twonominallyidenticalmagnesiumelectrodes wereconnectedtoindividualinsulatedcopperwireandembedded together in a single mould by epoxy resin (Fig. 1b). After polymerizationandmechanicalpolishing,oneofthetwo electro-deswasconnectedtotheWorkingandReference2cablesfromthe potentiostat, while the other electrode was connected to the Counter and Reference 1 cables. Thus, if considering only the electricalcircuitcomprisingthepotentiostat,theimpedancewas performedinatwo-electrodecellconfiguration,whereeachofthe twoelectrodesactedsimultaneouslyasworkingelectrodeandas counter electrode for the other. However, in order to enable synchronizationbetweenhydrogencollectionandimagingofthe surface and electrochemical measurement, a calomel reference electrode was added into the cell and the potential of each individual magnesium electrode was recorded by the NI USB-6009 controlled by the same software that acquired the electrodeimagesandthehydrogenweight.Thus,althoughtheEIS measurementwasperformedina2electrodeconfiguration,athird referenceelectrodewasplacedinthecellandthepotentialofeach individualelectrodewasrecorded.Thetwo-electrodecon figura-tion for impedance measurement was preferred to the more traditional3electrodesconfigurationinordertoensurethatthe
amountof hydrogencollected was directly proportional tothe metaloxidized.Ifhydrogeniscollectedonlyfromonemagnesium workingelectrode(andnotfromthecounterelectrode),duringthe cathodichalf-cycle,the hydrogenevolved fromthe magnesium working electrode surface doesnot directlycorrelate with the amount of magnesium oxidized, because the anodic reaction occursonthecounterelectrode.Byusingatwoidenticalelectrodes configurationfortheimpedancemeasurement,andbycollecting thehydrogenfrombothmagnesiumelectrodes,itisimmediately evidentthatthecathodiccurrentonone electrode(resultingin hydrogen evolution) is necessarily associated with an identical anodic current on the other electrode (magnesium oxidation). Thus,collectinghydrogenduringimpedancemeasurementsfrom both identical magnesium electrodes ensures that the amount hydrogen collected directly correlates with the amount of magnesium oxidized and, hence, with the corrosion rate. Additionally,byusingtheelectrodeconfigurationdescribed,the corrosionpotentialoftheelectrodepairisfreetovarywithtime, and therefore performing a series of impedance measurement does not modify the natural evolution of the potential-time transient observed for magnesium in the early stages after immersion. Although stationarity of the corrosion process is theoreticallyrequiredtoforreliableimpedancemeasurement,the directmeasurementofcorrosioncurrentrevealedthatstationarity wasrarelyattained(thecorrosioncurrentgenerallyinincreased withtime).Thus,itwasdeliberatelydecidedtoacquireimpedance spectrasequentially(inthefrequencyrange100kHzto5mHzand witha10mVamplitude,regardlessthattheaveragepotentialor thecorrosioncurrenthadattainedasteadyvalue.
3.Results
3.1.PotentiodynamicPolarization
Beforeconsideringtheresponsemeasuredduringimpedance measurements, it is useful to analyse the potentiodynamic polarizationresponseinproximityofthefreecorrosionpotential, for polarizations of the same order of those applied during electrochemicalimpedancespectroscopy(i.e.10mV).Itisworth recalling that, immediately after immersion in the aggressive electrolyte,themagnesiumsurfacedisplaysasilveryappearance but,ascorrosioninitiates,theair-formedoxide/hydroxidelayeris progressivelyconvertedinadarklayerofcorrosionproducts.The regions of the electrode where the air-formed film has been convertedintoadarkfilmofcorrosionproductsarereferredtoas ‘darkregions’inthiswork(Fig.1b).
Thetypicalpotentiodynamicpolarization resultsobtainedin 3.5% NaCl, starting the polarization from the free corrosion potential,arepresentedinFig.2.Thedesignation‘MostlySilvery’ referstoamagnesiumelectrodethatdisplayedlessthan5%ofthe total surface covered by the dark regions (immersed for approximately 900s in 3.5% NaCl) at the beginning of the potentiodynamic polarization, whereas the designation ‘Dark’ indicatesanelectrodethathasbeenimmersedintheelectrolyte for sufficiently long time (or anodically polarized) such as its surfaceappearedcompletelycoveredbydarkcorrosionproducts. FromFig.2a,itisevidentthatthecompletelyblackelectrode displayed a relatively well-defined linear relationship, with polarization resistancein the regionof 22–25
V
cm2, since theanodic and cathodic polarization curves had similar slopes. Conversely,for amostly silveryelectrode, theanodicbehaviour wasdifferentfromthecathodicbehaviour,withtheabsolutevalue ofcurrentincreasingmoremarkedlyforagivenvalueofanodic polarization that for the same value of cathodic polarization. Consequently, the terms ‘anodic polarization resistance’ and ‘cathodic polarization resistance’ are used hereto indicate the
reciprocaloftheslopeofthecurrentdensityvs.potentialcurves(in proximityofthecorrosionpotential)recordedduringanodicand cathodicpolarizationrespectively.Themostly silveryelectrodes displayedan anodic polarization resistance of 41
V
cm2, and a cathodicpolarizationresistanceapproximatelyfivetimeshigher (221V
cm2). The starting point of the cathodic polarization iscriticalindeterminingthebehaviourinproximityofthecorrosion potential. If the potentiodynamic polarization on a completely darkelectrodeisinitiated wellbelowtheopencircuitpotential (Fig.2b,datafrom[17]),theasymmetrybetweentheanodicand cathodicbehaviourobservedforthemostlysilveryelectrodesis observed also for the completely dark electrode. It should be stressedthatsuchsignificantdeviationsfromlinearbehaviourare observedinthesamepotentialrange(10mVaboveorbelowthe corrosionpotential) thatis probedduring impedance measure-ments. The overall potentiodynamic polarization behaviour for mostly silveryand darkelectrodes is presentedin Fig. 2c. It is evidentthatduringanodicpolarization,mostlysilveryand dark electrodes display similarbehaviours, whereas during cathodic polarization,darkelectrodessustainsignificantlyhighercurrents. Inordertogainfurtherinsight,thebehaviourduringaseriesof cathodicpolarizationsseparatedby1h30minoffreecorrosiona was investigated. The potential-time regime applied to the magnesiumelectrodeimmersedin3.5%NaClsolutionispresented in Fig. 3a, with the corresponding time evolution of the area fractionof theelectrode covered bydark regions,presented in
