Photochemical synthesis of a "cage" compound in a microreactor: Rigorous comparison with a batch photoreactor

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Photochemical synthesis of a ”cage” compound in a

microreactor: Rigorous comparison with a batch

photoreactor

Tristan Aillet, Karine Loubiere, Odile Dechy-Cabaret, Laurent E. Prat

To cite this version:

Tristan Aillet, Karine Loubiere, Odile Dechy-Cabaret, Laurent E. Prat.

Photochemical

synthe-sis of a ”cage” compound in a microreactor: Rigorous comparison with a batch photoreactor.

Chemical Engineering and Processing: Process Intensification, Elsevier, 2013, Vol. 64, pp. 38-47.

�10.1016/j.cep.2012.10.017�. �hal-00881067�

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: DOI:10.1016/j.cep.2012.10.017

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Eprints ID: 9908

To cite this version:

Aillet, Tristan and Loubiere, Karine and Dechy-Cabaret, Odile and Prat,

Laurent E. Photochemical synthesis of a “cage” compound in a

microreactor: Rigorous comparison with a batch photoreactor. (2013)

Chemical Engineering and Processing: Process Intensification, Vol. 64 .

pp. 38-47. ISSN 0255-2701

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Photochemical

synthesis

of

a

“cage”

compound

in

a

microreactor:

Rigorous

comparison

with

a

batch

photoreactor

Tristan

Aillet

a,b

_,

_Karine

_Loubiere

a,b,∗

_,

_Odile

_{Dechy-Cabaret}

a,c

_,

_Laurent

_Prat

a,b

a_{UniversitédeToulouse,INPT,ENSIACET,4alléeEmileMonso,BP84234,F-31432Toulouse,France} b_{CNRS,LaboratoiredeGénieChimique(LGCUMR5503),F-31432Toulouse,France}

c_{CNRS,LaboratoiredeChimiedeCoordination(LCCUPR8241),205routedeNarbonne,F-31077Toulouse,France}

Keywords: Flowphotochemistry Microreactor Batchphotoreactor Radiationfield Modeling

a

b

s

t

r

a

c

t

Anintramolecular[2+2]photocycloadditionisperformedinamicrophotoreactor(0.81mL)builtby windingFEPtubingaroundacommerciallyavailablePyreximmersionwellinwhichamediumpressure mercurylampisinserted.Arigorouscomparisonwithabatchphotoreactor(225mL)isproposedby meansofasimplemodelcouplingthereactionkineticswiththemass,momentumandradiativetransfer equations.Thisservesasabasistoexplainwhythechemicalconversionandtheirradiationtimeare respectivelyincreasedandreducedinthemicrophotoreactorrelativetothoseinthebatchphotoreactor. Throughthissimplemodelreaction,somecriteriafortransposingphotochemicalsynthesisfromabatch photoreactortoacontinuousmicrophotoreactoraredefined.

1. Introduction

Photochemistryconcernsthephysicalandchemicalprocesses triggeredbytheabsorptionofphotons.Photochemicalreactions are thusbased on theuseof light (ultra-violet, visible light or sunlight)toprovidetheactivationenergytoinducesynthesisof a targetedmolecule. Whenabsorbinglight, moleculesreachan electronically excited state, where their electronic and nuclear configurationsaredifferentfrom thosein ground state(from a fundamental point of view, these electronic transitions can be describedbymeansofground-stateandexcited-state potential-energyhypersurfacetopology[1]).Thisinducesmajorchangesin thechemicalpropertiesofthemolecules(inparticularreactivity), andoffersthenabroadenedspectrumofpossiblereactionschemes. Inmany cases,usingphotochemistry allowssynthesisroutesto beshortened,andpolycyclicor highlyfunctionalizedstructures tobeobtained,and/ormakesnewproductfamiliesavailablethat aredifficulttoachievewithusualroutes(e.g.byheatingorusing highactivityreagents)[2].Forthesereasons,syntheticorganic pho-tochemistryisanextremelypowerfulmethodfortheconversion of simple substratesinto complex products, openingnew per-spectives,inparticularforthepharmaceuticalindustry[3].Asthe

∗ Correspondingauthorat:CNRS,UniversityofToulouse,LaboratoiredeGénie Chimique(LGCUMR5503),F-31432Toulouse,France.Tel.:+330534323619.

E-mailaddress:Karine.Loubiere@ensiacet.fr(K.Loubiere).

photochemicalsubstrateactivationoftenoccurswithoutadditional reagents,theformation ofby-productsisalsominimized, mak-ingphotochemistryevenmoreattractiveinthemoderncontextof GreenChemistry.Someofthemainapplicationsofphotochemistry arephotopolymerization,photohalogenation, photosulfochlorina-tion, photonitrosation,photooxygenation or photocycloaddition

[2,3]. These photochemical reactions are commonly performed either in batch reactors irradiated from within or in systems includingexternalirradiationusingmultiplelamps(Rayonet-type apparatus)andfallingfilmreactors[1].Despitesomeimpressive large-scaleindustrialapplications(e.g.caprolactamsynthesisfor nylonproduction,vitaminDsynthesis),theindustrialuseof pho-tochemistryisstilllimitedbyconcernsaboutscalabilityoflight sources, efficiency (low selectivity, reactive intermediate com-pounds)andthesafetyofoperations(explosionscausedbyexcess heat).Themajorcauseofthatisconnectedwiththeintroduction andthecontrolofadequateillumination.

