An evaluation of thermodynamic models for the prediction of drug and drug-like molecule solubility in organic solvents

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_{Bouillot, Baptiste and Teychené, Sébastien and}

Biscans, Béatrice (2011) An evaluation of thermodynamic models for the

prediction of drug and drug-like molecule solubility in organic solvents.

Fluid Phase Equilibria, vol. 309 (n°1). pp. 36-52. ISSN 0378-3812



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An

evaluation

of

thermodynamic

models

for

the

prediction

of

drug

and

drug-like

molecule

solubility

in

organic

solvents

Baptiste

Bouillot

∗

_,

_Sébastien

_Teychené,

_Béatrice

_Biscans

LaboratoiredeGénieChimique,UMRCNRS5503,BP84234CampusINP-ENSIACET,4alléeEmileMonso,31030ToulouseCedex4,France

a

b

s

t

r

a

c

t

Predictionofsolubilityofactivepharmaceuticalingredients(API)indifferentsolventsisoneofthemain issueforcrystallizationprocessdesign.Experimentaldeterminationisnotalwayspossiblebecauseof thesmallamountofproductavailableintheearlystagesofadrugdevelopment.Thus,oneinteresting perspectiveistheuseofthermodynamicmodels,whichareusuallyemployedforpredictingtheactivity coefficientsincaseofVapour–LiquidequilibriaorLiquid–Liquidequilibria(VLEorLLE).Thechoiceofthe bestthermodynamicmodelforSolid–Liquidequilibria(SLE)isnotaneasytaskasmostofthemarenot meantparticularlyforthis.Inthispaper,severalmodelsaretestedforthesolubilitypredictionoffive drugsordrug-likemolecules:Ibuprofen,Acetaminophen,Benzoicacid,Salicylicacidand4-aminobenzoic acid,andanothermolecule,anthracene,arathersimplemolecule.Theperformanceofpredictive (UNI-FAC,UNIFACmod.,COSMO-SAC)andsemi-predictive(NRTL-SAC)modelsarecomparedanddiscussed accordingtothefunctionalgroupsofthemoleculesandtheselectedsolvents.Moreover,themodelerrors causedbysolidstatepropertyuncertaintiesaretakenintoaccount.Theseerrorsareindeednot negli-giblewhenaccuratequantitativepredictionswanttobeperformed.ItwasfoundthatUNIFACmodels givethebestresultsandcouldbeanusefulmethodforrapidsolubilityestimationsofanAPIinvarious solvents.Thismodelachievestheorderofmagnitudeoftheexperimentalsolubilityandcanpredictin whichsolventsthedrugwillbeverysoluble,solubleornotsoluble.Inaddition,predictionsobtained withNRTL-SACmodelarealsoingoodagreementwiththeexperiments,butinthatcasetherelevance oftheresultsisstronglydependentonthemodelparametersregressedfromsolubilitydatainsingle andmixedsolvents.However,thisisaveryinterestingmodelforquickestimationslikeUNIFACmodels. Finally,COSMO-SACneedsmoredevelopmentstoincreaseitsaccuracyespeciallywhenhydrogen bond-ingisinvolved.Inthatcase,thepredictedsolubilityisalwaysoverestimatedfromtwotothreeorders ofmagnitude.Consideringtheuseofthemostaccurateequilibriumequationinvolvingthe1Cpterm, nobenefitswerefoundfordrugpredictionsasthemodelsarestilltooinaccurate.However,infunction ofthemoleculesandtheirsolidthermodynamicproperties,the1Cptermcanbeneglectedandwillnot haveagreatimpactontheresults.

1. Introduction

Solubilityofsolidcompoundsinsolventsisobviouslyoneofthe mostfundamentalphysicochemicalproperties,particularlyuseful ina widevarietyofphenomenarelevanttobiological, pharma-ceutical,environmentalandotherorganic,physicalandanalytical chemistry, and engineering sciences. From a simple thermody-namicpoint ofview,solubilityis thefugacityequalitybetween thesolidstateandtheliquidstateofthesolutemolecule.In prac-tice, it is the maximum amount of the crystallineform of the compoundthatcanbedissolvedinagivenvolumeofsolventat

∗ Correspondingauthor.