Fig.3b.Forcomparison,thetimeevolutionoftheareafractionof the electrode covered by dark regions for a freely-corroding electrode is presented. In Fig. 3c, the optical images acquired duringtheexperimentofFig.3a,andusedtoestimatethetime evolutionoftheareaofthedarkregionsarereported.Eachofthe
-1.72 -1.70 -1.68 -1.66 -1.64 -1.62 -1.60 -1.58 -1.56 -1.54 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 R=221.5 Ω cm2
Mostly Silvery
Mostly Silvery R=41.2 Ω cm2 R=24.85Ω cm2 Dark Cur re n t Den s it y / m A cm -2 Potential / V (SCE) Dark R=22.3 Ω cm2
a
-1.64 -1.62 -1.60 -1.58 -1.56 -1.54 -1.52 -1.50 -1.48 -1.46 -1.44 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0b
R= 23.1 Ω cm2 R= 92.4Ω cm2 Cur rent Den s ity / m A cm -2Potential / V (SCE)
R= 8.8Ω cm2 1E-3 0.01 0.1 1 10 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2 -1.0
c
Mostly Silvery Dark
Dark
Mostly Silvery
Po te n ti a l ( S C E ) / V Current Density / mA cm-2
Fig.2.a)Anodicandcathodicpotentiodynamicresponsesofmostlysilveryand completelydarkmagnesiumelectrodesinproximityofthecorrosionpotential measuredstartingthepolarizationsatthecorrosionpotential.b)Potentiodynamic response of a completely dark magnesium electrode measured starting the polarizationat2.2Vvs.SCE.c)Potentiodynamicresponseofmostlysilveryand completelydarkmagnesiumelectrodesfarfromthecorrosionpotential,starting thepolarizationsatthecorrosionpotential(datafrom[17]).
Fig.1.a)Schematicrepresentationofthesetupusedtoperformelectrochemical measurementssimultaneouslywithreal-timehydrogenevolutionmeasurement andopticalimagingofthecorrodingmagnesiumsurface[17].b)Opticalimage acquiredduringEISmeasurementontwomagnesiumelectrodesandc)imageb) afterbinarization.
presentedimageswasacquiredbeforethecorrespondingcathodic polarization.Itisimmediatelyobservedthatthepropagationofthe darkregionswas substantially delayed compared tothe freely-corrodingcasebytherepeated applicationofcathodic polariza-tion.Further,corrosiononlypropagatedduringthestageoffree corrosion, while during cathodic polarization only abundant hydrogenevolutionwasobserved.Interestingly,itwasnotedthat, aftercathodicpolarization,corrosiondidnotpropagatefromthe previously active propagation front, but re-initiated at a new locations(Fig.3c).
Fig.4presentstheelectrochemicalresponsemeasuredduring the series of cathodic polarizations of Fig. 3a. In Fig. 4a, the cathodic response is plotted in linear scale, for variations of potential similar to those experienced during electrochemical impedance spectroscopy. For clarity, the curves have been arbitrarilytranslated on thepotential axis.It is evident that a significantchangeintheslopeofthecathodicpolarizationcurves wasobserved withinthefirst 2–6mVbelowthe freecorrosion potential. Generally, two regimes were found during cathodic polarization; a first regime, close to the corrosion potential displayed comparatively low apparent cathodic polarization resistance, and a second regime, for larger polarizations, with comparativelyhigher apparentcathodicpolarization resistance. Thedifferencebetweenthefirstandthesecondregimeintermsof apparentresistancedecreasedasthecorrosionprocessprogressed andtheareaofthedarkregionsontheelectrodesurfaceincreased. Examinationofselectedcathodicpotentiodynamiccurvesplotted inlogarithmic scale(Fig.4b)provides furtherinsight.Withthe progressionof thecorrosionprocess,thecurvesshiftedtowards higher current densities, but displayed similar cathodic Tafel
coefficients of about 0.331V. The values of the cathodic Tafel coefficientsmeasuredhereingoodagreementwiththeliterature [21,23].
3.2.Electrochemicalimpedancespectroscopy
Electrochemical impedance spectroscopy, coupled with real timehydrogenevolutionmeasurementswasperformedinorderto gainfurtherinsightintothecorrelationbetweenelectrochemical measurements and corrosion rates. The experiments were performedbyusingtwonominallyidenticalmagnesium electro-desmountedinresinasdescribedpreviously.Fig.5presentsthe time evolution of a) theindividual electrodes potential, b) the corrosioncurrent measuredby thehydrogencollectionmethod andc)thefractionoftheelectrodesurfacecoveredbydarkregions. Inordertoevaluatethevaluesofcorrosioncurrentassociatedwith each impedance measurement, the value of corrosion current obtained from hydrogen evolution measurement at the time correspondingtotheendofeach impedancemeasurementwas taken.Theprocedureisgraphicallyillustratedbythedashedlines inFig.5.
The corrosion current measured by hydrogen evolution for nominallyidenticalexperimental conditionsdisplayedrelatively largevariations.Fig.6presentsthetimeevolutionofthecorrosion currentforthreerepeatedhydrogen–EISmeasurements3.5%NaCl andtworepeatedhydrogen–EISmeasurementsin0.35%NaCl.The observedvariationsinthecurrent-timebehaviourareattributedto thestatisticalnatureofthecorrosionprocessandtotherelatively smallelectrodesize.Onasmallelectrode,thepropagationofan activecorrosionsitecouldbeinterruptedbyresinattheedges. Fig.3. a)Potential/timeregimeappliedtoamagnesiumelectrodeimmersedin3.5%NaClcomprisingaseriesofcathodicpotentiodynamicpolarizationsseparatedbyfree corrosion1.5h.b)correspondingtimeevolutionoftheareaoftheelectrodecoveredbydarkregionsduringthe(forcomparisonthetimeevolutionofafreecorroding electrodeisreportedfrom[17].c)OpticalimagesofthecorrodingsurfaceduringthemeasurementofFig.3a.Numbersontheimagescorrespondtothenumberofcathodic polarization.