Inthelastdecade,microreactiontechnologyhasbeen success-fullydeveloped,usingthefeaturespropertothemicrospace(small amounts offluid, shortmoleculardiffusiondistance,intensified heat and masstransfers, safety)to improvereaction selectivity and yield, particularlywhere by-productsformdue toreaction hot-spots[4].Forphotochemistry,microreactorsofferadditional advantages,namelyhigherspatialilluminationhomogeneityand betterlightpenetrationthroughouttheentirereactordepththan in large-scalereactors. Surprisingly, photochemicalsynthesis in microreactors is rarely encountered in the literature, whereas

Nomenclature

B0 Napierianopticaldensity C concentration(molm−3₎ G sphericalirradiance(Wm−2₎ k kineticconstant(s−1₎

L specificintensity(Wm−2_sr−1₎

LVREA localvolumetricrateofenergyabsorption(Wm−3₎ LVRPA local volumetric rate of photon absorption

(ein-steins−1_m−3₎

P photonic power received in the system (ein-steins−1₎

q radiativeenergyfluxdensity(Wm−2₎ R productivity(mols−1₎

RL radiusoftheexternalreactorwall(m) RW radiusoftheinternalreactorwall(m) r radialdistanceandlocalrateofreaction(m) STY spacetimeyield(molm−3_s−1₎

t time(s) Vr volume(m3) X conversion Greekletters

˛ Napierian molar extinction coefficient (Lmol−1_cm−1₎

1s definedinEq.(24)(m)

ε molarextinctioncoefficient(Lmol−1_cm−1₎  photonicefficiency(molesofproductpermoleof

photonsreceived)

 anglebetween Euand En(rad)  attenuationcoefficient(m−1₎  wavelength(m)

 dynamicviscosity(Pas)  massdensity(kgm−3₎ ˚ quantumyield(–)

 ratioofthedifferentparametersP,,STY,t ˝ solidangle(sr)

microreactionsystemshavebeenexaminedsuccessfullyinawide rangeofapplicationsofanalyticalandorganicchemistry.Mostof theseworksdealwithorganicsynthesisphotoreactionswhere sup-portedcatalystsareinvolved(titaniacoatedchips)[5–7]and,asyet, littleresearchisconcernedwithphotochemicalreactionswithout supportedcatalysts [8–15]. The knownadvantages of microre-actors for photochemistry are mainly the enhancement of the chemicalconversionandselectivity,andthereductionofthe irra-diationtime[16,17].Atpresent,therearenoreportsofattempts tounderstandandmodelsuchresultsfroma classicalchemical engineeringapproachinwhichreactionkineticsandconservation equations(mass,momentum,thermalenergyandradiative trans-fer)arecoupled.Forexample,aninterestingcomparisonbetween abatchRayonetreactorandvariousmicroreactorshasbeen pro-posedrecentlybyShvydkivetal.[18].Thecriteriausedconcern conversionrates(spacetimeyield),reactorgeometry(illuminated areaandvolume)andlamppowerperilluminated area,butno modelingisproposed.

Inkeepingwiththisscientificcontext,thispaperpresentsan application of microreactors for photochemistry. The synthesis ofpentacyclo[5.4.0.02,6_.03,10_.05,9_{]undecane-8,11-dionebyan} intra-molecular [2+2] photocycloaddition was chosen as the model reactionsincethispentacyclic‘cage’compoundcanbeof therapeu-ticinterest[19–21].Moreover,thisreactionofferstheadvantageof havingasimplekineticschemeasthephotochemicalexcitationof thereactantleadstoasinglenon-absorbingproduct.

Theobjectivesofthisworkwere,firstly,toquantifythe ben-efitsofmicroreactorsforperformingthisphotochemicalreaction (especiallywhencomparedtoaconventionalbatchphotoreactor) and, secondly, toidentifythe parameters required for compar-ingphotoreactorperformanceandfortransposingphotochemical reactions from batch to continuous reactors. For this purpose, experimentswereconductedinamicrophotoreactorandinabatch photoreactor.Foreachsystem,theconversionintothecage com-poundwasmeasuredasafunctionofirradiationtimesandreagent concentrations.Basedonradiationtransferandmassbalances,a modelisproposedandsomecriteriaforreactorcomparisonare defined.

2. Materialsandmethods

2.1. Photochemicalreactionandanalyticalmethods

Asdescribedin Fig.1,thephotochemicalreactionundertest was the synthesis of pentacyclo[5.4.0.02,6_.03,10_.05,9 ]undecane-8,11-dione 2 (the ‘cage’ compound) via the intramolecular [2+2]-photocycloaddition of 1,4,4a,8a-tetrahydro-endo-1,4-methanonaphthalene-5,8-dione1.Reagent1waseitherprepared through a Diels–Alder reaction involving cyclopentadiene and 1,4-benzoquinone[22],orpurchaseddirectly(CAS:51175-59-8).

ThereagentsolutioncouldbeformulatedfromtheDiels–Alder compound(174.2gmol−1_{)dilutedinethylacetate.Themaximum} absorptionof theresultingsolutionsoccurredbetween365and 372nm,asshowninFig.2a.At365nm,themolarabsorptivityof reagent1(ε1)wasdeterminedusingaspectrophotometer (Ultra-spec1000PharmaciaBiotech®_{),andfoundtobe}

ε1=61.81Lmol−1cm−1 (1)

Thisparameterisingood agreementwiththemolar extinc-tioncoefficientsfoundintheliteratureforelectronictransitions S0→S1ofthen→*type[1].Inaddition,itisinterestingtonote thatnoabsorptionofthecagecompound2wasobservedat365nm (Fig.2b).

Duringthephotochemicalreaction(i.e.atdifferentirradiation times),samples(0.8mLinthemicroreactor,4mLinthebatch reac-tor)weretakenandstoredinthedarkinarefrigerator.Then,the solventwasremovedunderreducedpressureandconversionwas calculatedby1_HNMRinCDCl

3.

2.2. Descriptionofthemicrophotoreactorandbatchphotoreactor AsillustratedinFig.3a,themicroreactorimplementedfor pho-tochemistry wasconstructedby winding tubing (508mm inner diameter,1587.5mmouterdiameter,4mlength)inasinglepass aroundacommerciallyavailableimmersionwellmadeofPyrex (50mm outer diameter, 200mm length). Fluorinated Ethylene Propylene(FEP)waschosenasthetubingmaterialbecauseitis veryversatile,solventresistantandhasexcellentUV-transmission properties [23]. Tubingwasfixedto thewellusing stickytape andwascoveredbyaluminumfoiltopreventtheescapeofUV radiation.

