Rheology of white paints: How Van Gogh achieved his famous impasto

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Rheology of white paints: How Van Gogh achieved his famous impasto

J. Salvant Plisson, Laurence de Viguerie, L. Tahroucht, M. Menu, G. Ducouret

To cite this version:

J. Salvant Plisson, Laurence de Viguerie, L. Tahroucht, M. Menu, G. Ducouret. Rheology of white

paints: How Van Gogh achieved his famous impasto. Colloids and Surfaces A: Physicochemical

and Engineering Aspects, Elsevier, 2014, 458, pp.134 - 141. �10.1016/j.colsurfa.2014.02.055�. �hal-

01516143�

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ContentslistsavailableatScienceDirect

Colloids and Surfaces A: Physicochemical and Engineering Aspects

jo u r n al ho me p ag e :w w w . e l s e v i e r . c o m / l o c a t e / c o l s u r f a

Rheology of white paints: How Van Gogh achieved his famous impasto

J. Salvant Plisson

^a

, L. de Viguerie

^b^,^c^,∗

, L. Tahroucht

^d

, M. Menu

^a^,^g

, G. Ducouret

^d^,^e^,^f

aCentredeRechercheetdeRestaurationdesMuséesdeFrance,C2RMF,PalaisduLouvre,14QuaiFranc¸oisMitterrand,ParisF-75001,France

bUPMCUnivParis06,UMR8220,Laboratoired’archéologiemoléculaireetstructurale,LAMS,ParisF-75005,France

cCNRS,UMR8220,LAMS,F-75005Paris,France

dUPMCUnivParis06,UMR7615,LaboratoiredeSciencesetIngénieriedelaMatièreMolle(SIMM),ParisF-75005,France

eCNRS,UMR7615,SIMM,ParisF-75005France

fESPCI,UMR7615,SIMM,ParisF-75005France

gInstitutdeRecherchedeChimieParis,IRCP,11ruePierreetMarieCurie,ParisF-75006,France

h i g h l i g h t s

•The rheological properties of 19th century white paint formulations havebeencompared.

•Lead and zinc white paints both exhibitviscoelasticproperties,char- acteristicofpastesuspensions.

•Yield stressand elastic moduliare strongly dependant on the nature, treatmentandproportionofoil.

•Atall studied concentrations, yield stressandelasticmodulusat1Hzare higherforzincwhitepaints.

•Thiszincwhitepropertycanexplain itsspeciﬁcusebyV.VanGogh,tocre- ateimpasto.

g r a p h i c a l a b s t r a c t

a r t i c l e i n f o

Articlehistory:

Received4October2013

Receivedinrevisedform5February2014 Accepted8February2014

Availableonline12March2014

Keywords:

Paintreconstructions Zincandleadwhite Impasto

VincentVanGogh Rheology Oilpaints

a b s t r a c t

Paintsbasedonwhitepigmentsarethebasicmaterialsfoundingroundlayersofready-madecanvases aswellasinpaintinglayersmixedwithothercolours.ItissurprisingthatVincentVanGogh,whose uniquestyleisworldfamous,resortedtonotonebuttwotypesofwhitepaints.Indeed,VanGoghoften usedbothleadwhiteandzincwhiteintheverysamepainting,contrastingthenwiththemajorityof hiscontemporarieswhohaveonlyusedthetraditionalleadwhite.Totracetheevolutionofhispainting techniqueandtorespondtotheissuesofauthentication,datingandpreservationraisedbyhisartwork, itisessentialtohaveagoodknowledgeofthepaintingmaterialsheusedandhowheusedthem.

Thispaperdescribesthereconstructionsof19thcenturywhitepaintformulationsandtheirrheological characterizationinordertocomparetheirflowproperties:byadjustingthem,differentpaintfinishes fromsmoothsurfacestohighimpastoscanbeproduced.Wedefineageneralprocedureforpaintrheology characterization,usefulforoldrecipesreconstructionsinthefieldofconservationscience.Bothleadwhite andzincwhitebasedpaintsexhibitasimilarrheologicalbehaviour,withafluidtosolidtransition,and variationsoftheirpropertiessuchasyieldstressandelasticmoduli,dependingontheirformulation(oil nature,content,andtreatment).Anexplanationonthespecificuseofzincwhitecanbeproposedasit allowshigherimpastosthanaleadwhitepaintcontainingthesameoilcontent.

∗Correspondingauthorat:CNRS,UPMC,UMR8220,LAMS,F-75005Paris,France.Tel.:+33144278226.

E-mailaddress:laurence.de[email protected](L.deViguerie).