Consequently, the location where corrosion initiated and the direction of propagation (which are both random) can have a relativelylargeeffectontheoverallcorrosionrate,dependingon whetherthecorrosionfrontisfreetopropagateoritisstoppedby theresinattheedgeoftheelectrodeandcorrosionisforcedto initiate at a new location. As a result of the variations in the current-time behaviour, significant variations in the values of impedance measured under similar conditions were observed. However,thegeneralappearanceoftheimpedancespectrawas similar.Typicaltimeseriesofimpedancespectrarecordedforhigh andlowconcentrationofsodiumchloridearepresentedinFig.7a andbrespectively.
Athighfrequency,thesolutionresistanceeffectsdominated,at medium-highfrequenciesaregionofmainlycapacitivebehaviour, followed by a medium frequency plateau was observed. As expected,thesolutionresistancewashigherintheless concen-tratedelectrolyte.Atlow frequencies,areductioninimpedance modulusandacorrespondingpositivephaseshift,associatedto theinductivebehaviour,wasrevealed.Generally,withincreasing immersiontime, themodulusof theimpedancedecreased.The
inductivebehaviouratthelow-frequencyendofthespectrawas more visible for the measurement performed in the more concentratedNaClsolution.
Theimpedancespectrawerefittedwiththecircuit,proposedin [21] and reported in Fig. 8a, in order to extract the values of resistancesthatcouldbeusedtoestimatethecorrosionrate.As discussed in more detail later, Cox and Cdl account for the
-1.624 -1.596 -1.568 -1.540 0 2 4 6 8 0 2000 4000 6000 8000 10000 12000 0.0 0.2 0.4 0.6 0.8 1.0 Pot e nt ia l (SC E )/ V
a
b
C o rr os ion Cu rr ent / mA c m -2c
Dar k Ar ea F rac ti onTim
e / s
Fig. 5.a) Time evolution of the electrode potentials during a sequence of impedancemeasurementperformedbyusingthe‘modified’twoelectrodecell configurationin3.5%NaCl.Correspondingtimeevolutionofb)thecorrosioncurrent estimatedbyreal-timehydrogenmeasurementandc)thefractionoftheelectrode areacoveredbydarkregions.
-1.88 -1.84 -1.80 -1.76 -1.72 -1.68 -1.64 -1.60 -1.5 -1.0 -0.5 0.0 109.8 Ω cm2 68.8 Ω cm2 242.7 Ω cm2 6 5 4 3 2 C u rre nt density / m A cm -2
Potential (arbitrary shift vs. SCE) / V
1
106.4 Ω cm2
a
1E-6 1E-5 1E-4 1E-3
-1.90 -1.85 -1.80 -1.75 -1.70 -1.65
b
6 3 Potent ia l (SC E ) / VCurrent density / mA cm-2
bc=0.331 V
1
Fig.4.Cathodic potentiodynamicpolarization responsesmeasured duringthe experimentofFig.3.a)Responseinproximityofthecorrosionpotential(linear currentscale),translatedarbitrarilyonthepotentialaxistoimprovereadability. OCPvaluesforcurves1–6:1.703(1),1.639(2),1.636(3),1.632(4),1.629(5) and1.625(6)Vvs.SCE.b)Responseforlargecathodicpolarizations(logarithmic currentscale).Thenumbersonthecurvescorrespondtothenumberofcathodic polarizationinFig.3a. 0 2000 4000 6000 8000 10000 12000 0 1 2 3 4 5 6 C u rr en t De nsity / m A c m -2 Time / s 3.5% NaCl 0.35% NaCl
Fig.6. Timeevolutionofthecorrosioncurrentobtainedfromreal-timehydrogen measurementduringrepeatedEISmeasurementin3.5%and0.35%NaCl.
capacitanceofoxide/hydroxidelayersandchargeseparationatthe locations where hydrogen evolution takes place. Ra and Rcp
represent the resistances associated to local environmental changes(precipitationof gels, presence of bubbles) nearbythe anodicandcathodicregions.Finally,Laaccountsforthevariationof
the extension of active anodic regions during the sinusoidal polarizationand RCTaccountsfor thechargetransfer resistance
associatedtothereactionofhydrogenevolution. Typicalfitting resultsarecomparedtotheexperimentaldatainFig.8bandc. Generally, the simulated and experimental impedance spectra werecloselysimilar, exceptfor thefirst spectrumof theseries wheresomesignificantdiscrepanciesbetweenthesimulatedand theexperimental spectrum were occasionallyobserved. This is likely to be the consequence of the rapid evolution of the magnesiumsurfaceduringtheearlystagesofimmersion,resulting inacorrodingsystemthatisfarfrombeingstationary.Tables1and 2 presentthe numerical resultsof thefitting procedure. Fig. 9 illustratestherelationshipbetweenthecorrosioncurrentdirectly measuredbyhydrogenevolutionandthereciprocalofa)the zero-frequencyresistance(RAinparallelwiththeseriesofRCPandRCT),
b)theseriesofRCPandRCTandc)RCTalone.Itisevidentthatalinear
relationship between corrosion current and reciprocal of the resistancewasobserved,for allthethree resistancevalues.The points representing the experimental data, however, appeared morescatteredwhenthezero-frequencyresistancewas consid-ered,comparedtothecase whenthechargetransferresistance alone (RCT) or the series between charge transfer (RCT) and
corrosionproduct(RCP)resistancewereused.Itshouldbestressed
that, even if the time evolution of the corrosion current and
impedance spectra recorded under nominally identical condi-tionswasnotwellreproducible,thereciprocalof theresistance and the corrosion current were linearly correlated for all the experimental points.Thisobservation suggeststhatthelackof reproducibility in the corrosion current is due to statistical variation in thecorrosionprocess but the combined measure-mentofcorrosionratebyimpedancespectroscopyandhydrogen evolutionisreliable.