Aluminumfoilwasalsousedtoprotectthesupplysyringeand theinletandoutletsectionsofthetubingfromUVlight,thus ensur-ingthatthephotochemicalreactiontookplaceonlyinthetubing sectionwoundaroundthewell,andthattheirradiationtime(tirrad) couldbeassumedequaltotheresidencetime(tS)inthiswound section(4mlong).Thesolutiontobeirradiatedwasfedintothe reactor tubing by a syringe pump (PHD2000 Harvard). Atthe exitofthetubing,sampleswerecollectedafterasteadystatehad beenreached(threetimestheresidencetime).Theflowrate(Q)

Fig.1. Photochemicalreactionundertest(synthesisofacagecompoundviaanintramolecular[2+2]-photocycloaddition). 0 0.5 1 1.5 2 300 350 400 450 500 550 600 Wavelength (nm) Absorbance (-) Absorbance (-) 0 0,5 1 1,5 2 300 350 400 450 500 Wavelength (nm) (a) (b)

Fig.2. Absorptionspectrumwithanopticaldepthof10mmof(a)the1,4,4a,8a-tetrahydro-endo-1,4-methanonaphthalene-5,8-dionecompound(1)inanethylacetate solution(CA0= 0.02 mol L

−1

),and(b)the‘cage’compound(2)inanethylacetatesolution(CA0= 0.02 mol L

−1

).

variedbetween0.8and98mLh−1_{,thuscoveringarangeof} irradi-ationtimesfrom30sto1hdefinedaccordingto:

tirrad=tS=Vr

Q (2)

where Vr isthevolume inthewound tubing section(0.81mL). Considering ethyl acetate as the liquid phase (=894kgm−3_, =0.552mPas),thecorrespondingReynoldsnumbersvariedfrom 1.8to116.

Thelampwasinsertedinside thewell,whichwasequipped withadoublejacketconnectedtoanexternalcoolingunitanda refrigeratingwatercirculator.Thetemperaturewasnotmeasured

directlyinsidethemicrophotoreactor:onlythestabilityofthe tem-perature(8◦_{C)ofthecoolingwatercirculatinginthedoublejacket} waschecked,assumingthatsuchadevicethermallyisolatedthe reactionmixturefromtheheatinglamp.

Thelampwasamercuryvapordischargelamp(medium pres-sureHgBa/Srlamp,125W,HPKHeraeus®_{)havingthedominant} emissionlineat366nm,correspondingtothewavelengthdomain where the absorption of the reactant solution was maximum (Fig.2a).

Forcomparison,thephotochemicalreactionundertestwasalso operatedinaconventionalbatchphotoreactor(Fig.3b)havingthe sameimmersionwellastheoneusedforthemicrophotoreactor.

Table1

Technicalcharacteristicsofthephotoreactors.

Parameters Batchreactor Microreactor Depthoflightpenetration(cm) 0.62 0.0508 Irradiatedareaa_(cm2_{) 300 16}

Irradiatedvolume(cm3_{) 225 0.81}

Irradiatedarea/volumeratio(m2_m−3_{) 1.33 19.75} a_{Calculatedconsideringareactorwithannulargeometry(seeFig.5):S}

irrad=

Vr/1swhere1siscalculatedwithEq.(24).

Table2

Photochemicalreactionstepsandassociatedkineticrate.

Reactionsteps Kineticrate

Activationstep:A−→Ah ∗ _r∗

= (LVRPA),A

Deactivationstep:A∗_{→ A r} d= kd· CA∗

Reaction:A∗_{→ B r}

B= kr· CA∗

Thevolumeoftheirradiatedsolution,Vr,was225mLhere(against 0.81mLforthemicroreactor).Thedepthoftheirradiated solu-tionwas6.2mmforthebatchreactor(annularspacebetweenthe immersionwellouterwallandtheinnerreactorwall)whereasit was508mminthemicroreactor(tubinginnerdiameter).Themain technicalcharacteristicsofthereactorsarelistedinTable1.

3. Theoreticalconsiderations 3.1. Reactionkineticsandmassbalance

Whendealingwithphotochemicalreactions,itisfirstnecessary toevaluatetherateoftheradiationactivationstep.

The mechanism of the present photochemical reaction was three-step kinetics in homogenous phase, as schematically describedinTable2.Arepresentsthenon-excitedreagent1,A* reagent1intheelectronicallyexcitedstateandBthesinglereaction product2,whichisanon-absorbingspecies(at365nm).

Intheactivationstep,theactivatedmoleculeA∗_wasproduced byphotonabsorption;theassociatedratewasthusdirectly pro-portionaltotheradiantenergyabsorbed inthereactorperunit ofvolume.This“useful”energyhasbeencalledthelocal volumet-ricrateofradiant energyabsorption(LVREAinWm−3_)[24],or, preferably,thelocalvolumetricrateofphotonabsorption(LVRPA inmol-photonm−3 _{orineinsteinm}−3_{).Definedatagiven} wave-lengthandforagivenspeciesA,thesetwoparametersarelinked accordingto: (LVRPA),A= 1 Na ·h·c  ·(LVREA),A (3)

Fig.4. Generalparametersusedtodefinetheradiationfield.

wherehisthePlanckconstant(6.6256×10−34_Jsphoton−1_),cthe speedoflight(2.9979×108_ms−1_)andN

atheAvogadronumber (6.023×1023_mol−1_).

Onceproduced,theactivatedspeciesA∗_{eithergavethe} com-poundB(reactionstep)ordisappeared(deactivationstep).Forthe reactionundertest,thedeactivationstepcorrespondedonlytoa returnofthemoleculetothegroundstatebyradiative (phospho-rescence,fluorescence)ornon-radiativedeactivationmechanisms. Notethat,inamoregeneralcase,additionaldeactivation mech-anismsmayalsoexist, inparticulartheonesresultingfromthe transformationofradicalintermediates.Inthiscase,theequation fordeactivationreportedinTable2isthesumofdifferent pro-cesses.