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1. Introduction

Paintbasedonwhitepigmentsisoneofthemostcommonly used by artists: indeed, white paints, often mixed with small amountofcolouredpaints,constitutethebasisofmanypainting layers.Forexample,ifonehasalooktotheordersofoilpainttubes byVincentVanGogh(1853–1890),preciselydescribedinhislet- ters,itappearsclearlythatheusedaverylargeamountofwhiteoil painttubestoproducehisartworksknownfortheirbrightcolours [1].Thiswasalsoconﬁrmedbydifferentstudiesperformedinthe past:analyseshaveshownthatcolouredpaintinglayersarecom- monlymadeofwhitepigmentswithasmallamountofcoloured pigment[2].Attheendofthe19thcentury,twotypesofpigments wereavailabletoproducewhitepaints:leadwhite(generallymix- tureof leadcarbonates,PbCO3/2PbCO3·Pb(OH)2)and zincwhite (zincoxide,ZnO).SinceAntiquity,leadwhitehasbeenoneofthe onlywhitepigmentusedinoilpaintingasitpossessesexcellent properties.Itwasproducedindustriallyduringthe19thcenturyby usingtheDutchStackprocess,consistinginexposingmetalliclead stripstovinegarfumes(aceticacid)andmanureinaclosespacefor severalmonths.Leadwhiteremainedtheonlywhitepigmentused inoilpaintinguntilleadwhitetoxicitybecameanimportantcon- cern[3].Thisiswhy,fromtheendofthe18thcentury,therewasa crucialneedtodevelopanalternativewhitepigmentforoilpaint.

Zincwhiteappearedtobethebestalternative.Afterimprovingthe manufacturing,zincwhitebecameavailableonanindustrialscale aroundthemiddleofthe19thcentury[4].

Zincwhiteremainedofverylittleusetoartistsfromthesecond halfofthe19thcentury,suchastheImpressionists,whousually chosetousethetraditionalleadwhite,probablybecausezincwhite wassaidtobeslowertodryandhadpoorcoveringpower,(i.e.the abilityofapainttoobscurethesurfaceuponwhichitisapplied)[5].

Unlikehiscontemporaries,VanGoghusedbothzincwhiteandlead whitepaintstoproduceartworks:indeed,ordersoflargeamountof oilpainttubesofblancd’argent(referringtoleadwhite)andblancde zinc(referringtozincwhite)areregularlymentionedinhisletters [1].Additionally,VanGoghoftenusedbothzincwhiteandlead whitepaintssimultaneouslyintheverysamepaintingaccording topreviousresearch[6–10].Despitecomplaininginmanyletters abouttheslowdryingofzincwhite[11],VanGoghindicatedthatit hadotheradvantages[12]thathedidnotspecify.Onecanwonder whichspeciﬁcadvantagesVanGoghfoundineachtypeofwhite paintandhowhewasusingtheminhisartworks.

Ascanbefoundinancientcataloguesfrompaintsuppliers(Le PèreTanguycataloguedatingfromca.1888to1890or1876Lefranc catalogue)[5,9],leadandzincwhiteoilpainttubeswerethesame price.Somemajordifferencesbetweenleadwhiteandzincwhite paintpropertieshavealready beendescribedin literature.Lead whitepainthasashorterdryingtimeandabettercoveringpower, whereaszincwhitegivebettercoloursinmixturewithpigments [4–6,13,14].Amongappearanceanddryingproperties,thepaint textureandconsistencyarealsocrucial,particularlyinthecase of VanGogh, well-known forhis highimpastos,resultingfrom theapplicationofpaintinthicklayerstoproduceatexturedsur- face(Fig.1).Indeed,artistsbyadjusting paintconsistenciesand

textures can produce very different effects, ranging from very smoothsurfacetoveryhighimpastos.

Basedonreconstructionsof19thcenturyoilpaints,weinves- tigatedtheuseofwhitepaintsbyVincentVanGoghinrelationto theirconsistencyandtexture.Togetabetterunderstandingonthe differentuseofleadandzincwhitepaintsinVanGogh’sartworks, theirrheologicalpropertieshavebeencharacterized.Adiscussionis thenproposedonthelevellingpropertiesofpaintmaterialsapplied toVanGogh’spaintlayers.

2. Materialsandmethods

2.1. Paintsamplesreconstructions

Reconstructionsof19thcenturyoilpaintwerepreparedaccord- ingtopreviousinvestigationsand tothespecificoilabsorption value of each pigment investigated [2–4,15,16].Three different pigmentswereusedtopreparetheformulations:zincwhite,lead whiteandcobaltblue(suppliersindicatedinTable1).Theywere firstimagedbySEM(seeSupportingInformation,S1).Paintmade of37%volofzincwhitewereprepared,groundwithdifferentoils (nature,treatmentandsupplierin Table1)inordertocompare theirrheologicalpropertiesandchooseanappropriateoilforfur- thermeasurements.Weusedlinseedandpoppyoilssimilartooils thatwerecommonlyemployedduringthe19thcentury.Thetwo linseedoilsfromLaverdurearebothcoldpressedbuttheirtreat- mentsaredifferent:oil“cat.B”,whichhasbeenchosenforfurther experiments,hasbeenrefinedwhereastheoil“cat.A”hasbeen purified.

Paintswithlinseedoil(“cat.B”)anddifferentproportionsofone ortwowhitepigment(s)werepreparedandtestedaccordingto theproportionslistedinTable2.Thepaintsbasedonrespectively zincwhite/leadwhite/cobaltbluearenotedZW/LW/CBtogether withnumbersindicatingthepigmentvolumiccontent(%vol).As anexample,thepaintnamedZW30-CB10contains30%volofzinc white,10%volofcobaltblueandthus60%volofoil.Forthemix- turesoftwopigments,theoilcontentisﬁxedat60%vol,whichhas beenestimatedastheusualconcentrationinVanGoghwhitepaints estimatedbyacombinationofPIXEandRBStechniques[17].