E-mailaddress:baptiste.bouillot@ensiacet.fr(B.Bouillot).

a given temperature and pressure. This stateis theexpression oftheGibbsfreeenergyofmixing,whichisthecombinationof twocontributions.Theenthalpiccontributionwhichreflectsthe solute–solute and solute–solventinteractions; and theentropic contributionwhichtakesintoaccountthemolecularsizeandthe potentialfor non-randomdistributionof moleculesin the mix-ture.Then,themolecularsizeandthepotentialfornon-random distributionarealsoimportant.Fromapracticalpointofview, sol-ubilityhasa considerableinfluenceonthechoiceofsolventfor performingpolymorphism,saltandco-crystalscreeninganditis thekeyparameterfortheprocessdesignofanewdrugby crys-tallization,asitwilldeterminetheamountofcoolingrequiredto yieldagivenamountofproductandwillinfactdetermineifcooling willprovideareasonableproductyieldandthusdefinethe crys-tallizationprocessitself(cooling,evaporation,orantisolvent).In

addition,attheearlystagesofanewdrugmoleculedevelopment, smallamountofproduct(typicallylessthan5mg)isavailable,so classicalsolubilitymethodscannotbeusedsincetheyareproduct consumingandareneitherrapidnorcosteffective.Toovercome theseissues,high-throughputsolubility-screeningprotocolshave beendevelopedbasedonsystemsusingeitherrobots[1]ordroplet microfluidic[2].Allthesemethodsrelyonkineticdetermination ofdissolutionandre-crystallizationsteps.Theprocessof dissolu-tionofacrystallinecompoundintoasolventgenerallyshowsan asymptoticprofile[3]:astheconcentrationofthecompoundin solutionincreases,theprocessbecomesprogressivelyslower,and saturationistheoreticallyneverreached.Inaddition,polymorphic phasetransitionmayoccurduringtheseexperiments,leadingto misinterpretationoftheresults.

Evenwhenproductsareavailable,theexperimental determina-tionofsolubilitymustbepreparedandcompletedbypreliminary calculations.Indeed,in classicalsealedflaskmethods,saturated solutionsarepreparedwithanexcessofsolidatagiven temper-ature.Thesuspensionisthenfiltratedorcentrifugedtoensurea solutioncompletelyfreefromundissolvedsolute.First, bytheir nature,this traditional solubilitymethodis timeconsuming. In addition,thefiltrationorcentrifugationstepsareoftenperformed at a lower temperature than the saturationexperiments, what entailsashiftinsolubilityvalues.

Indeed,experimentalmethodsofsolubilitymeasurementsare timeconsuming,expensiveandoftenhavetechnicalproblems,in spiteoftheobtainedvaluesvaryinginthedegreeofaccuracyand precision.Toguidetheseexperimentsandtolimit misinterpreta-tion,thermodynamicmodellingofSolid–LiquidEquilibrium(SLE), usingaminimumofexperimentaldata,wouldbeofagreatvalue. BasedontheactualSLEthermodynamics,aquestionarises:canthe existingmodelsbeusedasguidefordesigningsolubility experi-ments?[4]showedthattheoriginalUNIFACmodelcouldpredict SLE.But,theresultswereaccurateonlyforrestrictedcompounds. [5]discussedthelimitsoftheUNIFACmodeland theequilibria equationsusedforSLE,butdidnotfocusonthetemperature depen-denceorcomparewithothermodels.[6]showedthatCOSMO-SAC isaninterestingmodeltocalculateapriorisolubilities,butitis notveryaccurateforSLE.Inaddition,thesepapersdidnot investi-gateneitherthecompleteequilibriumequationnortheinfluence oftemperatureonsolubilitypredictions.[7]usedNRTL-SACforSLE predictionandfounditpromising,butdidnotcomparedtheresults toamuchmoremodels.Morerecently,[8]comparedUNIFACmodel toCOSMO-RSmodelforsomeorganiccompounds.