The net balance for the intermediate molecule A* can be expressedas:

dCA∗

dt =r ∗

−rd−rB (4)

Asthelife-timeoftheexcitedstateisveryshortandthesource oflightenergyiscontinuousandmoderate,theassumptionofthe quasi-steadystatefortheintermediatemoleculeA*_{canbeapplied:}

dCA∗

dt ≈0 (5)

Thus,therateofformationofBislinkedtotherateof consump-tionofA(rA=−r∗),suchthat:

rA,=−rB,=−kr·CA∗=−kr·

(LVRPA),A kd+kr

=·(LVRPA),A (6) isthequantumyieldofthereaction,definedastheratiobetween therateof molarproduction ofBandtherateofphotonmolar absorption: = rB r∗  = kr kd+kr (7) wherekrandkdarethekineticconstantsofthephotochemical reac-tionandofthedeactivationreactionrespectively.Eqs.(6)and(7)

showthatthequantumyieldandtheLVRPAdependonthe wave-lengthconsidered,implyingthattherateofrecoveryofAshould berigorouslydefinedforeachwavelength.

The complete modeling of a conventional chemical reactor requiresthemomentum,thermalenergyandmassconservation equationstobesolvedtogetherwiththekineticsequations.Inthe caseofaphotoreactor,theradiationequationmustbeadded[24]. Inthepresentstudy,somesimplificationscanbemadebased onthefollowingassumptions.Firstly,theenergybalancecanbe neglected.Variousexperimentsperformedatdifferent tempera-tures(from8◦_Cto40◦_{C)havesuggestedthatthephotochemical} reactionundertestisnot temperaturesensitive.Inaddition,all theexperimentswereperformedatafixed,controlledtemperature (closeto20◦_C).

Secondly, themass balanceinthecase of photochemistryis directlycoupledwiththeradiationequationbymeansofthe reac-tionrateterm(Eq.(6)).Theconsequenceisthataheterogeneous fieldofconcentrationisinevitablygeneratedinsidethereactordue tophotonabsorptionbythespeciespresent.Nevertheless,this spa-tialnon-uniformityofconcentrationscanbeattenuatedinpresence ofgoodmixingconditions[24].WhenthereactantAisthe sin-gleabsorbingspecies,theimpactonthisnon-uniformityisalso reducedbecauseofthechangeoftheradiationfieldwiththe chem-icalconversion.Thefirstabsorbingzones(i.e.theonescloseto theopticalfaceofthereactor)becomeclearer(lessabsorbing)as theconversionincreases,allowinglighttopenetratefartherinto thedepthofthereactor.Inthisstudy,twomodel caseswillbe considered:

Fig.5.Specificparametersusedtodefinetheradiationfieldinthebatch photore-actorandinthemicrophotoreactor.

-Forthebatchphotoreactor,perfectlymixedbehaviorwitha con-stantvolume.

-Forthemicrophotoreactor,plugflowbehavior.

Undertheseassumptions,itcanbedemonstratedthatthe fol-lowingequationcanbeappliedforthecompoundAinthebatch reactor:

<rA,>= dCA

dt =−·<LVRPA,A> (8) wheretheconcentrationCAofcompoundAisafunctionoftimetin thebatchphotoreactor(asspatialhomogeneityinthewhole reac-torvolumeisassumed),and<LVRPA,A>isthelocalvolumetric rateofphotonabsorptionduetoreagentAaveragedoverthewhole volumeofthebatchphotoreactor.

Itisinteresting toobservethat,inthemicrophotoreactor,in whichplugflowbehaviorisconsidered,anequationidenticalto Eq.(8)canbeobtainedbyreplacingtheaxialpositionxbytime,t, accordingto:

dt=dx

U (9)

whereUisthemeanvelocityofthereactantsolutioninthe microre-actortube.

3.2. Radiationfieldinsidethephotoreactor 3.2.1. Definitions

Let us recall a few definitions. The basic quantity is the monochromaticradiantenergyfluxdensityvector[25,26]:

E q=

Z

4

L(Er, Eu)· Eu ·d˝ (10) where Eu istheunitvectorrelatedtothedirectionofradiation propa-gation, Er thepositionvector,andd˝thesolidangleelementaround thepropagationdirection Eu (Fig.4).L is thespecific intensity, whichrepresentstheradiativeenergyflowperunitoftime,unit

ofsolidangleandunitofsurfacenormaltothepropagation direc-tion.Intheliterature,itisalsocalledradianceorluminance,andis sometimesnotedI_insteadofL.

Hence,thedotproductof Eqand En(theunitvectornormalto receptorsurface)givesthenetradiativeenergyfluxdensitypassing throughthesurfaceofdirection En,whichisexpressedinwattsper unitofreceptorsurface:

q=

Z

4 L(Er, Eu)· Eu ·d˝· En =

Z

4 L(Er, Eu)· Eu · En ·d˝ =

Z

4

L(Er, Eu)·cos·d˝ (11) whereistheanglebetween Euandthenormal En tothesurface considered(Fig.4).

We also define the monochromatic spherical irradiance (or scalarirradiance)astheintegraloverallthedirectionsofthe spe-cificintensityL

G(Er)=

Z

4

L(Er, Eu)·d˝ (12)

Thisphysicalquantityplaysanimportantrolein photochem-istry as, in an element of reactor volume, the monochromatic radiantenergyabsorbedbyacomponentjisgivenby:

LVREA,j=,j·G(r) (13) where,jistheabsorptioncoefficientoftheradiationduetothe speciesj.

3.2.2. Radiationbalanceinafixedcontrolvolume

For a homogeneousand non-emitting mediumin which the radiationattenuationisdueonlytoabsorptionbythemedium(i.e. noornegligiblescatteringeffects),theradiativetransferequation (RTE)iswrittenas[24,27,28]:

E

u·−−→grad(L)=−·L (14) Notethat,inthisform,theRTEisequivalenttothewellknown Lambert’slaw.

Theintegrationof thesimplifiedRTE(Eq.(14))overallsolid angles˝leadstothefollowinggeneralformofthelocalradiation balanceforanon-emitting,homogeneouscontrolvolume[27,29]: div(Eq)=−·G=LVREA (15) 3.2.3. Expressionoftheaveragevolumetricrateofphoton

absorption<LVRPA>

Inthefollowing,wehavechosentoreducetheproblemtoa one-dimensionalannularcylindricalsystem(theangularandaxial symmetryconditionsareverifiedinbothreactors)withradiationin asingledirectionandnormaltothewallsurface(Fig.5).Withthis

convenientsimplification,amathematicalsolutionforexpressing LVRPAcanbedeveloped,asshownbelow.