10–20gofpaintwaspreparedfromrawpigmentsandoilat thedifferentcompositions.Firsttheappropriateamountofoilwas addedtothepigmentandmixedwiththepaletteknife.Themix- turewasthenroughlydividedintothreepartsandeachthirdwas groundunderthemulleronaglassplateduring120s(Fig.1).The threepartswerethenmixedtogethertohomogenizethewhole anddividedagainbythirdandgroundfor40s.

Someformulationswereunstableoverfewdaysandreleased oil.Moreover,itwasobservedthatsomeleadwhitebasedformu- lations,whenallowedtorest,getspontaneouslymoreﬂuentwithin ashorttime.Suchabehaviourwasnotdetectedforzincwhiteand cobaltbluepaints.Thischangeofconsistencycouldbeexplainedby theimprovementoftheoil-wettingofleadwhitepigmentsand/or bytheoildiffusionwithtimeintheaggregatesthatremainpoorly dispersed,leadingprogressivelytoabetterlubricationofpigment

Table1

Differentoilsandpigmentstested.Theoilsviscositywasmeasuredandestimatedatc.a.5×10⁻²Pa.s.

Nature Supplier Density Preparationandtreatment

Oil Linseed Laverdure Cat.A:cold-pressed,puriﬁed

Linseed Laverdure Cat.B:cold-pressed,reﬁned

Poppy Kremer Reﬁned

Pigment ZincWhite Kremer(No.46,300) 5.6

Leadwhite(mainlyhydrocerussite) NaturalPigments 6.5 Dutchstackprocess

CobaltBlue Kremer(No.45,710) 4.3

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Fig.1.DetailoftherakinglightphotographofLaChambredeVanGoghàArles(57cm×73cm,oiloncanvas,LaFaillenumberF483,Muséed’Orsay,Paris-©C2RMF,E.

Lambert)paintedbyVincentVanGoghin1889,showinganexampleofveryhighimpastosfoundinVanGogh’sartworks(left);photographofthetypeofmaterials(muller andglassplate)usedforthepreparationofreconstructedoilpaintsamplesfromoilandrawpigmentpowder(right).

particles.Tolimittheseeffects,thepaintswerepreparedandtheir rheologicalpropertiesinvestigatedonthesameday.

2.2. Rheology

Therheologicalmeasurementswereperformedat25^◦C.Yield stressanddynamicalpropertiesweremeasuredusingastraincon- trolled rheometerTA instrumentsARES (LS1) equipped with a serratedplate/plategeometry(diameter:25or40mm)orarough coneandplategeometry(diameter:50mm,angle:0.04radian,gap:

0.045mm).ThestresscontrolledrheometerHaakeRS600equipped witharoughconeandplategeometry(diameter:35mm;angle:

0.04radian),oraserratedplate/plate(diameter:35mm)wasalso usedwhenrequired.Allthegeometriesarestainlesssteelexcept thetitaniumconeoftheARES.Thegapfortheplategeometries wasﬁxedatvaluesinbetween0.5and2.1mmdependingonthe amountofpaintadded.Eachmeasurementwasrepeatedtwiceto checkthereproducibility.Anothersamplewiththesamecompo- sition,preparedinthesameconditions,wasalsoanalyzedandits propertiescomparedtotheﬁrstone.

Foralltheformulations,thefollowingdynamicalmeasurements havebeenperformed:

-strainsweeptestsinthelinearregime(from0.01%strainto theendofthelinearviscoelasticplateau),atω=1Hz,inorderto determinetheextentofthelinearregime,

-frequencysweeptests,from0.1 to100rads⁻¹ at constant straininthelinearregime,

-strainsweep tests,atω=1Hz, forstrain furtherthelinear regime.

Theyieldstresshasbeenevaluatedusingtwodifferentmeth- ods:creeptest andflowmeasurements.Asageneralprocedure onlytheflowmeasurementmethodhasbeenused;thecreepmea- surementsarereportedintheSupportingInformation.Theflow measurements(shearratesweeptest)weremeasuredfrom0.001

to200s⁻¹(waitingtime:30s,measurementtime:20s).Insome cases,theﬂowmeasurementwasperformedwithbothincreasing anddecreasingtheshearrate.

Asageingfeaturesareexpectedinconcentratedsuspensions, wetriedtoestimatethepaintageing(deﬁnitioninSection3.1.2).

Thesamplewassubmittedtoamechanicalfluidificationinorder toputthesysteminafluidstateindependentfromitshistory.The protocoloffluidificationwasempiricallydetermined:thesamples weresubmittedtoanoscillatorystrainofamplitude100%,atafre- quencyof1Hzduring100sinordertogetreproduciblemechanical responses.Aftertheprotocoloffluidificationatt=0,thesample evolvedspontaneouslyduringawaitingtimetw.Att=tw,asmall strainof0.2%(inthelinearregime)wasappliedandtherelaxation ofthestresswasmeasured.Thismeasurementwasperformedfor differentwaitingtimes:tw=10,100,1000and10000s.