It is also important to emphasize that, regardless of the underlying kinetic of the electrochemical processes, a linear relationship betweencorrosion current and reciprocal of resis-tance is directlyobserved. Thus, althoughthe potentiodynamic results indicate that the system does not follow a Tafel-type behaviour,theplotsofFig.9enabletoextractdirectlyvaluesof ‘apparent’Stern–Gearycoefficientbyconsideringthat
icorr¼
B
R (1)
Whereicorris thecorrosion current density,B is the‘apparent’
Stern–Gearycoefficient,andRisthevalueofresistanceobtained fromfittingoftheEISspectra.Consequently,theapparentStern– Gearycoefficient can be directlyestimated fromthe graphsof Fig.9,byconsideringtheslopeofthefittinglines
B¼icorr
R1 (2)
Clearly,dependingontheresistanceselectedforthe calcula-tion, the‘apparent’ Stern–Geary coefficient is different; for the
0.01 0.1 1 10 100 1000 10000 100000 100 1000 3.5% NaCl 6 5 4 3 2 Im pedan c e M odul us / Ω cm 2 Frequency / Hz 1
a
0.01 0.1 1 10 100 1000 10000 100000 60 40 20 0 -20 -40 -60 -80b
6 5 4 3 2 Ph a s e Sh if t / D e g Frequency / Hz 1 6 1 3.5% NaCl 0.01 0.1 1 10 100 1000 10000 100000 100 1000 10000c
Imp e dance Mo dul us / Ω cm 2 Frequency / Hz 0.35% NaCl 6 5 4 3 2 1 0.01 0.1 1 10 100 1000 10000 100000 40 20 0 -20 -40 -60d
P h a s e S h if t / D e g Frequency / Hz 0.35% NaCl 6 5 4 3 2 1Fig.7.Typicalsequenceofimpedancemodulus(a,c)andphase(b,d)spectrameasuredin3.5%(a,b)and0.35%(c,d)NaCl.Thespectrawereacquiredsequentiallyandare labelledfrom1(firstspectrumacquired)to6(lastspectrumacquired).
zero-frequencyimpedance(RAinparallelwiththeseriesofRCPand
RCT) the apparent Stern–Geary coefficient was 116mV, for the
seriesbetweenthecharge transferresistanceand thecorrosion product resistance it was 255mV and for the charge transfer resistancealoneitwas223mV.
Fig. 10 presents the correlation between the area fraction coveredbythedarkregionsandthesumoftheoxidecapacitance and the double-layer capacitance (COX+CDL). Although the
estimationoftheareafractionisnotaspreciseasthehydrogen evolutionmeasurement,andthedatapointsappearsignificantly more scattered compared to the previous datasets, a linear correlationbetweencapacitanceandareafractionisobserved. Fig.8.a)EquivalentcircuitusedforthefittingoftheEISdata.Comparisonbetween
calculatedandmeasuredimpedancemodulusb)andphasec)spectra.
0.000 0.005 0.010 0.015 0.020 0.025 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 C u rrent D ensi ty / mA cm -2 RZF-1 / (Ω cm2)-1
a
0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5b
Cu rr e n t D e n s it y / m A c m -2 (R CP+RCT) -1 / (Ω cm2 )-1 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5c
Cu rr e n t De n s it y / m A c m -2 RCT-1 / (Ω cm2)-1Fig.9.a)Corrosioncurrentasafunctionofa)thereciprocalofthezero-frequency resistance(RAinparallelwiththeseriesofRCPandRCT),b)thereciprocalofthe
seriesofRCPandRCTandc)thereciprocaloftheseriesofRCT.Theslopeofthefitting
lineprovidesdirectestimationofthe‘apparent’Stern–Gearycoefficients.Filled symbols are obtained from measurement 3.5% NaCl, empty symbols from measurementin0.35%NaCl.
4.Discussion
The potentiodynamic polarization measurements performed withinapotentialrangesimilartothatusedtoacquireimpedance spectraindicate thatcorroding magnesiumelectrodes displaya complex behavioureven for very small polarizations above or belowthefreecorrosionpotential.Inparticular,theslopeofthe anodicpolarizationcurveis,inmostcases,significantlydifferent formtheslopeofthecathodicpolarizationcurve,asevidentfrom Fig. 2. Additionally, close scrutiny of the cathodic polarization behaviour,indicatesthatavariationintheslopeofthecurvesis observedwithinthe firstfew millivoltof cathodicpolarization, with the apparent resistance being lower for small value of polarization(2–6mV)andhigherforlargervaluesofpolarization. Thesevariationsinapparentresistanceoverthepotentialwindow usedforEISindicatethattheestimationofazero-frequencyvalue of impedance from fitting of impedance data is of little fundamental interest. In other words a single value of zero-frequencyresistanceis notcapableofreproducingthecomplex behaviour of the magnesium electrode in proximity of the corrosionpotential.
Fromapracticalviewpoint,however,thecorrelationbetween the measured impedance spectra and the corrosion rate is of interest, since electrochemical impedance spectroscopy is a relativelynon-destructiveelectrochemicaltestthatcanbeused to investigate in real-time the corrosion rate. From the presentedresults, itis evidentthatthereisa goodcorrelation between the values of resistance estimated from EIS and the corrosion rate. Furthermore, the direct measurement of the corrosioncurrentsimultaneouslywiththeimpedance measure-mentenables to determinedirectlythe proportionalitycoef fi-cient that links the corrosion current with the various resistances estimated from EIS. It is found that, if the zero-frequency resistance is used, the pointsappear comparatively more scattered and the apparent Stern–Geary coefficient is significantly lower (approximately a factor of 2) compared to whenthevaluesoftheRCPin serieswithRCTor RCTresistance
aloneareused.