Theaboveassumptionscanbewrittenmathematicallyas: L(Er, Eu)=L(r)·ı(Eu − Ei) (16) where Eiis the unit vector related to the single direction that coincideswiththeradialaxis.L(r),thespecificmonochromatic intensitydefinedatagivenpositionrandaveragedoverallthe directionsofradiationpropagation(¯L(r)isthusexpressedinwatts persurfaceunit)andıtheDiracfunction(insr−1_{)isdefinedas:}

ı=







Z

˝ ı(Eu − Ei)d˝=1 if _uE= Ei ı(Eu − Ei)=0 if _{u /}E= Ei (17)

WhenthisexpressionforL(Eq.(16))isputintothe expres-sionsforthenetradiationfluxandthesphericalirradiance(Eqs.

(11)–(12)), Eq. (15)becomes (in thecase of a one-dimensional cylindricalcoordinatesystemwithsingle-directionalradiation): ∂(r· ¯G(r))

r·∂r =

∂(r·¯q(r))

r·∂r =−· ¯G(r) (18) where ¯q(r)= ¯G(r)(thedirectionoflightemissionisassumed nor-maltothereceptorsurfaceofthereactor).Thisequationisalso well-knownastheradialmodel[25,30].

istheabsorptioncoefficientofthereactingmixture (includ-ingreagentsandproducts)andisconsideredtobealinearfunction oftheconcentrationoftheabsorbingspecies.Thus[24,30]:

,j=˛,j·Cj (19)

where˛,j is themolarNapierian absorptivityofthe radiation-absorbingspeciesjatagivenwavelength,andCjisthemolar concentrationofthespeciesj.Notethatchemistsgenerallyusethe molarabsorptivityε,jdefinedas:

˛,j=2.303·ε,j (20)

Whenseveralspeciesabsorbradiationinthesystemandwhen moderateconcentrationsareinvolved,theassumptionof absorp-tionadditivitycanbeappliedaccordingto:

=

X

j ˛,j·Cj=

X

j ,j (21)

AstheconcentrationCjchangeswiththechemicalconversion, theLVREA,jwillalsobedependentonthechemicalconversion(Eq.

(15)).

TheintegrationofEq.(18)fromtheirradiatedwallsurfaceof thereactor,Rw(hereequalto25mmforbothreactors,seeFig.5) toaradialpositionrinsidethereactorleadsto:

G(r)=GW· Rw

r ·exp[(−·(r−Rw))] (22) whereGW

 isthemonochromaticsphericalirradiancereceivedat thewallsurfaceofthereactor.NotethatEq.(22)isvalidonlywhen theconcentrationCjisuniforminthecontrolvolume.

Theaveragevolumetricrateofenergyabsorption<LVREA,A> canbecalculatedas:

<LVREA,A>= 1 V

Z

Z

Z

V ,A·G(r)·r·dr·d·dz =G W 
s · ,A  ·(1−exp[−·(RL−Rw)]) (23)

whereasshowninFig.5,RLcorrespondstotheouterradial posi-tionofthereactor(RW+0.62cm forthebatchphotoreactorand RW+508mmforthemicrophotoreactor)and1sisdefinedby: 1s=R 2 L−R2W 2RW (24) InEq.(23),GW

 isexpressedinwattsperunitofsurfaceareabut canalsobeconvertedintoeinsteinperunitoftimeandperunitof surfacearea(GW,photon_ )byusingEq.(3).

3.3. Couplingbetweenradiationfieldandmassbalance

Forthephotochemicalreactionundertest,compoundAisthe onlyabsorbingspeciesandthisleadsto:

,A==˛A·CA and ,A



=1 (25)

Rigorously speaking, a reaction rate equation (Eq. (6))may bewrittenforeachemittedwavelengthatwhichthecompound absorbs,andthustheknowledgeofGW

 and˛,jmayberequired foreachwavelengthconcerned.Theglobalratewouldthenbethe sumofalltherateequations.Withoutlossofaccuracy,wewill considerasinglewavelength,365nm,inthisstudyasthereactant mainlyabsorbsatthiswavelength(Fig.2a)whichcorrespondstoa significantemissionrayofthelamp.Consequently,inthefollowing, theindex“”willnolongerbeattachedtothevariables.

Theconcentration,CA,ofcompoundAcanbeexpressedasa functionofthechemicalconversionX:

CA=CA0·(1−X) (26)

where CA₀ is the concentration of the compound A initially introducedintothereactor(att=0).Finally,thecouplingofthe massbalance(Eq.(8))withtheexpressionoftheaverage volumet-ricrateofphotonabsorption<LVRPA>(Eq.(23))canbeformulated as: CA0 dX dt =−· GW,photon 1s ·(1−exp[−B0·(1−X)]) (27) whereB0istheinitialNapierianopticaldensitydefinedby B0=CA₀·˛A·(RL−Rw) (28)

WhenEq.(27)isintegratedovertime,thefollowingexpression isobtained: CA0·



X+ 1 B0 ·ln

h

1−exp(−B0) 1−exp(−B0·(1−X))

i

=·G W,photon 1s ·t (29) FromEq.(29),itcanbeshownthatcompletemodelingofthe reactorrequires theknowledge of thequantum yield  and of thesphericalirradiancereceivedatthewallsurfaceofthereactor (GW,photon_≈GW,photon

365 ).Generally,thisisdeterminedeitherfrom thelampemissionmodelorfromexperiments(actinometry). 4. Resultsanddiscussion

4.1. Variationofconversionwithconcentrationandirradiation time

Firstly,theeffectoftheinitialconcentrationofthecompoundA (CA0)ontheconversionoftheDiels–Aldercompoundintothe‘cage’

compound (X)wasinvestigated asa functionof theirradiation timesinthemicrophotoreactor(Fig.6a).Asexpected,forafixed irradiationtime,conversiondecreasedwithincreasing concentra-tions.Thisisconsistentwiththeradiativetransfermodelpreviously established(Eq.(22)):foranyradialpositionRw<r<RL,anincrease ofCA₀(i.e.oftheabsorptioncoefficientA)inducesadecreaseofthe exponentialfactorandthusadecreaseofthesphericalirradiance

0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 G / G w C = 0.318 mol/L C = 0.637 mol/L C = 0.955 mol/L r ₋ Rw RL− Rw

Fig.7.Initial(namely,att=0,X=0)lightattenuationprofilesalongthedepthofthe microphotoreactor(inthekey,CcorrespondstoCA0).

