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SheddingLightonMarinePollution 165

SheddingLightonMarinePollution

BrittanyHarrisChasePeasleeKylePerkins

CarrollCollegeHelena,MT

Advisor:PhilipRose

MassiveamountsofplasticwastehavebeenaccumulatingintheGreatPacificGarbageGyreandareposingathreattothemarineenvironment.Sincelittleisknownaboutthedegradationofplasticsinthismarinesetting,weadoptthegoalofmodelingthephotodegradationofacommonplastic,polyethylene,inseawater.Plasticintheoceanisexposedtoultraviolet(UV)lightfromthesun,whichcausesphotodegradation,anaturalsourceofplastic

position.

Wedeveloptwomodelstodescribetherateofphotodegradationofpoly-ethylenefloatinginseawater,aLow-TransmittanceofLightModel(LTM)andaHigh-TransmittanceofLightModel(HTM)UsingtheconstantrateofUVirradianceandtheaveragebonddissociationenergyofcarbon-carbonsinglebonds(C–C),wecalculatethemasslostperunitoftime.

Theresultsfromourmodelsarerealistic.TheHTMpredictsthatarect-angularprismofpolyethylene1×1×2cmweighing1.87gwilllose1.27gofmassinoneyear;theLTMpredictsthatahollowspherewiththickness0.0315cm,radius5cm,andweight9.145g,partiallysubmergedinlow-transmittancewater,willlose0.190gofmassintheyear.Thedesignofourmodelsallowsustomodelothershs,adjusttheintensityofUVlight,andrealisticallypredictthephotodegradationofpolyethylene.

Introduction

Theaccumulationofplasticdebrisinouroceansisquicklycomingtolightasoneofthemostprevalentanddevastatingthreatstothemarineenvironment.The“GreatPacificOceanGarbagePatch”isoneofmanyar-easofwind-currentconvergencewheremassiveamountsofdebriscollectandstew.The“garbage”isnotprimarilyintheformofbottlesandbags,

TheUMAPJournal31(2)(2010)165–174.?cCopyright2010byCOMAP,Inc.s.Permissiontomakedigitalorhardcopiesofpartorallofthisworkfor alorclassroomuseisgrantedwithoutfeeprovidedthatcopiesarenotmadeordistributedforprofitorcommercialadvantageandthatcopiesbearthisnotice. ingwithcreditispermitted,butcopyrightsforcomponentsofthisworkownedbyothersthanCOMAPmustbehonored.Tocopyotherwise,torepublish,topostonservers,ortoredistributetolistsrequirespriorpermissionfromCOMAP.

166TheUMAPJournal31.2(2010)

butratherastinyparticlesreferredtoasneustonicplastics.Theseneustonicplasticsaretheproductsofdegradationofpost-consumerandindustrialwastesandmayposegreatriskformarinelife.Thenatureofthedegrada-tionofplasticshasthus eanimportanementinthestudyofthisenvironmentalcatastrophe.

Wefocusspecificallyonthephotolyticdegradationofpolyethyleneplas-ticaccumulatinginthegyre.Weconsider

theUVradiationreachingthesurfaceoftheocean;

theenergyrequiredtobreakthebondsinpolyethylene;and

physicalconsiderationsconcerningbuoyancy,mass,andsurfaceareaoftheplasticparticles.

DescriptionoftheProblem

Weconsiderthedegradationoffloatingpolyethylenefragmentsbypho-tolyticdegradation.Thefragmentsareconsideredtobehollowspherespartiallyfilledwithseawater,torepresentcommonpost-consumerwastecontainers.Thefragmentsarepartiallysubmergedinwaterwitheitherloworhightransmittanceoflight.High-transmittancewatercanusetheentireeffectivesurfaceareaofthefragmenttomodeldegradation,whileforfragmentsinlow-transmittancewateronlytheportionofthefragmentabovewaterwillbesusceptibletophotolyticdegradation[Ivanhoff,Jerlov,andWaterman1961].

Ultravioletlightisassumedtohitthefragmentorthogonallytotheplaneoftheocean,therebyexposingatwo-dimensionalsurfaceareaofeffectiveareac.Werelatectotheradiusrofthefragment;themassmofthefragmentdependsonboth.Thegoalistomodeltheserelationshipsovertimetodescribethelossofmassexperiencedbyapolyethylenefragment.

PhotolyticDegradationofPolyethylene

Polyethyleneisapolymerconsistingoflongchainsofthemonomerethylene[CareyandSundberg2007].Therearetwotypesofbondspresentinpolyethylene:carbon-carbonsinglebonds(CC)andcarbon-hydrogensinglebonds(CH)[Leeming1973].Polyethylenehasthestructure

?(CH2?CH2)n?

wherenisthenumberofmonomersinthechain.