Based on this experimental observation, it is necessary to speculateonthephysicalmeaningoftheapparent Stern–Geary coefficient,andoftheTafelcoefficientofmagnesium.TheStern– Gearycoefficientisgivenby
Table1
FittingresultsfortheEISmeasurementsperformedin3.5%NaClandcorrosioncurrentdensitiesobtainedfromsimultaneousmeasurementofhydrogenevolution.
Measure# RS COX LA RA RCP CDL RCT Icorr Vcm2 m Fcm2 Vscm2 V cm2 V cm2 m Fcm2 Vcm2 mAcm2 1 15.5 3.06 4420 153 502 7.84 297 0.56 2 16.3 2.50 1830 69.1 58.0 8.29 194 1.39 3 16.5 3.02 1370 67.1 24.9 21.3 109 2.18 4 16.6 3.77 1440 80.8 15.1 34.0 83.2 2.61 5 16.7 4.86 1560 73.9 10.2 41.4 75.5 2.80 6 16.6 6.94 1680 89.5 7.06 45.7 69.4 3.16 7 16.7 14.5 1970 95.1 5.95 43.1 67.8 3.37 8 16.6 29.3 3510 114 9.81 36.0 60.9 3.37 1 19.1 2.60 7170 184 241 2.20 705 0.25 2 19.3 2.68 3840 139 69.7 5.99 398 0.67 3 19.1 2.99 2380 90.5 38.2 12.7 223 1.30 4 18.8 3.49 1510 65.3 20.7 24.7 132 1.92 5 18.9 4.43 1420 64.4 12.1 38.4 98.6 2.50 6 18.8 6.74 1800 129 7.83 49.0 84.4 2.46 7 18.9 11.7 9270 293 6.45 51.5 93.7 2.06 8 19.2 25.0 12600 135 9.67 44 104 1.97 1 17.5 3.18 2830 261 412 12.3 286 0.63 2 17.7 2.84 1260 130 69.7 8.32 169 1.29 3 18.0 3.52 1170 104 30.1 17.2 128 1.63 4 17.7 4.32 1040 82.1 18.1 23.6 104 2.08 5 17.7 5.92 878 78.4 11.3 29.7 87.3 2.72 6 17.7 9.52 824 75.7 7.88 35.2 74.4 3.34 Table2
FittingresultsfortheEISmeasurementperformedin0.35%NaClandcorrosioncurrentdensitiesobtainedfromsimultaneousmeasurementofhydrogenevolution. 0.35%NaCl Measure# RS COX LA RA RCP CDL RCT Icorr Vcm2 m Fcm2 Vscm2 V cm2 V cm2 m Fcm2 Vcm2 mAcm2 1 118 3.23 98700 2250 1324 172 1750 0.14 2 118 2.19 19200 1320 379 4.54 1120 0.21 3 118 2.25 15700 968 229 6.76 961 0.37 4 118 2.39 10300 637 153 9.84 739 0.52 5 119 2.64 7710 514 111 14.6 539 0.62 6 120 3.09 622 519 80.8 21.3 405 0.72 7 118 3.91 8630 585 63.0 30.0 342 0.75 8 118 4.42 11800 480 56.5 35.7 331 0.81 1 109 3.24 264100 2960 1390 546.0 1650 na 2 113 2.73 19800 861 1730 2430 7080 0.05 3 109 2.11 14500 813 252 6.96 713 0.21 4 110 2.47 13500 558 161 11.8 470 0.37 5 109 2.87 8510 403 106 17.9 313 0.68 6 109 3.60 9540 334 69.8 26.7 231 0.93 7 109 4.66 12500 436 51.0 33.7 195 1.24 8 110 5.95 15100 331 41.9 39.6 170 1.59
B¼ babc
2:3ðbaþbcÞ
(3) Wherebaand bc are theanodic and cathodicTafel coefficients
respectively. For the case of magnesium, the cathodic Tafel coefficient can be experimentally measured; by performing a cathodicpolarization awell-defined linearregionin theEvan’s diagram is evident (Fig. 4b). The measurement of the anodic coefficientismoredifficultsincemagnesiumoxidizesfastunder anodicpolarizationandohmicdropeffectsbecomesoondominant
[17]. Suchohmic dropeffects canbe tosomeextentcorrected
during or after the measurement, but the correction is not particularlyreliablemainlybecausethepresenceofbubblesdueto copioushydrogenevolutionandtheformationofhydroxideand gelsinproximityoftheanodicallypolarizedelectrodeduetopH increase.Thesephenomenamightresultinvaluesofohmicdrop dependentontheappliedpotentialandpossiblyontheprevious polarizationhistory.
Inthiswork,forthefirsttime,valuesofapparentStern–Geary coefficientweredirectlymeasuredformagnesium,togetherwith thecathodicTafelcoefficient.Ifthesystemcouldbedescribedbya Tafel-typekinetic,inprincipleitshouldbepossibletodetermine precisely the anodic Tafel coefficient for magnesium by using Eq. (3) with the experimentally measured values of B and bc.
Howeverthis routeproves tobeunsuccessfulsince,in orderto obtainavalueofB=116mV(theloweramongthethreecoefficient measured) withthe measuredvalueof bc (331mV), a valueof
ba=1400mVis required. Sucha highvalue of theanodic Tafel
coefficient is clearly incorrect, since it would imply that the increaseincurrentislesssteepintheanodicdirectioncomparedto thecathodicdirection.Thisisnotthecaseeitherfornon-IRdrop correctedcurvesorforIRdropcorrectedcurves(seeforexample Figure3in[21]).FortheothervaluesofBexperimentallymeasured inthiswork,negativevaluesanodicTafelcoefficientsareobtained fromEq.(3).