(G).Whenconsideringtheinitiallightattenuationalongthereactor depth(deducedfromEq.(22)andrepresentedinFig.7),weclearly observedthatthelightpenetrationwaslowerwhenconcentrated solutionswereinvolved,thusreducingthefractionofthevolume insidethereactorthatwasilluminated.

Fig.6aalsoshowsthat, whatevertheinitialconcentration,a fewminutesweresufficienttoachievehighphotochemical conver-sions.Itisparticularlyinterestingtonotethatthefullconversion (X=100%) was achieved at 1min for the lowest concentration (0.318molL−1_{)andat2minforC}

A0 =0.637 mol L

−1

andCA0=

0.955 mol L−1.

Theseperformancelevelswerecomparedwiththoseobtained inthebatchphotoreactor,thelatterreactorbeingtheconventional deviceforphotochemistry.The criterionchosenfor comparison wastheconservationofthesameorderofmagnitudeoftheinitial opticalNapieriandensitiesB0(andthusofirradianceattenuation profilesinsidethesolution)inbothphotoreactors.Thelight pene-trationdepth(RL−RW)beingdependentonthereactor,theinitial concentrations CA0 thus neededto beadjusted (usingEq. (28))

forexperimentsinthebatchphotoreactor(Table3).Notethatit wasnotpossibletousemoreconcentratedsolutionsinthebatch photoreactorastheywouldhaveinducedtoohighareactant con-sumption.

The variation of theconversion withthe irradiation time is plotted in Fig. 6b for the batch photoreactor. Here too, for a given irradiation time, more concentrated solutions generated smaller conversions. Whatever the concentrations, a minimum of30minirradiationtimewasrequiredtoachieve thefull con-version,comparedwith1or2mininthemicrophotoreactor.For comparisonpurposes,it wasinterestingtoestimatethereactor efficiencyby introducingthe space-time yield(STY), a parame-tercommonly usedbychemists.Itrepresentsthetotalamount ofproduct (cagecompound)per reactorvolumeperirradiation time,as:

STY= CA0·X

tirrad

(30) It was calculated here for a conversion of 90% and an averageinitialconcentration CA₀ in each reactor(0.637molL−1 in the microphotoreactor and 0.0324molL−1 _{in the batch} Table3

InitialconcentrationofDiels–AlderandassociatedopticalNapieriandensityinthe microphotoreactorandinthebatchphotoreactor.

Microphotoreactor Batchphotoreactor

CA0(molL −1_{) B} 0 CA0(molL −1_{) B} 0 0.319 2.3 0.0162 1.4 0.637 4.6 0.0324 2.9 0.955 6.9 0.0485 4.3

photoreactor). In these conditions, STY was found to be equal to 573mmolL−1_min−1 _{in the microphotoreactor and} 2.3mmolL−1_min−1 _{inthebatchphotoreactor.Fromthis,wecan} concludethatusingamicrophotoreactorsignificantlyimprovedthe space-timeyieldsor,inotherwords,decreasedtheminimal irradi-ationtimerequiredtoachievecompleteconversionwhileworking withmoreconcentratedsolutions.Inagreementwiththeresults alreadyreportedintheliterature[4–18],this firstfindingoffers promisingperspectivesforimplementingphotochemicalsynthesis inmicroreactors.Nevertheless,someunderlyingquestionsmustbe addressed:Howcansuchresultsbeexplained?Whichcriteriashould bedefinedtorigorouslycompareperformanceindifferent photochem-ical reactorsand/or totransposeresults frombatch to continuous microphotoreactors?

4.2. Dataanalysisbasedonthemodelcouplingreactionkinetics, conservationandradiationtransferequations

4.2.1. Determinationoftheproduct·GW,photon

Inkeepingwiththequestionsposedabove,asimplifiedmodel (Eq.(29))haspreviouslybeenproposedtolinktheradiation trans-fer balance (1D annular cylindrical system, homogeneous and non-emittingmedium,negligiblescatteringeffect,single absorb-ing species,monochromatic and single-directionallight source) andmassbalances(three-stepkinetics,perfectlymixed,plugflow behavior).Theapplicationofthismodeltotheexperimentaldata supposesthatthequantumyieldofthereaction()andthe irra-dianceatthewallsurfaceofthereactor(GW,photon_)areknown.As thiswasnotthecase,theproduct·GW,photon_wasdirectly deter-minedbyfittingEq.(29)withexperimentalmeasurements.This ledto·GW,photon_{=0.029 einstein s}−1

m−2_forthebatch pho-toreactorandto·GW,photon_{=0.404 einstein s}−1 _m−2 _forthe microphotoreactor.Theratioofthesetwoquantitieswascloseto 0.07,andwasmainlyexplainedbytheratiobetweentheirradiated surfacesinthemicroreactorandinthebatchreactor(Table1),as shownbelow:

Sirrad,microreactor Sirrad,batch

= 16

300≈0.053 (31)

The deviation could be attributed to some approximations (calculation of the irradiated surface in the microphotoreactor, reflectionsneglectedandassumptionofamonochromatic emis-sion)and/ortoapossiblechangeofthequantumyield(therange ofconcentrationsbeingsignificantlydifferentinthetwo photore-actors).

Lastly,itisinterestingtonotethatthismodelingdescribesthe variationofexperimentalconversionwithtimewell,whateverthe initialconcentrationandreactor(Fig.6).

4.2.2. Definitionofsomeconsistentratiosforreactorcomparison purposes

Toexplainthedifferencesobservedintermsofirradiationtime betweenthetworeactors,letusintroduceseveralsupplementary physicalparameters.