Photodegradationisaprocessbywhichchemicalbondsarebrokenwhenstruckbylight[CareyandSundberg2007;Okabe1978].Thelightmustcarryenoughenergytocleaveabond,whichcanbeestimatedusing

SheddingLightonMarinePollution 167

theaveragebonddissociationenergy[Leeming1973].Theequation

E=hc,

λ

wherehisPlanck’sconstantandcisthespeedoflight,canbeusedtofindtheminimumwavelengthλoflightthatcarriesenoughenergytobreakthebond[Skoog,Holler,andCrouch2007].Forexample,theenergytocleaveaCCsinglebondis5.778×10?19kg·m2/s2.Usingh=6.626×10?34kg·m2/sandc=3×108m/s,wefindλ344nm,awavelengthintheultraviolet.

Thus,whenpolyethyleneisexposedtoultravioletlight(UV)withawavelengthof344nm,CCsinglebondsarecleavedandfreeradicalsareformedthatreactquicklywithO2toformperoxyradicals.Theneithertheperoxyradicalscontinueachainreactionofradicalformationorelsetwofreeradicalsreacttoterminatethechainreaction[CareyandSundberg2007;McNaughtandWilkinson2007;TrozzoloandWinslow1967].ThepathwayoffreeradicalchainreactionsandterminationreactionscanbeseeninFigure1.

Photooxidativereactionmechanism:

RH+UV?→R·

R·+O2?→ROO

ROO+R·H?→ROOH+R·

Photooxidationterminationreactions:R·+R·?→RR

ROO·+R·?→ROOR

Figure1.Reactionsofperoxyradicals.

ThecleavageofCCsinglebondsbreaksthepolyethyleneintofrag-mentsandthepolyethylenelosesmass.TherateofdegradationcanbeestimatedbyassumingthateverytimeaCCbondiscleavedbyUVlight,amonomerisremovedfromtheoriginalmassofpolyethylene.Therateat

whichtheCCbondscanbecleaveddependsontheamountofUVlightemittedbythesun,whichis0.0005watts/m2J/s·m2[Karam2005].SincetheenergytobreakaCCbondis5.778×10?19JandthereareAvogadro’snumber(6.022×1023)moleculesinamole,wecanfindviaunitconversiontherateofphotodegradationofpolyethylene:

168 TheUMAPJournal 31.2(2010)

1CCbond

5.778×10?19J

× 0.0005J

1s·1cm2

× 1molepolyethylene

6.022×1023CCbonds

×28gmonomerpolyethylene

1molepolyethylene

4.02×10?8gmonomerpolyethylene

= s·cm2 .

GeneralAssumptions

Sincemechanicaldegradationduetotorqueonplasticisminimalduetothesmallsizeofplasticparticles[Tipler2004],andcollidingplasticparticlesarerareduetolorticledensity[Moore,Lattin,andZellers2005],inourmodelweneglectmechanicaldegradation.

Polyethyleneparticlesfloatinseawater,sincemedium-densitypolyethy-lene’sdensityis0.937g/ml[ChevronPhillipsChemicalCompanyn.d.]andaveragedensityof35pptsalineseawaterat15?Cis1.0255g/ml.Weneglectwatercurrents.

ThesourceofUVlightisaconstantaverageatsealevelinthePacificNorthwest[Karam2005].

PolyethyleneinthemodeldoesnotcontainUVstabilizersandismediumdensity.

PolyethyleneiscomposedofethylenemonomersandtheaveragebonddissociationenergyforCCsinglebondsisusedtopredicttheenergyneededtocleavetheCCbonds[Leeming1973].

OnlytheportionsoftheplasticfragmentsthatareperpendiculartotheUVlightaresubjecttophotolyticdegradation.

OnlytheeffectivesurfaceareaabovewatercanreceiveUVlight.

ThephotolyticcleavageofCCbondinthemodelisafastforwardreaction(Krxn?1)andthereversereactionisveryslow.Immediayafterthebondiscleaved,thefreeradicalformsandisquenchedbyanyoftheterminationreactionsthatalsohaveaKrxnb?1.Wealsoassumed100%quantumefficiencyofthesereactions.