Theaboveconsiderationsare inagreementwiththe experi-mental observations during potentiodynamic polarization, dis-closingacomplexbehaviourdeviatingsubstantiallyfromlinearity even for very small polarizations that cannot therefore be approximatedbyTafel-typebehaviour.Consequently,attempting toestimatetheanodicTafelcoefficientprovesunsuccessful.Even thoughtheStern–Gearycoefficientcannotbedirectlyestimated reliablyfrompotentiodynamicpolarizationcurves,however,the impedanceresponseiswellcorrelatedtothecorrosionratebyan
‘apparent’ Stern–Gearycoefficient. Thevalueofsuchcoefficient dependsonwhichresistancesinthefittingcircuitareselected.If the zero-frequency resistance is used B=116mV,if the charge transferresistanceisusedB=223mV,iftheseriesbetweencharge transfer resistance and corrosion product resistance is taken, B=253mV.
4.1.Electricalmodelforthecorrodingmagnesiumsurface.
Based onthe experimental evidencesgathered,an electrical modeldescribingtheelectrochemicalbehaviourofthemagnesium surfaceduringcorrosioncanbeproposed.Duringcorrosion,the appearanceoftheelectrodesurfacechangesfromsilverytodarkas a result of the propagation of corrosion. Similarly to what suggestedpreviously[32]thefreecorrodingmagnesiumsurface canberepresentedasinFig.11a. Theschematicillustratesthat corrosion propagatestowards the silveryregionby magnesium oxidation.Thus,theanodiccorrosionfrontproceedsand,asaresult of the air-formed film disruption, hydrogen evolution on the freshly exposed metal is possible due to the low corrosion potential. As a result of hydrogen evolution, the pH increases and either magnesium hydroxide precipitates or the oxide/ hydroxidefilmgrowingdirectlyonthemetalsurfaceisstabilized. Regardlessoftheexactnatureoftheprocessinvolved,closetothe corrosionfront,thecorrosionproductlayermustberelativelythin and, consequently, hydrogen evolution is abundant. Generally, substantially more intense hydrogen evolution is observed in proximityofthepropagatingcorrosionfront[14,19].Ontheother hand,farfromthecorrosionfront,thecorrosionproductlayeris thickerandlesshydrogenevolutiontakesplace.Asa result,the corrosionfrontadvancesandthesilveryregionssupportingtheair formedoxideareprogressivelyconvertedintodarkregions.Thus, there is a stage when theunderlying metal is to someextent exposedtotheelectrolyte(oronlypartiallycoveredbyanoxide/ hydroxidelayer)becausetheair-formedfilmhasbeendisrupted; at thislocation, hydrogenevolution isfavoured. Suchhydrogen evolutionincreasesthepHandthispromotestheformationofa filmthatlimitshydrogenevolutionitself.Thealloycomposition and the presence of impurities and/or second phase particles mightplayaroleinthemodulatingthepropertiesofthegrowing corrosionproductlayer,butthisaspecthasnotbeeninvestigated indetailhere.
Atthecorrosionpotential, theprocessesis controlledbythe rateofthecathodicreactionofhydrogenevolution,sincecorrosion of magnesium is cathodically controlled, as evident from the potentiodynamicpolarizationcurves.Thus,ifthecorrosioncurrent is steady,theoverall areaof theanodic regionis constant and determinedbythecathodicreactionrate;consequently,therateat whichtheair-formedfilmisattackedequalstherateatwhichthe darkoxideadvancesinthesamedirection.Giventhatnotallthe dark surface equally supports the cathodic reaction (hydrogen bubblesare generallyobservedinproximityof thepropagating corrosionfront[14,19])thereisnodirectcorrelationbetweenthe totalareaofthedarkregionsandthecorrosionrate.
Whenan anodicpolarization is applied(Fig.11b)additional electronscomparedtothoseconsumedbythecathodicreactionon the magnesium electrode are taken bythe external circuit(or, equivalently,ananodiccurrentisprovided).Thus,theareaofthe anodicregionisfreetoincreaseandtheoverallrateofcorrosion propagationincreases.
During cathodic polarization, electrons are injected intothe corroding electrode (or, equivalently, a cathodic current is provided) and the rate of the cathodic reaction of hydrogen evolution increases whereas the rate of the anodic reaction decreases.Asaresult,thepHinproximityoftheregionscapableof supportinghydrogenevolutionincreasesandtheformationofthe
0 10 20 30 40 50 60 70 80 90 100 0.0 0.2 0.4 0.6 0.8 1.0 D a rk R egi o n s A rea Fr ac ti on
Total Capacitance /μF cm-2
Fig. 10.Fractionoftheelectrodesurfacecoveredbydarkregionsasafunctionofthe totalcapacitance(CDL+COX).
dark-corrosionproductsfilmproceedsfasterthantheattackofthe silvery air-formed oxide. Thus, the area of the anodic region progressivelydecreasesuntilitbecomesnegligibleandcorrosion doesnotpropagateuntilthecathodicpolarizationisterminated. Theeffectofthisprocesscanbedirectlyobservedbyconsidering thetimeevolutionoftheareaofthedarkregionsduringaseriesof cathodicpolarizationsseparatedbyaperiodoffreecorrosion.The propagationofthedarkregionsdoesnotoccurduringcathodic polarization (Fig.3).A further effectof this process is directly observedinthecathodicpolarizationcurvesinproximityofthe corrosion potential; during the first few millivolt of cathodic polarization the propagation of the regions covered by dark corrosion products takes place at the expenses of the anodic regions.Duringthisstage,thecathodicpolarizationresistanceis comparatively low. Once all the anodic regions have been consumed and the electrode surface is entirely covered either by the residual air-formed film or the relatively thick dark corrosion product layer, hydrogen evolution becomes more difficultand acomparativelyhighercathodicpolarization resis-tanceisobserved.(Fig.4a)
Inthelightofthequalitativemechanismproposed,itispossible torelateeachelementoftheequivalentcircuitproposedwitha specificphenomenontakingplaceontheelectrodesurfaceduring impedance measurement or potentiodynamic polarization. In Fig.12a,theelementsoftheequivalentcircuitareoverlappedwith theschematicofFig.11(omittingthesolutionresistance).Twoof the three capacitors, CAF and COX account for the capacitive
behaviouroftheoxide/hydroxidefilms(air-formedandcorrosion productsfilm,respectively)presentonthemagnesiumsurfaceat any time. The two capacitors are connected in parallel by the electrolyteandbythemetalandthereforecannotbedistinguished byfittingtheimpedancedata.Forthis reason,intheequivalent circuitusedforthefittingthesethetwocapacitancesaregrouped togetherinasinglecapacitorCox.