The main objective of this paper is to test and analyze existingpredictive(UNIFAC,UNIFACmod.,COSMO-SAC)and semi-predictive(NRTL-SAC)thermodynamicmodelsforthepredictionof solubilityofsixcompounds(fivedrugsordrug-likemoleculesand onehydrocarbon)inseveralsolvents.Fourclassicdrugswere cho-senbecauseofthelargenumberofexperimentalsolubilitydataand ofthedifferentchemicalgroups(Ibuprofen,Acetaminophen, Ben-zoicacid,andSalicylicacid).Tocompletethisset,4-aminobenzoic acidwasalsochosengivenitsaminegroup,andanthracene,aquite simplemolecule(onlyACHgroups).

Inthis work,thethermodynamicmodelswerechosenbased ontheirvariousapproaches,andtheirabilitytobeusedwithor withoutexperimentaldata.UNIFACanditsmodificationsaregroup contributionmethods.Theyonlyrequirebinaryinteraction param-eters betweenthefunctional groups. Thesemodels relyonthe useofaspecificdatabaseofgroup–groupinteractionparameters. Whentheseparametersarenotavailable(formoleculescontaining cyclicSorNforinstance),thesemodelscannotbeused. COSMO-SAC,isbasedonquantummechanicsandrequiresprofilesofthe chargedensityaroundthestudiedmolecules(called-profile).The challengeisthedeterminationofthe“good”-profilewhichtakes intoaccounttherightconformationsofthemoleculeinthe

solu-tion.NRTL-SAC isbased onpolymerNRTL andtobeused,four parametersrepresentingthebehaviourofthemoleculeshavetobe calculatedfromexperimentaldataregression.Oncethese param-etershavebeencalculatedforonemolecule,theymaybeusedfor anyothersolubilitypredictionsinanysolvent.Thatiswhythere isnoneedtoregresseachtime,asinthecaseofmostthe semi-predictivemodelslikeUNIQUACorWilson.

Thesefourmodelswillbecomparedanddiscussedregarding solubilitypredictionatseveraltemperatures.Inaddition,the rela-tiveimportanceofthepuresolidstateproperties(i.e.themelting temperature,melting enthalpyandtheheat capacity difference betweenthesupercooledliquidandthesolid)onthe thermody-namicmodellingisdiscussed.

2. Theory

2.1. Equilibriumequation

Phaseequilibriaaredescribedbytheequalityofchemical poten-tials,,ineachphase.Thegoverningequationofsolubilityofthe compoundinagivensolventiswrittenasfollows:

S=_Sat (1)

Thesuperscript‘S’denotesthesolidphase,andthesuperscript‘Sat’ thesaturatedsolution.Thechemicalpotentialofthesoluteinthe saturatedsolutionis:

Sat=0+RTln( SatxSat) (2)

where0 _{isthechemicalpotentialinthereferencestate,Tthe}

temperature,and theactivitycoefficient.Theactivityofthesolute (a= x)inthesolventisobtainedbycombiningEqs.1and2: ln( Sat_xSat₎₌ S−0 RT = gS_−g0 RT = 1gm RT (3)

where1gmisthechangeofpartialmolarGibbsenergyofthesolute

fromasolidstatetothereferencestateatconstanttemperatureand pressure.Thislastequationgivesarelationshipbetweensolubility andactivitycoefficients,whichcanfinallybewrittenas[9]: ln( Sat_xSat₎₌ 1Hm(Tm) R