•ThefirstoneisthepowerP(expressedineinsteins−1_)defined accordingto:

P=Vr··G W,photon

1s (32)

Itcorrespondstothemaximumpowerthancanbereceived inthephotoreactor,i.e.whenallthephotonsareabsorbedby thereactionmixture(notransmittance).AsdefinedbyEq.(32), this value alsointegrates the quantum yield of the reaction, which gives the ratio betweenthe rate of molar production ofBandtherateofthephotonmolarabsorption.Finally,this

powermakestheconnectionbetweenthelightemittedbythe lampand thedesign of thereactor or, in otherwords, is an expressionof themannerin which thereactoris exposed to thelamp.

•Thesecondparameterofgreatimportanceisthephotonic effi-ciency.Notedas,dependingX_{ontheconversionX,itrepresents} theefficiencyofthereactor,thatistosaytheratiobetweenthe numberofmolesofcompoundBproducedandthenumberof molesofphotonsreceived:

X= CA0·Vr·X P·tX

irrad

(33) Expressingt_irradwithEq.(29)andPwithEq.(32),weobtain:

X₌ X

(X+(1/B0)·ln[(1−exp(−B0))/(1−exp(−B0·(1−X)))]) (34) IfX_{→1,allthephotonsreceivedinthesystemareusedto} reachthedesiredconversion.Incontrast,ifX_{→0,theefficiency} ofthereactorislow,meaningthatmanyofthephotonsreceived inthe reactorarenot absorbed (i.e.are transmittedover the outersideofthereactor)becauseofalowopticaldensityinthe reactor.Consideringthisdefinition,itisclearthatthe photore-actorwilloperatebetterwhenhighopticaldensityisinvolved. Varyingbetween0and1,thisphotonicefficiencymustnotbe confusedwiththequantumyield,whichisaparameter intrin-sictothephotochemicalmechanismandrepresentstheamount ofabsorbed photonsnecessary toconverta given amount of reactantmolecules(Eq.(7)).Incontrast,thephotonicefficiency definedbyEquation34dealsonlywiththeradiationattenuation profileinthemedium.

•Thethirdparameteristheproductivity,which representsthe molarquantityproducedperunitof irradiationtime andalso dependsontheconversionX,as:

RX₌ CA0·Vr·X tX irrad =P·X =P· X (X+(1/B0)·ln[1−exp(−B0)/1−exp(−B0·(1−X))]) (35) •Itisalsointerestingtodescribethespace-timeyield(STY)

previ-ouslyintroduced(Eq.(30))asfollows:

STYX=CA0·X tX irrad = P Vr X = P Vr · X (X+(1/B0)·ln[(1−exp(−B0))/(1−exp(−B0·(1−X)))]) (36)

Tocomparetheperformance inthetworeactors,five crite-riaaredefined,correspondingtotheratiosbetweenthepower received,thephotonicefficiency,theproductivity,the irradia-tiontime,andthespace-timeyieldinthemicroreactorandin thebatchreactor.TheyarebroughttogetherinTable4.

FromTable4,wecanobservethat:

-theratios related tothe powerreceivedand to thephotonic efficiencyaretheonesgoverningtheothers,asX

R =f(P,X), X

t =g(P,X)andXSTY=h(P,X),

-thepowerratioP lets uscompare theexposuretothelight sourcein thetwo photoreactors and depends directlyonthe geometryofthephotoreactors.IfP→1,thephotoreactorsare exposedtothesametotalamountofradiantenergy,

-thephotonicefficiencyX

compares,foragivenconversion,the radiationfieldinthetwophotoreactors.IfX

→1,theirradiance attenuationalongthereactordepthisthesameinboth photore-actors.

4.2.3. Comparisonofthetworeactorsbasedonthecalculationsof thepreviousratios

AlltheparametersinvolvedinEq.(32)beingknown,thepower ratio,P,canbecalculated.Itisfoundtobe0.73,meaningthatthe microphotoreactorasdesignedinthepresentexperimentsreceives fewerphotonsthanthebatchreactor.Thisresultisnotsurprising becausethetubingconstitutingthemicrophotoreactorwaswound aroundthestraightsectionoftheimmersionwell,andonlyover afewcentimetersinheight(Fig.3a)whereas,forthebatch pho-toreactor,thesolutionvolumewasalsolocatedunderandontop ofthelamp(Fig.3b).Moreover,becauseofthetubingcurvature, someoftherayscouldbereflected.Theimportantideatonoteis thatthisratiocanbeeasilyimprovedbywindingthetubingaround theentireheightoftheimmersionwellasalreadydonebyHook etal.[13].

ConcerningthephotonicefficiencyratioX

,Fig.8presentsthe iso-curvesofthisratioforaconversionof90%,andtheirchange withtheinitialNapierianopticaldensities(B0)ineach photoreac-tor.Itisconvenienttodefinethreemainareasonthisgraph: - AreaA:thephotonicefficiencyinthebatchphotoreactorisbetter

here(0.90

 <1).Inotherwords,thefractionof“wasted”photons (i.e.transmittedoutsidethereactor)islowerinthebatch pho-toreactorthaninthemicrophotoreactor,duetoahigheroptical density.

-AreaC:thisistheoppositeofareaA.

-Area B: this area corresponds to the part of Fig. 8 between theiso-curves1.05 and 0.95,implying that theefficienciesin thereactorsareapproximatelythesame(|(microreactor−batch)/ Table4

Ratiodefinedtocomparethemicrophotoreactorandbatchphotoreactor.

Ratioof Definitions

PowerreceivedP P=Pmicroreactor

Pbatch PhotonicefficiencyX X = X microreactor X batch = F X batch FX microreactor ProductivityRX X R= RX microreactor RX batch = P· X IrradiationtimetX X t = tX microreactor tX batch = 1 X ·P· Vr,micro Vr,batch· C_A0,micro C_A0,batch

Space-timeyield(STY) X STY=P· X · Vr,batch Vr,micro WithFX microreactor= X+ 1 B0,microln



1−exp(−B0,micro) 1−exp(−B0,micro·(1−X))



FX batch= X+ 1 B0,batchln



1−exp(−B0,batch) 1−exp(−B0,batch·(1−X))



Fig.8. Iso-curvesofthephotonicefficiencyratiotoreachaconversionof90%(0,90 ).