2.3. Roughnessmeasurements

To investigate the topography and particularly the surface roughnessofa painting,we usedtheMicromesurefromSTIL, a non-contactextendedﬁeldconfocalimagingsystem.Itconsistsin motorizedx,y,zstagesandaCHR150confocalsensor.Itiscon- trolledwiththeSurfacemapsoftware.Thedataareprocessedwith theMountainsMapUniversalsoftware.Opticalpenof3000␮mwas usedtoscananareaof25mm×25mmat100Hzwithastepof 50␮minxandydirections.

3. Results

3.1. Rheologicalbehaviourofpaintsamples 3.1.1. Generaldescription

Allthepaintsstudiedexhibitviscoelasticproperties,character- isticofpastessuspensions(Fig.2).

Table2

Compositionofpaintswithlinseedoil(in%vol),fromLaverdure.Thevolumefractionwascalculatedfromtheweightintroducedandthedensityofthematerials.

Paints Referencename Zincwhite Leadwhite Cobaltblue Linseedoil

Zincwhite(ZW) ZW 19.9–48.5 0 0 52.5–80.1

Leadwhite(LW) LW 0 35–59.1 0 40.9–65

Zincwhiteandcobalt blue(ZW-CB)

ZW30-CB10 30 10 60

ZW35-CB5 35 5 60

ZW39-CB1 39 1 60

Leadwhiteandcobalt blue(LW-CB)

LW30-CB10 30 10 60

LW35-CB5 35 5 60

LW39-CB1 39 1 60

Zincwhiteandlead white(ZW-LW)

ZW25-LW75 8.5 25.5 60

ZW50-LW50 17 17 60

ZW75-LW25 25.5 8.5 60

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Fig.2. Strainsweeptestforapaintsample(zincwhitegroundinlinseedoilwitha volumicpigmentcontentof37%vol)showingtheevolutionoftheelasticmodulus GandtheviscousmodulusGinfunctionofthestrainatconstantfrequency(1Hz).

Thepaintsexhibitaviscoelasticbehaviour.

At low strains, the elastic modulus G is higher than the viscousmodulusGandthereisnotmuchevolutionofbothmod- uli: the systemis elasticon allthis strain range that is called thelinearviscoelasticregion.Beyondacriticalstrainc,related to the dynamic yield stress c, the elastic modulus decreases and thesystembecomes viscous(G>G), thepaintﬂows.This typeofbehaviour,characteristicofsuspensionspastes,hasbeen observedforexampleinsilicasuspensionsandmicrogelsuspen- sions[18].

Flowmeasurements(Fig.3)duringtheramp-downarealmost identicaltotheonesduringtheramp-upuntiltheyieldstressis reachedwhentheshearratesweepis slowenoughtoperform measurementsattheequilibriumofthesample(totaltimemea- surementofabout80min;Fig.3a):agoodreversibilityisobserved forthemeasurementsbetweentheramp-upandtheramp-down.

Thesystemhasrestructuredandexhibitsagainitselasticproper- ties.Itisinterestingtonotethatstressmeasurementsduringthe ramp-downareslightlylowerthantheonesduringtheramp-up,as ithasalsobeenobservedforothersystems,suchasgranularpastes [19].Theevolutionofthestressinfunctionofshearratefollows the Herschel-Bulkley model [20,21]. On the other hand, when measurementsareperformedwithafastshearratesweep(total time measurementsof about6min;Fig. 3b),a phenomenon of

hysteresisisobserved,showingaslightthixotropicbehaviour[22]

ofthepaint.

Asa consequence ofthis time-dependant behaviour,several parameters, suchas thetime betweensample preparation and measurementsandthewaitingtimebetweenmeasurementswere identiﬁed as having an inﬂuence on the measured rheological behaviour.Bycontrollingthoseparameters,weobservedagood reproducibilitybetweenthemeasurementswitha dispersionof about20%foralltheformulations(exceptlinseedoilA).

3.1.2. Ageingmeasurements

To explore thehistory-dependent effectin rheological paint measurements,weperformedageingmeasurementsbasedonthe experimentalproceduredescribedbyDerecetal.[23]forconcen- tratedcolloidalsuspensions(seeexperimentalconditionsabove).

Indeed, in those systems rheologicalageing hasbeenobserved [23–28]:theresponsetoa mechanicalperturbationdependson thetimeelapsedafterpreparation[25].Atshorttimes,anelastic responseofthesample,anincreaseofthestress,isobservedasa consequenceofthe0.2%constantstepstrainperturbationthesam- pleissubmittedto(Fig.4).After0.05s,thestressisrelaxing.The stressrelaxationproﬁleisthesamewhateverthewaitingtimet_w is,buttherelaxationisslowerwhenthewaitingtimeincreases.