₁ Tm −1 T



−1Cp(Tm) R

h

ln



Tm T



−Tm T +1

i

(4) where1Hmisthemeltingenthalpy,Tm,themeltingtemperature

and1Cpthedifferencebetweentheheatcapacityofthe

super-cooledmeltandtheheatcapacityofthesolid.Inpractice,thislast termcanbeverydifficulttomeasureespeciallywhensublimation, decomposition[10]orparallelreactionoccursduringmelting,and isoftenneglectedbecauseitisusuallythoughtthatitscontribution isnegligible.InthatcaseEq.(4)issimplifiedasfollows:

ln( SatxSat)= 1Hm(Tm) R



₁ Tm −1 T



(5) 2.2. Groupcontributionmodels(classicandmodifiedUNIFAC)

UNIFACmethod,forUNIQUACfunctionalgroupactivity coef-ficient [11],is basedontheUNIQUAC model. Themain ideaof thisapproachisaseparationoftheactivitycoefficientofthepure compoundintotwoparts:

ln =ln C_+ln R ₍₆₎

C_{isthecombinatorialterm.Itrepresentstheentropic}

contribu-tiontotheactivitycoefficientwhichtakesintoaccounttheshape andsizeofthemolecules.This C _{dependsonthemolefraction}

Waalsarea(ri)andvolume(qi)(thesuperscript‘i’designatesthe compound): ln C i =ln 8i xi +5qiln i 8i +li−8i xi

X

j xj 5 rj−qj

− rj−1

(7) R_{istheresidualpartwhichrepresentsthecontributionofinter}

andintramolecularinteractions(enthalpiccontribution).Itisasum oftheactivitycoefficientsofthefunctionalgroupsweightedby theirnumberinsolution.

ln R i =

X

k

v

(i) k

h

lnŴk−Ŵ(i)_k

i

(8) where

v

_kand

v

i

karethenumberofgroupsofkindkinthemixture

andincomponenti.ŴkandŴikare,respectively,theresidual

activ-itycoefficientofgroupkinthemixtureandinasolutionofpure componenti.Theydependontheareaandsegmentfractionthe compoundsandonadjustablebinaryinteractionparametersamn

(theinteractionsbetweenthefunctionalgroups)thatareregressed usuallyfromVLEexperimentaldata:

lnŴk=Qk

"

1−ln

!

X

m 2m9mk

#

−

X

m 2m9km/

X

n 2n9nm

%

(9) with: 9mn=exp



−amn T



(10) InUNIFACmod.(Dortmund),by[12],amodifiedversionof UNI-FAC,issupposedtotakeabetteraccountofthetemperaturein theresidualactivitycontribution.Thenewcombinatorialtermand interactionparameterarewrittenas,respectively:

ln C i =1−ln



₈ i xi



−5qi



1−8i i +ln



8i i



(11) and 9mn=exp



−amn+bmnT+cmnT 2 T



(12) UNIFACandmodifiedUNIFACarefrequentlyusedfortheprediction ofVapor-LiquidandLiquid-Liquidequilibriaforsimplemolecules. Thesemodelscanbeappliedtoallmoleculesprovidingthatthe binaryinteractionparametersexist,whichisnotalwaysthecase. Moreover,theconformationandisomerismofmoleculesarenot considered.

2.3. Segmentactivitycoefficientmodels 2.3.1. COSMO-SAC

COSMO-SACisbasedonCOSMO-RSmodel[13,14].First pub-lished by Lin and Sandler [15],this model is a combination of aquantumchemicaltreatmentofsolutesandsolventswith sta-tisticalthermodynamics procedurefor thedeterminationofthe molecularsurfaceinteractions.