Closetothecorrosionfront,thecathodicreactionofhydrogen evolutionproceeds fast,due toeithertheabsence,thereduced thicknessorthenon-protectivenatureoftheformingcorrosion productfilm.Acrosstheinterfacewherethecathodicreactionis takingplace,chargeseparationispresentatasubstantiallysmaller scalecomparedtotheregionssupportingtheair-formedfilmora stablecorrosionproductfilm.Inordertoaccountforthis,CDLis
Fig.11.Qualitativemodelrepresentingthecorrodingmagnesiumsurfacea)atthe corrosion potential, b) during anodic polarization and c) during cathodic polarization.
Fig.12.a)EquivalentcircuitoverlappedwiththemodelofFig.11a,highlightingthe physicalmeaningoftheindividualcomponents.
present in theequivalent circuit.In parallelwith CDL, a charge
transferresistanceRCTaccountsfortheprocessofelectrontransfer.
Asa resultof thecathodicreaction,hydrogen(bubbles)and pH increase resulting in the possible precipitation of magnesium oxide/hydroxide gelstakeplace, modifyinglocally the environ-mentortheoxidepropertiesabovetheactivecathodicsitesanda resistorRCPisneededtoaccountforsuchphenomena.Forsimilar
reasons,a resistanceRAisplaced inserieswiththeinductorLA
representingthebehaviouroftheactiveanodicregions.
Theinductivebehaviouroftheanodicregionsdeservesfurther clarification.Qualitatively,thekeycharacteristicofaninductoris thatitoffersnoelectricalresistanceatzerofrequency,whileithas infiniteresistanceathighfrequency.However,thereisnophysical reasontoassumethattherateoftheanodicreactionshouldbe frequencydependent.Thus,fromthephysicalviewpoint,aresistor RA0mustbepresent,inparallelwiththeLA,toaccountforthefact
thattheanodicreactionratecannotdecreasetozeroduringhigh frequencymeasurement. Indeed,usinga circuitcomprisingRA0,
producesagoodfitoftheexperimentaldata,buttheuncertainty onthevaluesoftheotherresistancesbecomesveryhigh.Thisis duetothefactthatthevaluesofRCP,RCT,RAareinthesameorderof
magnitudeandRA0isshort-circuitedbyLAatlowfrequencieswhile
RCTisshort-circuitedbyCDLathighfrequencies,andthereforeitis
difficulttodistinguishtheireffectsontheimpedancespectra.From thecorrosionprospective,however,thepresenceorabsenceofRA0
isnotaconcern,sinceitisshort-circuitedbytheinductoratlow frequency.
In orderto understandthenatureof the inductanceon the corroding magnesium electrode it is useful to consider the behaviourof an ideal inductor. Aninductor can beseen asan electrical component that resists to a variation in current by producingapotentialdifferenceproportionaltothederivativeof thecurrent,suchasthepotentialdifference acrosstheinductor acts in the direction of opposing the current variation. Thus, increasing thecurrent acrossan inductor, resultsin a positive potential. On the otherhand, decreasingthe current acrossan inductor,generatesanegativepotential.Thesignofthepotentialis such as it contrasts the variation in current. If a sinusoidal perturbationisconsidered,athighfrequency,thetimederivative of thecurrent ishigh; thereforethepotential producedby the inductor is substantial. Vice versa, at low frequencies, the derivativeof thecurrent is low and thepotential producedby theinductorisirrelevant.
Suchbehaviourcanbereadilytranslatedtotheanodicreaction occurringonacorrodingmagnesiumelectrodewithreferenceto
Figs.11and12.Atthecorrosionpotential,theareaoftheactive
anodicregionsislimitedbytherateofthecathodicreactionandit attains a relatively steady value. When a sinusoidal current perturbation(similarargumentsapplyforapotentialperturbation, butitiseasiertoconsidercurrents)isapplied,thesizeoftheactive anodicregiontendstoincrease,tobalancetheadditionalcurrent providedbytheexternalcircuit(Fig.11b).Iftheincreaseincurrent is sufficiently slow, the active anodic region can propagate accordingly,andnoadditionaloverpotentialisneededtosustain theincreasedcurrent,sincetheactualcurrentdensityontheactive anodicregionsisunchanged,duetopropagation.Thisbehaviouris similartothebehaviourofaninductoratzerofrequency,i.e.the the current value has no effect on the potential. Generally, however, the propagation (orcontraction) of the activeanodic regionisnotinstantaneous.Asaconsequence,adependenceofthe potential response on the frequency of the sinusoidal current perturbationisobserved.Athighfrequency,theareaoftheactive anodic region cannot follow the fast current variations and, similarlytothecaseoftheidealinductor,alargeover-potentialis neededtoacceleratethe anodicreaction ontheexisting active anodicregions(i.e.increasingthecurrentdensityontheavailable
anodic regions). Again, this behaviour is similar tothat of an inductorathighfrequency.ThediodesinFig.12ahavebeenadded toaccount(qualitatively)forthefactthattheinductivepartofthe circuitrelatestotheanodicreactionandthecapacitivepartofthe circuit relates to the cathodic reaction, and that the corrosion current flows in the direction indicated by the arrows. The presenceofthediodesalsoaccountsforthedifferenceinslopeof theanodicandcathodicpotentiodynamicpolarizationcurves in proximityofthecorrosionpotential.Additionally,italsoaccounts for the observation of King et al. [21], who revealed an enhancement of the inductive behaviourwhen performing EIS onmagnesiumabovethefreecorrosionpotentialanda suppres-sionoftheinductivebehaviourwhenperformingEISbelowthe freecorrosionpotential.