Theelasticmodulus,calculatedfromthemaximumstressvalue (whichismuchlowerthantheyieldstress)increasestogetherwith higherwaitingtime(Fig.4).Thisisduetothefactthattherewas longertime for thematerialtorestructurewithhigher waiting time.Higherelasticmodulusvalueshighlightamoreimportant reorganizationofthematerial.

3.2. Inﬂuenceofpaintformulation 3.2.1. Inﬂuenceofthenatureofoil

Wecomparedtherheologicalbehaviourofpaintformulations containing37%volofzincwhite,groundindifferentoilsfollow- ingthesameprocedure.Theyieldstressandtheelasticmodulus Gmeasuredat1Hzforthedifferentformulationsareindicatedin Table3.Whereastheinitialviscositiesoftheoilsalonearequite close (c.a.5 × 10^-2Pas)the rheologicalproperties ofthe paint obtainedappearedtobequitedifferent.Duringthepaintprepa- rationstep,thiswasalreadyvisibleaspigmentsweredispersed veryeasilyinsomeoilsandwithgreaterdifﬁcultyinothers.The twooilsfromLaverdureonlydifferfromthetreatment,although theoilabsorptionvalueandtheneededgrindingtimetoobtaina homogeneousformulationaredifferentforboth.Wechosetokeep constantthoseparametersinthisexperimentbutthereisnodoubt apainterwouldslightlymodifytheseforproperuseifnecessary.

Fig.3. (a)Slowﬂowmeasurementsforapaintsample(zincwhitegroundinlinseedoilwithavolumicpigmentcontentof32%vol):evolutionofthestressduringthe applicationofaslowincreasingshearratesweep(ramp-uprepresentedbyblackdiamonds)followedbyaslowdecreasingshearratesweep(ramp-downrepresentedby greytriangle)(totaltimemeasurementofabout80min).(b)Rapidﬂowmeasurements:evolutionofthestressduringtheapplicationofarapidincreasingshearratesweep (ramp-up,blackdiamonds)followedbyaslowdecreasingshearratesweep(ramp-down,greytriangles)(totaltimemeasurementofabout6min).

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Fig.4.Ageingmeasurementsonpaintsamples:(a)schematicrepresentationofthe experimentalprocedurethesamplewassubmittedto;(b)evolutionoftheelastic modulus(maximumstressvaluedividedbythestrain,i.e.0.2%),infunctionofthe waitingtimet_w.

Table3

ElasticModulusG,measuredat1Hzandyieldstress,dependingontheoilinpaints containing37%volofzincwhite.

G(1Hz)inPa YieldstressinPa Linseedoil,catA,Laverdure 108,000 430

Linseedoil,catB,Laverdure 15,300 155

Poppyoilreﬁned,Kremer 52,000 540

Notonlythenatureofoilbutalsotheprocessingmethodhasa strongimpactonthepaintrheology.Indeedforrefinedlinseedoil, themeasuredGat1Hzisc.a.15,000Pa,whereasitisrespectively of52,000Paforrefinedpoppyoil,andof108,000Paforpurified linseedoil(Table3).Thisstronginfluenceoftheoilnatureand treatmenthasalreadybeenobservedintheliterature[15,29,30]:it isparticularlytrueinthecaseofleadwhiteandmuchlessimportant forpigmentssuchasvineblackorumber.Dependingonitsnature andprocessingmethod,theoilcompositionisdifferentandthusits reactivityandpigmentaffinitycanbemodified.Exceptotherwise stated,weusedtherefinedlinseedoilfromLaverdure(“cat.B”),as itallowedgoodreproducibilityofourmeasurements.

3.2.2. Inﬂuenceofpigmenttypeandconcentration

Westudiedtheevolutionoftheyieldstressandtheelasticmod- ulusGat1Hzinfunctionofthepigmentconcentrationforlead whiteandzincwhiteoilpaints.Allthepossiblerangeofpigment concentrationproviding asuitable pastetopaintwasexplored.

Fig.5showstheevolutionoftheyieldstressinfunctionofthevol- umefractionofpigmentforthetwotypesofpaints.Thevolume fractionsofpigmentswerecalculatedfromtheweightfractionsof pigmentsusedintheformulation,thepigmentdensitiesindicated bythesuppliers(Table1)andadensityof0.93g/cm³forlinseedoil asmentionedintheliterature[31].

Atallstudiedconcentrations, theyield stressand theelastic modulusat1Hzaremuchhigherinthecaseofzincwhitebased paints,comparedtoleadwhite.For eachtypeofpigments,they increasewiththevolumefractionofpigments,whichisfullycoher- ent.Theyieldstressandtheelasticmodulusat1Hzvaryinfunction ofthevolumefractionofthepigment()withpowerlaws(c∼^B andG∼^B withBandBpositiveconstants).Agoodcorrelation isobservedbetweentheevolutionoftheelasticmodulusat1Hz andtheoneoftheyieldstressinfunctionofthepigmentconcen- trations.For zincwhitepaints,thetwoexponentsofthepower lawsrepresentingtheelasticmodulusandtheyieldstressvaria- tioninfunctionofthevolumefractionofpigmentareverysimilar (respectivelyof5.6and5.5).Thisisfullyconsistentwithwhathas beendescribedbyMahautetal.[32]forcolloidalsuspensionsys- tems.However,thisisnotwhatwasobservedforleadwhitepaints, wheretheexponentsare4.1and7.3fortheelasticmodulusandthe yieldstressrespectively.Oneexplanationofthisdifferencecanrely