Theblacksquaresymbolscorrespondtoexperimentalphotonicefficiencyratios.

batch|<0.05).Inthiscase,thefractionof“wasted”photonsis equivalentinbothphotoreactors(thelightattenuationprofiles remainidenticalwhatevertheconversion).

TheexperimentalefficiencyratiosarealsoreportedinFig.8

(blacksquares).Itcanbeobservedthat,dependingontheinitial opticaldensity,thedifferentareasarecoveredbytheexperimental conditions.

ConcerningtheproductivityratioX

R,theycanbeeither cal-culated using the product P·X (Table 4)or estimated from experimentaldataas:

0.9 R =

(CA0·Vr·0.9/t_irrad0.9 )_micro (CA0·Vr·0.9/t0.9_irrad)_batch

(37)

Table5reportsthecalculatedandexperimental(inbrackets) productivityratios.Itisclearthattheinitialopticaldensity(B0) hasadrastic impactontheproductivityratiovalue.Thislatter parameterB0isthusthekeyparametertomaintainconstantwhen transposingaphotochemicalsynthesisfromabatchreactortoa continuous(micro)reactor.

Itisimportanttokeep inmindthatthisfindingistrueonly becausethephotochemical reactionschemeunder testisA→B withasingleabsorbingspeciesA.Formorecomplexreactions(in particularwhenthereareseveralstronglyabsorbingspeciesinthe medium),itwillbenecessarytoaccountfortheroleof hydrody-namics(mixing)onthespatialandtimedistributionsoftheactive speciesinthedifferentlightlevelareasexistinginthereactor.For this,thepresentmodelmaybeextendedbyconsidering,inthe pre-viousequations,theabsorptioncoefficientofeachspecies,the two-(orthree-)dimensionalcharacteroftheflow,andthecomplete reactionalscheme.

Table5

Experimentalandcalculated(inbrackets)productivityratios.

B0batch 1.43 2.85 4.28 B0microreactor 2.29 0.9(1.0) 0.56(0.64) 0.45(0.54) 4.6 1.5(1.39) 0.83(0.90) 0.68(0.75) 6.90 1.73(1.99) 0.98(1.17) 0.82(0.91)

Regardingtheirradiationtimeratio0.9

t (ataconversionXof 90%),theexperimentalratios(deducedfromFig.6)arefoundto varybetween0.044and0.1.Suchafindingcanbedirectlyexplained bythemodelproposed,inwhich0.9

t dependsonP,0.9 ,reactor volumesandinitialconcentrations.LetusconsiderapowerratioP of0.73andarepresentativephotonicefficiency0.9

 of1(implying identicalinitialopticaldensity).Thetimeratioisthenexpressedas (Table4): X t = 1 1×0.73· Vr,micro Vr,batch ·CA0,micro CA0,batch = 1 1×0.73· Vr,micro Vr,batch ·˛A·(RL−RW)batch ˛A·(RL−RW)micro (38)

Consideringthegeometricalcharacteristicsofthetworeactors, 0.9

t is found to be equal to 0.06, which is in perfect agree-mentwiththeexperimentaltimeratios.Thisdemonstratesthat theimprovementinirradiationtimespreviouslyobservedinthe microphotoreactorwasmainlyduetothedifferenceinthenumber ofabsorbingmolecules(Vr×CA0).

ItisinterestingtoobservethatthevaluesoftheSTYratios,X STY, aremainlycontrolledbythereactorvolumeratios.Again,ifapower ratioPof0.73andarepresentativephotonicefficiency0.9 of1 areassumed,Eq.(36)leadstoX

STY≈200,whichagreesperfectly withtheexperimentalvaluesdiscussedinSection4.1.

4.3. Synthesisandfirstconclusions

Fromthesimplemodelproposed,twomaincriteriahavebeen identifiedfordesigningandcomparingphotoreactors:thepower receivedinthesystem(P)andthephotonicefficiency(X_).These twoparametersshouldbeequalifequivalentproductivityistobe obtainedinbothphotoreactors,thephotonicefficiencybeingthe parameterofinterestfromanindustrialpointofview.

Finally,fromthesefindings,somesuggestionscanbemadefor improvingperformanceinthemicrophotoreactor:

-thetubelengthwoundaroundtheimmersionwellcaneasilybe increasedsoastoreceivemaximumradiationfromthesource. In thisway,thepowerreceivedin themicrophotoreactorcan belargerthaninaconventionalbatchimmersionphotoreactor (P>1);

-keepingthephotonicefficiencyidenticalinbothreactorsimplies workingwithhigher concentrations inthe microphotoreactor (smaller optical length). Asit caninduce somelimitations in termsofcompoundsolubilityinthesolvent,thenumberoftubing passesaroundtheimmersionwellcanbeincreasedoraslightly largerinnerdiameteroftubingused.

5. Conclusion

Inconclusion,thesimpleandeasy-to-construct microphotore-actorproposedcanensurethecontinuousphotochemicalsynthesis of a pentacyclic‘cage’ compound, and reach full conversionof highly concentratedsolutionin a shortirradiationtime. In this study,acomparisonhasbeenmadebetweenthe microphotore-actor and a conventional batch photoreactor by introducing a simplified model combiningreaction kinetics, conservationand radiativetransferequations.Thisstudypointsoutthattwomain criteriaareessentialfordesigningandcomparingphotoreactors: thepowerreceivedinthesystem(P)andthephotonicefficiency (X_{).Keepingthesetwocriteriaconstantinbothphotoreactorswill} inevitablyleadtoequivalentproductivity.Theapproachpresented inthispaperisonlyvalidforthecaseofanA→Breactionscheme,

withasingleabsorbingspeciesA.Themixingeffectisthusreduced, enablingsomesimplificationstobeused.

Aspecificresearcheffortshouldbemadeinthefuturetopropose amorecomplexmodelabletotakeaccountoftheimpactofthe shortdiffusiondistancesinthemicrophotoreactorwhenseveral speciesareabsorbinginthemedium.Inthesecases,theeffectof mixingbecomesacriticalparametertoensureefficientspatialand timedistributionsoftheactivespeciesinthedifferentlightlevel areasexistinginthereactor.

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