TheCOSMO-SACmodelisbasedonthecalculationofthe sol-vationfree energy1G*sol _{whichdefines thefree energychange}

comparingtoanidealsolutionatconstanttemperatureand pres-sure,whenthesolutemoleculesareintroducedintothesolvent.In COSMO-basedmodels,thistermisdividedintotwoparts.First,the solutechargesareturnedoff,anditsmoleculesareinsertedinto aperfect conductor(withaninfinitedielectricconstant



).This firststepgivesthecavitationformationfreeenergy,1G*cav_,which

dependsonthemoleculespecificdimensionandrepresentsthe entropiccontributionoftheactivitycoefficient.Whenthecharges

areturnedon(thesolventbecomesarealsolvent),thefreeenergy ofrestoringthecharges,1G*res_{,correspondstotheenthalpic}

con-tribution.Combining these two steps,theactivitycoefficient is expressedas:

ln i=ln C+

1G∗res

i/S −1G∗resi/i

RT (13)

Tocalculatetherestoringfreeenergy,a-profileofeachmolecule isneeded.Thisprofilecorrespondstotheprobabilityoffindinga surfaceofthemoleculewithachargedensity.Theyarecomputed fromquantumchemicalsimulations.Oncetheyhavebeen calcu-lated,themoleculesaredividedintosegments.Theseconceptual segmentsareportionsofthemoleculesurfacewiththesamecharge density.Theequationfortheactivitycoefficientisthenwritten: ln i=ni

X

m

pi(m)[lnŴS(s) −lnŴi(m)] + _iC (14)

whereŴs(m)andŴi(m)aretheactivitycoefficientsofsegmentm

insolutionandinpureliquid,respectively.InCOSMO-SACmodel, theactivitycoefficientisobtainedbysummingthecontributions ofeachsegment.

The -profiles used in this work were taken from Mullins database [6,16]. Unlike other group-contribution methods, this modelisnotstrictlyapair-wiseadditiveone,sincethe-profiles takeintoaccountthegeometryofmoleculesandhydrogen bond-ing. As the -profiles take into account the geometry of the molecules,eachmoleculeanditsconformationhaveitsownprofile [16].

2.3.2. NRTL-SAC

NRTL-SAC model [17] is based on the original NRTL (Non-RandomTwo-Liquid)[18]andpolymerNRTL[19].TheNRTL-SAC modelcharacterizesthemoleculesintermsofpre-defined concep-tualsegments.Thesesegmentsaccountfortheinteractionsofeach moleculeinthesolution.[17]havedefinedfourtypesofconceptual segments:hydrophobicX,repulsiveY−_{andattractiveY}+_polar,and

hydrophilicZ.LikeinUNIFAC,theNRTL-SACmodelcomputesthe activitycoefficientforcomponentifromthecombinatorialterm C

andtheresidualterm R_{(Eq.(6)).Thecombinatorialtermisthen}

calculatedfromtheFlory–Hugginsapproximationfortheentropy ofmixing: ln _iC=ln8i xi +1−_ri

X

j 8j rj (15) whereriand8iare,respectively,thetotalsegmentnumberand

thesegmentmolefractionofcomponenti.

Theresidualterm R _{iscalculatedfromthelocalcomposition}

(lc)interactioncontribution[19]appliedtoeachsegment: ln _iR=ln Ilc=

X

k rk,I

h

lnŴlc_k −lnŴlc,i_k

i

(16)

Thesegment–segmentinteractionparametersandtheconceptual segmentvaluesofsolventsweredeterminedbytheregressionof experimentalvapor–liquidandliquid–liquidequilibriumdata[17]. Thesegmentvaluesforasoluteareobtainedbytheregressionof solubilitydatainatleastfoursolvents:onehydrophilic(i.e.water), onepolarattractor(i.e.alcohol),onepolardonor(i.e.ketone),and onehydrophobic(i.e.n-alkane).As suggestedby[17],it isalso possibletoestimatepuresolidpropertiesusingEq.(4)or(5). How-ever,inthisstudy,inordertocomparethemodelperformances withtheother,wechosetouseexperimentalsolidstateproperties, sincetheyareavailableintheliteratureandareeasilyaccessible experimentally.Oncethesegmentvaluesofthesoluteareobtained, theycanbeusedtopredictsolubilityinothersolventsorsolvent mixtures.