Fig.5. Evolutionofyieldstressinfunctionofvolumefractionofpigmentsforzincwhite(blackdiamonds)andleadwhitepaints(greyrectangles).SEMimagesofthetwo typesofwhitepigmentsusedtopreparetheoilpaintarealsopresented(right).Forcomparison,thepigmentcontent,ofabout40%vol,estimatedinleadwhiteandzincwhite paintsusedbyVanGogh,isindicatedontheﬁgure.Additionally,numericalapplicationshavebeencalculatedforVanGogh’spaints(layerthicknessh=100␮m;widthof brushmarks=0.6mm)withEq.(2)(see4.1)toestimatethelimitstressvaluesofpaintsrequiredinfunctionofthedesiredlevelling(=depthofbrushmarkd):highimpastos (d≥85␮m)orasmoothsurface(d≤5␮m).Theselimityieldstressvalues(respectively120Paand7Pa)havebeenreportedontheﬁgureandtherangesofyieldstress correspondingtohighimpastosandsmoothsurfacesareindicatedasgreyareas.

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Fig.6. Comparisonoftheyieldstressofoilpaintmixturesmadefrom40%volpig- mentand60%vollinseedoil.Eachrectanglerepresentsapaintformulationandits heightrepresentsthemeasuredyieldstress(inPa)oftheformulation.Formulations madeofonepigmentaloneorofthemixtureofawhitepigment(leadwhiteorzinc white)withcobaltbluehavebeenstudied.Thefollowingcolourcodehasbeenused:

whiteforleadwhite,greyforcobaltblueandstripedforzincwhitepaint.Forpaints composedoftwopigments,theproportionofgreyindicatesthevolumicproportion ofcobaltblueinthetotalvolumiccontentofpigmentof40%(1/4,1/8or1/40in volume).

onthepeculiarshapeoftheleadwhitegrains,whichmakethem moredifﬁculttodisperseinoil.IndeedtheSEMobservationsofthe pigments(seeFigs.S1and5)showthattheusedleadwhitewas mainlyconstitutedofhexagonalplateletshapedpigmentsofabout 1–2␮m(hydrocerussitegrains),whereasthezincwhitewascom- posedofmoreisotropicgrainsofsmallersize(<1␮m).Theprecise inﬂuenceofthesizeandshapeofthegrains,aswellasthechemical interactionsbetweenoilandpigments,shouldbeinvestigatedfur- thertoconcludewhetheritcanexplaintherheologicaldifferences betweenleadandzincwhite.

3.2.3. Inﬂuenceofpigmentmixtures

Westudiedtheinfluenceoftheadditionofathirdpigmentin whitepaintsinordertocomparethetwotypesofpaints:thestud- iedformulationsarebasedonVincentVanGogh’scolouredpainted layers,wherewhitepaintsareoftenusedinmixturewithasmall amountofcolouredpigment.Theinfluenceoftheadditionofcobalt blue,abluepigmentoftenusedbyVanGogh,ontherheological propertiesofwhitepaintswasinvestigated.Forthepaintmixture ofzincwhiteandcobaltblue(totalvolumefractionofpigment40%), theadditionofasmallamountofcobaltblue(1%involumeofthe totalpigmentcontent)producesanimportantdecreaseoftheyield stressofthepaint(110Pa)comparetothezincwhitepaintwith- outotherpigments(210Pa)(Fig.6).Thesameevolutionisobserved fortheelasticmodulusat1Hz:itisimportantforzincwhitepaint, butitrapidlydecreaseswhenzincwhiteismixedwithanother pigment.Dissimilarlyfortheleadwhitebasedpaints,theaddi- tionofcobaltbluedoesnotmodifysignificantlytheyieldstress andtheelasticmodulus,evenwhenhigheramountofcobaltblue isadded.Themeasuredyieldstressforleadwhitepaintmixtures remainsofthesameorderofmagnitude(around4–7Pa)whatever thecobaltbluecontent;thesmallvariationsobservedarerelated tothemeasurementprecision.

Alltheseresultspointoutthatthephenomenonprovidingzinc whitepaintswithanimportantyieldstressandelasticmodulus isnotpreservedwhenzincwhiteismixedwithanotherpigment, evenwhenpresent inminoramount.Itsuggeststhatthere isa speciﬁcinteractionbetweenzincwhiteandoilthatplaysamain roleontheobservedrheologicalbehaviourandprovidesanhigher yieldstressandelasticmodulustozincwhitepaintscomparedto leadwhitepaintsatthesamevolumepigmentcontent.