The experimental evidences obtained in this work can be interpretedonthebasisoftheabovemodel.Firstly,thesimilarity in behaviour observed during anodic polarization for a dark electrodeandasilveryelectrodearediscussed.Accordingtothe proposed model,theanodic currentdirectlycorrelates withthe areaoftheanodicregionswhich,atthefreecorrosionpotential,is limitedbythecathodicreaction;whenanodiccurrentisprovided throughtheexternalcircuit,theareaoftheanodicregionadjuststo the external current, regardless of the pre-existing surface condition.Asaconsequence,theinitialstateofthesurfacedoes not affect substantially the anodic polarization response. The changeinslopeoftheI/Vcurvesinproximityofthefreecorrosion potential relatestothefactthat,unlikefor Tafelbehaviour,the anodicreactionlargelydominatesonthecathodicreactionseven forsmallanodicpolarizations,duetothefactthattheactiveanodic regionrapidlyadjuststothetotalcurrentavailable.For polariza-tioninthecathodicdirection,thepassivationoftheactiveanodic regionsoccursrapidly(Fig.11c)andthereforeevenafewmillivolts below thefreecorrosionpotential thecathodicreactionlargely dominatesontheanodicreaction.Thisbehaviourisrepresentedby thediodesinFig.12.
Thechangeofslopeinthecathodicpolarizationcurves(Fig.3) can be explained similarly. At the free corrosion potential, the electronsgeneratedatactiveanodicregionsarebalancedbythose consumedattheactivecathodicregions.Thebalanceisperturbed bythecathodicpolarizationthatresultsinincreasedavailabilityof electronsthatultimatelyinducesexcessalkalinisationcompared tofreecorrosionandconsequentpropagationofthedarkcorrosion productfilm(Fig.11c)fasterthanthepropagationofthecorrosion front. During the early stages of cathodic polarization, the propagation of the corrosion product film towards the active anodicregionsispossibleandtheapparentresistanceisrelatively low. Once all the active anodic regions have been consumed (Fig.11c)thepropagationisnolongerpossibleandtheapparent resistanceincreases(Fig.3a).Thisisconfirmedbytheobservation thatthedarkregionsdonotpropagateduringcathodic polariza-tion(Fig.4c).Afterthepropagationstageisfinished,thecathodic reactiononthedarkcorrosionproductfilmfollowsTafelkinetics, possiblyduetothefactthatthelimitingstepisthechargetransfer acrossthedarkfilm.
Concerning the interpretation of the correlation between measuredcorrosioncurrentandresistancevaluesobtainedfrom impedancemeasurement,thereducedscatteringobservedwhen considering the charge transferand theseries between charge transferandcorrosionproductsresistance(ratherthanthe zero-frequencyresistance)isduetothefactthatthecathodicreaction providesthelimitingstepforcorrosionpropagation.Thereforethe corrosionrateisdirectlyproportionaltothevaluesofRCPandRCT.
Indirectly,thevaluesofRCPandRCTdeterminethevalueofRA,and
thereforealsothezerofrequencyresistancecorrelateswellwith thecorrosionrate.However,duetothelessdirectdependence,the pointsintheplotsforthedeterminationoftheapparentStern–
Gearycoefficientappearmorescattered.Basedonthese consider-ations, it appears that from the practical viewpoint, the most reliableestimationofthecorrosioncurrentfromEISdataislikely tobeprovidedconsideringtheseriesofRCPandRCT(sincethese
twovaluesaccountfortherate-determiningcathodicreaction)and usingforthecalculationstherelevantvalueofapparentStern– Gearycoefficient(B=253mV).
5.Summary
Thecorrosionbehaviourofmagnesiumhasbeeninvestigatedby potentiodynamic polarization and electrochemical impedance spectroscopy. Potentiodynamic polarization revealed significant deviations fromlinear behaviour in proximity of the corrosion potential,indicatingtheestimationofthecorrosioncurrentbyusing aStern–Gearycoefficientobtainedfrompotentiodynamic polariza-tioncurvesisnotadequate.However,directmeasurementofthe corrosioncurrent byhydrogencollection,performed simultaneously withEISmeasurements,revealedthatthereciprocalofthevaluesof resistanceestimatedbyEISarelinearlycorrelatedwiththecorrosion current. The experimentally measured proportionality constant providesan‘apparent’Stern–Gearycoefficientthatcanbeusedto evaluatethecorrosioncurrentfromEISdata.Fromthevalueofthe experimentallymeasuredapparentStern–Gearycoefficientandof thecathodicTafelcoefficient,itisnotpossibletoobtainareliable valuefortheanodicTafelcoefficient,sincemagnesiumcorrosion doesn'tfollowTafel'stypekinetics.
Based on the behaviour observed during potentiodynamic polarizationand on equivalent circuit analysisof EIS spectra, it canbeconcludedthatcorrosionproceedsbymagnesiumoxidation atactive anodic regions. Wherethe air-formed oxide/hydroxide layer isdisrupted,hydrogenevolvesvigorously,increasingthepHand inducingthe precipitation of magnesium hydroxide behind the corrosionfront.Oncetheprecipitatedfilmissufficientlythick,the rateofhydrogenevolutionbehindthecorrosionfrontdecreases. Corrosion proceeds by translation of the active anodic region towards the uncorroded silvery regions, which is followed by propagation of the dark regions. Application of an anodic (or cathodic)polarizationresultsinfaster(orslower)propagationofthe activeanodicregionwithrespecttothepropagationdarkregions. Acknowledgements
EPSRC is acknowledged for provision of financial support throughtheLATEST2ProgrammeGrant(EP/H020047/1).ProfM. DiNataleisacknowledgedforhelpfuldiscussions.
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