High-TransmittanceModel

Thismodelconsidersthedegradationofasquareprismofpolyethyleneonaflatsurfaceonlandorinwaterwithaveryhightransmittanceoflight.OneofthefacesoftheprismfacesdirectlyperpendiculartotheUV

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SheddingLightonMarinePollution 169

lightsource.LetK1therateofdegradationfromthecalculationonp.168,

4.02×10?8(gmonomerpolyethylene)/s·cm2.Then

y? x? t

0 0 0

K1dtdxdy=K1txy,

duetothesimplegeometry.Theresultisasimplelinearmodelofdegra-dationbasedontimeandarea.

Considerasquareprismwiththedimensionsof1cm×1cm×2cm,withanarea1cm×1cmexposedtoUVradiation.Ithasaninitialmassof1.87g[ChevronPhillipsChemicalCompanyn.d.].AfteroneyearofUVexposure,

abouttwo-thirds1.27gofpolyethyleneislostasaresultofphotolyticdegradation.

Low-TransmittanceModel

AprimaryfactorindescribingtheamountofUVlightthatafragmentofplasticabsorbsistheeffectivesurfacearerpendiculartodirectsun-light.SincetheNorthPacificGyreisacollectionoffloatingdebris,weuseArchimedes’principletorelatethebuoyancyofapieceofplastictoitseffec-tivesurfacearea.Forsimplicity,weneglecttheeffectofairinthecontaineronbuoyancy.Archimedes’principlestatesthat“thebuoyantforceonasubmergedobjectisequaltotheweightofthefluidthatisdisplacedbythatobject”[Hodanbosi1996].Inaddition,sincetheplasticisinkineticequilib-riumintheverticaldirection,itsbuoyantforcemustbeequalinmagnitudetoitsweight:

Fbuoyant=Wplastic=Mplasticg=Mwaterdisplacedg=Vplasticsubmergeddwaterg,

whereMismass,Wisweight,Visvolume,disdensity,andgisaccelerationduetogravity.Thus,wehave

Mplastic=Vplasticsubmergeddwater,

whoseright-handsidecanbecalculatedfromthetripleintegral

π? 2π? h

d·ρ2sinφdρdθdφ,

x 0 r?h

wherehisthethicknessoftheplasticandxistheanglefromthezenithtothepointonthesphere’ssurfacewherethespherecontactsthewaterlevel(seeFigure2).Settingthisintegralequaltothetotalmassoftheplastic,wecanfindx.TrigonometryrelatestheradiusrofthesphereandtheanglextotheeffectivesurfaceareacofthesphereexposedperpendicularlytoUVrays,asindicatedinFigure2.

170 TheUMAPJournal 31.2(2010)

Figure2.Geometryofasphereattheocean’ssurface.

!

AsshowninFigure2,theeffectivesolarradiusis

re=rcos

π?x.

2

Bysubtractingthevolumesoftwoconcentricsphereswith?r=h,thenmultiplyingbythedensityloftheplastic,weget

"# $

M= 4πr3

# $%

— 4π(r?h)3 l.

3 3

Wesolveforr: & # $

πh2± π2h4?πh 4πh3?m

r= 3 l .

2πh

WedefineaconstantCbasedontherelationshipbetweenthemass(ingrams)ofplasticandthetotalbondenergies(injoules)withinthatmass,basedonthemolarmassandtheaveragebondenergyofpolyethylene:

C≡1J×1mole×28g=8.046×10?5g/J.

348000J 1mole

Ultravioletlightisthesourceofenergyinthismodel.AtrueempiricalvaluefortheamountU(J/cm2·yr)wouldneedtobemeasuredonsite.The

SheddingLightonMarinePollution 171

productUChasunitsofg/cm2·yr.Tosolveforatotalchangeingramsoveraspecifictimeandarea,weintegratethetermwithrespecttotimeandthenwithrespecttoarea:

t? 2π? re

e

UC·rdrdθdt=?m=UCr2πt.

0 0 0

Subtractingfromtheinitialmass,wehave

e

Mfinal=m?UVCr2πt.

UsingtheLow-TransmittanceModel,considerahollowspherewiththickness0.0315cm,radius5.00cm,andinitialmass9.145g.AfteroneyearofUVexposure,thelossinmassis0.190gofpolyethylene.TherateofdegradationcanbevisualizedinFigure3.

Figure3.Degradationofmassofpolyethylenesphereovertime.

ComparisonsandLimitations

WedeveloptwomodelstodeterminemasslosttophotodegradationfromapieceofpolyethyleneplasticexposedtoUVlight.TheHigh-Transmit-tanceModelmodelsthepolyethyleneasarectangularprism;theLow-TransmittanceModelmodelstheexposedeffectivesurfaceareaofahol-lowsphereofaparticularthickness,partiallysubmerged.Dependingontheconditionsofthewater(densityandtransmittance)andtheshoftheobject,themodelscanbemodifiedtodescribephotodegradationofpolyethyleneinmanyothershsinhigh-orlow-transmittancewater.