4. Applicationtoartists’paintspropertiesandﬁnish

4.1. Levellingofpaints

Therheologicalcharacterizationofpaintscanbeinterpretedin relationwiththe«finish»of theartwork,thatistosaythefinal visualsurfaceaspectofthepaintingafterdrying,andthuscanhelp forreverseengineeringofmastersrecipes.Thelevellingproperties areofparticularinteresthere.Surfaceforcestendtoproduceflow oftheappliedfilm,smoothingthesurfaceirregularitiesinciden- taltoapplicationbybrushing.Manypublications[33]proposethat yieldbehaviouraffectlevellingprocess.Firstitcauseslevellingto ceasewhenthesurfacetensionstressbecomeslessthantheeffec- tiveyieldstress;anditinfluencesthelowshearviscosity,through remnantsofthestructureresponsiblefortheyieldbehaviour.Smith etal.derivedtheequationsofplanestrainforanelasticsolidin1961 todescribethislevellingprocess[34].Orchardextendeditinterms ofFourierseries,foranyroughsurface.Thegeneralexpressionof theroughnessamplitudeisthen[35]:

a=a0exp

− f

₂_h

1 dt

, (1)

withthewavelength,hthelayerthickness,and,respectively theﬁlmsurfacetensionanditsviscosity.

Thisequationcanbesimpliﬁedconsideringaviscosityanda surfacetensionindependentoftime,andwithapproximationsfor smallorbigthicknesses:onecanthencalculatethemaximumshear stress(leadingtotheyieldvalue).Neglectinggravitycomparedto thesurfacetension,andconsideringsmallamplitudedisturbances (d),andsmallﬁlmthickness(h)[33,34],theauthorsobtain thefollowingexpressionforthemaximumshearstressf:

f= 4³dh

³ (2)

withdthedepth,thebrushstrokesaveragewavelengthandhthe layerthickness,accordingtoFig.7a.findicatesthepaintyieldvalue inducingbrushstrokesofsuchshape.

Latermanytheoreticalorexperimentalfurtherdevelopments attemptedtotakeintoaccountthestressor shearratehistory, theeffectsofthinﬁlmgeometry,theevaporationduringdrying, possiblethixotropy[36],effectofelasticity,etc....In1992,Kris- tiansen,showedfromanexperimentalstudy,thattheOrchardEq.

(2)isstillaccuratewhena/h<0.2.Eley’sreviewrecallsthedifferent publicationsontheestimationoflevellinginpaintindustry[37];

howeverhisconclusionunderlinesthefailureinobtainingageneral predictivemethodusefulinpaintindustry.

Inourcase,theaimistocomparedifferentpaintformulations usedforartintermsoflevellingability.Weneglectgravity,and evaporationeffectisnotrelevantforoilpaint.Moreoverweneglect theviscositytime dependence of ourpaint:it obviously exists, butcanbeneglectedregardingtheaveragevaluesandasamat- ter ofcomparison. We canthus usethe Orchardformula asan estimation oftheaveragebrushmark heightdependingonthe paintyieldstress.Wefocusonlayersandpaintsthatrespectthe limitconditions:smallamplitudedisturbances(d),andsmall film thickness (d).As an example, for h=5␮m, =0.5mm, =25mNm⁻¹(attheinterfaceoil–air)andd=1␮mwhichisthe minimumvalueforavisiblebrushmark,a valueoff=0.12Pais obtained.Thisiseventoolowtobemeasuredinstandardmeasure- ments(usingourequipment).Thisconditionofperfectlevellingis obtainedinthecaseoflowviscosityglazes,closedtoNewtonian fluids,usedbyRenaissancepainterssuchasVanEyckorLeonardo daVinci.Theywereusedasthinlayerssuperimposedtoachieve aperfectfinish[38].Laterpaintersusedbrushstrokestoexpress feelings,movement,orgiveasensationofvolume.

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Fig.7. CasestudyonaVanGogh’spaintingtoevaluateVanGogh’sbrushstrokescharacteristics:(a)Generalrepresentationofthepaintsurface,(b)photographyofLetrain bleu(46cm×50cm,oiloncanvas,LaFaillenumberF398,MuséeRodin,Paris-©C2RMF,E.Lambert)paintedbyVincentVanGoghin1888.Thewhitecrossindicates whereamicrosamplehasbeentakenintheblueskyontheedgeofthepainting,whiletheblackrectangleindicatesthelocalizationoftheareainvestigatedbyroughness measurements;(c)detailoftheareaofthepainting(up)whereaproﬁle,indicatedbyablackarrow,ofroughnessmeasurementhasbeenperformed(bottom).Theroughness measurementallowstogiveanestimationoftheaveragedepthofbrushstrokesdandthedistancebetweenbrushstrokes;(d)opticalmicroscopeimageofthemicrosample takenfromtheblueskyofLetrainbleuandpreparedascross-sectionwherethethicknesslayerhcanbeevaluated.

4.2. VanGogh’suseofwhitepaints

Therheologicalmeasurementshaveshownthatifwecompare leadwhiteandzincwhitepaintat40%volforexample(Fig.5),the yieldstressisabout30timeshigherforzincwhitethanforlead white.Zincwhitepaintispastywhileleadwhitepaintisﬂuid:zinc whiteismoresuitabletoleavebrushmarksvisible.Thisistruefor whitepaintlayersbutalsoforpigmentmixturesinzincwhiteand leadwhitebasedpaint.