Toincreasetheaccuracyofourmodels,afewmainpointsneedaddi-tionalresearchandrefinement:

172 TheUMAPJournal 31.2(2010)

ThevalueUusedforirradianceofUVlightintheNorthPacificOceanneedstobeverified.

Mechanicaldegradationwillalsotakeplaceandshouldbeincluded.

Themodelsdonotdescribethefactthatparticlestendtoconvergeonasimilarsizearound35mm[YamashitaandTanimura2007].

ManypolyethyleneproductscontainUVstabilizersthatincreasethelongevityoftheplasticbyinhibitingthefree-radicalchainreaction[CareyandSundberg2007].

Polyethylenecanvaryindensity.Ourmodelusesmedium-densitypoly-ethylene(MDPE).

Plasticsarenotjustontheoceansurfacebutalsoatdepthsupto100ft.

Polyethylene,althoughverycommon,isnottheonlyplasticintheNorthPacificGyre.

DiscussionofImpacts

OurmodelsdescribetherateatwhichUVlightbreaksdownpolyethy-lene.Theprocessisslow,andthereisinconclusiveevidenceastowhetherplasticseverdegradeentirelyintheGyre.Plasticsarethusaprevalentlong-termenvironmentalantagonist.Possibleecologiceffectsoftheaccu-mulationofmassiveamountsofplasticinthePacificOceanGyreincludeingestionofplasticparticlesbymarinelife,thedisturbanceofthetrans-mittanceoflightbelowthesurfaceofthewater(whiayaffectmanyanisms’abilitytosynthesizeenergyfromphotosynthesis),andthedis-tributionofhydrophobicpollutants.Ourmodelrelatestotheingestionofplasticparticlesbymarinelifebecauseitpredictsthemassoffragmentsatagiventimeandmarineanismsmayconfuseplasticfragmentsthataresimilarinsizetotheirnormalfoodsource.

Contributingtothegrowingproblemofplasticpollutionintheoceanisthelackofernmentalregulationonpollutionbycruiseships.Dur-

ingaone-weektrip,atypicalcruiseshipproduces50tonsofgarbage.Regulationsaretrickythough,becauseinternationalwatersdonothavewell-definedenvironmentalauthoritystructures,andmonitoringismini-mal[StateEnvironmentalResourceCenter2010].Strongerregulationsandmonitoringsystemsarerequiredtodecreasetheimpactofpollutionbycruiseships.

Land-basedsourcescontributeupto80%ofmarinedebris,65%ofwhichisfrompost-consumerplasticsthatwereimproperlydisposedof[AlgalitaMarineResearchFoundation2009].Thismeansthattheplasticsarelit-tered,notjustthattheyarenotrecycled.Manystateshavelawsagainst

SheddingLightonMarinePollution 173

littering,butmonitoringeffortsneedtobeimproved.Educationandmoni-toringprogramsmaybeexpensive,butthecostwouldlikelybesmallwhencomparedtothepotentialforenvironmentalprotection.

Conclusion

roposetworealisticmodelsforthephotodegradationofpolyethy-lene.Themodelisforasolidchunkofpolyethyleneeitheronlandorinwaterwith100%transmittanceoflight.Thesecondmodelismorecomplexandconsidersapartiallysubmergedhollowsphereofpolyethylenethatisdegradedonlyovertheeffectivesurfacearea.Ourmodelscanaccuraydescribedegradationofpartiallydegradedorintactplasticproducts,sincetheinitialphysicalproperties(size,mass,etc.)ofpolyethylenecanbevar-iedinbothmodels.Theeaseofcustomizationandthoroughconsiderationofrealisticvariablesmakeourmodelssuitableforuse.

References

AlgalitaMarineResearchFoundation.2009.Frequentlyaskedquestions(FAQs). .

Anthoni,J.Floor.2006.Thechemicalcompositionofseawater.http:

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Carey,FrancisA.,andRichardJSundberg.2007.AdvancedanicChem-istry:PartA:StructureandMechanisms.5thed.NewYork:Springer.

ChevronPhillipsChemicalCompany.n.d.Blownfilm..

/bl/polyethylene/en-us/Pages/BlownFilm.aspx .

Hodanbosi,Carol.1996.Buoyancy:ArchimedesPrinciple.

buoy_Archimedes.html.

Ivanhoff,Alexandre,NilsJerlov,andTalbotH.Wat