Toevaluatetheobtainedbrushstrokes, weappliedEq.(2)to thepaintings“LetrainBleu”producedbyVanGoghin1888while stayingin theSouth ofFrance,inArles (Fig.7b).Microtopogra- phyonthebluecolourofthesky(Fig.7c)indicated anaverage depthofbrushstrokesof85␮mandthedistancebetweenbrush- strokesaround0.6mm.Thethicknesslayerswereestimatedon alargepanelofcross-sectionstakenfromVanGogh’spaintings [17]rangingbetween20 and 600␮mwithanaveragevalueat about100␮m.Thisthicknessisverysimilartotheoneobserved inthecross-sectionstakenfromtheskyofLetrainbleu(Fig.7d).

Wecanestimatetheyieldstressinducingsuchbrushmarks:about 120Pa.Howeverweareclosetothelimitconditionsoftheused approximation: small amplitudedisturbances (d<), and small ﬁlmthickness(h<).Thisexactvaluehastobetakencautiously:

it just gives an estimation and allows to betterﬁgure out the behaviourofthepaintusedbyV.VanGoghinthispainting.

ThisstudyprovidesnewinsightsonthemotivationofVanGogh tousetwodifferentwhitepigments.Inadditiontobetteroptical propertiesinpigmentmixtures,zincwhitewouldmoreeasilyallow highimpastostobeachieved.Thisexplanationwouldbeconsistent withthetrendobservedonasmallcorpusof37crosssectionsmade frommicrosamplesfrom16VanGogh’spaintingsdatedbetween

1886and1890:onthiscorpuszincwhiteisusedmoreoftenonthe surfacelayersthanleadwhite[2].Moreover,theuseofleadwhite ratherthanzincwhiteintheunderlayerswouldbeconsistentwith leadwhiteabilityofdryingfasteranditshighcoveringpower.

5. Conclusion

Therheologicalbehaviouroftwowhitepigmentsbasedpaints hasbeeninvestigated,accordingtoreconstructionsof19thcentury artisticformulations.Asparticulatepastes,theirmacroscopicrhe- ologyisdominatedbytheexistenceofaﬂuid-to-solidtransition.At stressesabovetheso-calledyieldstress,thematerialsﬂowlikevis- cousliquids,whereastheybehavelikesolidsatlowerstresseswith propertiesthatevolveslowlywithtime.Wecouldunderlinethe effectofpaintformulation(pigmentcontentandnaturebutalso oiltreatment)ontherheologicalpropertiesofzincandleadwhite.

Thedifferencesbetweenbothpigmentsarerelatedtotheirchem- icalcompositioninducingdifferentinteractions withoil,aswell astotheirspeciﬁcsizeandshapeofgrains.Theleadwhitegrains areindeedparticularlyanisotropic(“needle”-shapedforcerussite grainsorhexagonalﬂatgrainsinthecaseofhydrocerussite),con- trarytothemoreisotropicgrainsofzincwhite.

Themaindifﬁcultyoftheseexperimentslayinthenatureof thesamples:theyexhibitacomplexbehaviourwithpossibletime dependenteffects.Moreoverthedatainterpretationisalsocompli- cated.Itisnotpossibletopredictbehaviourofpaintformulations afterapplicationwithprecision:onlyanestimationoftheirlevel- lingpropertiescanbeprovided.Thisquestionremainsabigissuein thepaintindustryasmanyotherparametersthantheyieldstress valuewouldhavetobeconsideredespeciallyinthecaseoftime dependentﬂuids.

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Thisrheologicalstudygives usnewclues tounderstandthe artist’spractice.Zincwhiteinduceshigheryieldstressandelas- ticpropertiesthanleadwhite-basedpaints.Thiscanpartlyexplain itsspeciﬁcusebyVanGogh.Manystudiesinartconservationsci- encedealwitholdrecipesreconstructionsincludingaqualitative descriptionofthepainttexture.Toimprovethediscussionsand exchangesbetweenconservators,conservationscientists,rheolo- gistsandindustrialpaintexperts,thepaintﬂowpropertieshave beendescribedmoreprecisely.

Acknowledgements

TheauthorsarepleasedtoacknowledgeFreddyMartinforthe SEMobservationsofpigmentsandMathieuCaillaufortherheo- logicalmeasurementsperformedduringhisinternship.Wealso expressourgratitudetoDr.GuillaumeOvarlezforhiscarefulread- ingofthemanuscriptandhiscommentsandtoThierryMoutard Martinforhisexpertiseonpaintpreparationsandmanyfruitful discussions.WearealsogratefultoNadineLehni,chiefconserva- toroftheMuséeRodin,Paris,forallowingustostudythepainting LeTrainBleu.Lastly,weacknowledgeDr.MarcWalton,seniorsci- entistatNU-ACCESS,forbeingour«nativeEnglishspeaker»tohelp makingthemanuscriptsmoother.

AppendixA. Supplementarydata

Supplementary data associated with this article can be found,intheonlineversion,athttp://dx.doi.org/10.1016/j.colsurfa.

2014.02.055.

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