2.4. Howtheerrorsonthethermodynamicpropertiesimpactthe modelspredictions?

AsthesemodelsareusedwiththeSLEequation,thesolidstate propertiesandtheexperimentaluncertaintieshaveanimpacton theparameterdeterminationormodelprediction.Indeed,andas showninthenextsection,measurementsofthethermodynamic propertiesof thesolidsarescarcelyaccurateandtoinvestigate themodelperformances,theirexperimentaluncertaintieshaveto betakenintoaccount.Thus,thesolidstateproperties,1Hm,Tm

and1Cp,aredefinedbymeanvalues withstandard deviations.

Using Eq.(4), there arethree parameters(two forEq. (5)).The influenceoftheexperimentaluncertaintiesonsolubility predic-tionisevaluatedbyusingaclassicMonteCarlomethod.Solubility predictionsareperformedbychoosingrandomlyvectorsofmean valueandstandarddeviationcorrespondingtotheexperimental data,anddescribeditbyaGaussianlaw.Then,thepredicted sol-ubilitystandarddeviationiscalculated(aboutathousandrandom simulations).

3. Experimentalsolubilityandpurecompoundproperties 3.1. Referencedrugs

Inthis paper,MainlyformIofacetylp-aminophenol (parac-etamol),2-(p-isobutylphenyl)propionicacid(ibuprofen),benzoic acid, and2-hydroxybenzoic acid(salicylicacid) werechosenas modeldrugs.Thesemoleculeswerechosenmainlybecauseofa significantamountofsolubilityexperimentaldataavailableinthe literature[20–32]andtheycontainvarioususualfunctionalgroups (OH, COOH, NH, NH2).To complete this solubility database,

4-aminobenzoicacidwasconsideredbecauseofitsstructure(amine group)despitethereisfewdataavailable[31–34],andanthracene becauseofitssimple structure(ACHfunctionalgroups)andthe manysolubilitydataavailable[35–39]althoughitisnota drug. ThemoleculesstructuresareshowninFig.1.

3.2. Experimental

Inthisstudy,inspiteoftheexperimentalresultsbeingtaken from the literature, some data were missing. The solubility of ibuprofeninoctanolandheptane,paracetamolinheptaneat30◦_C

weremeasured.Then,themeltingtemperatureandenthalpyof ibuprofen,paracetamol,salicylicacidandbenzoicacidwere mea-sured.Combiningwiththeliteraturedata,thegoalwastohave meanvaluesandstandarddeviationfortheseparameters.

3.2.1. Materials

Salicylic and benzoic acid were bought at Fisher Scientific (>99.5%),IbuprofenatBASF(Ibuprofen25>98.5%),and paraceta-molatSigma–Aldrich(>98%).Heptaneandoctanolwereboughtat AnalaRNORMAPUR(>99%).Theywereusedwithoutfurther purifi-cation.

Fig.1. (a)Ibuprofen,(b)paracetamol,(c)salicylicacid,(d)benzoicacid,(e) 4-aminobenzoicacidand(f)anthracene.

3.2.2. Determinationofthethermodynamicpropertiesofthe solids

Thethermodynamicpropertiesofthesolidsweredeterminedby DifferentialScanningCalorimetry(ThermalAnalysisQ2000DSC). Themeasuringmethodwasa1◦_{C perminuteramp from}

ambi-enttemperatureto110◦_C,220◦_C,210◦_Cand165◦_{Cforibuprofen,}

paracetamol,salicylicacidandbenzoicacid,respectively.

3.2.3. Solubilitymeasurements

Solubilitymeasurementswerecarriedoutinwaterwith physi-calmixturesofenantiomersbytheanalyticalshake-flaskmethod, usingconstant-temperaturejacketedglasscells.Aconstant tem-peratureof30◦_C(±0.1◦_{C)wasmaintainedwithacirculatingwater}

bath.Thewayofpreparingthesaturated solutionswasslightly modifiedcomparedtotheclassicalmethod.Here,solubilitywas determinedbyaddingweighedquantitiesofpowdermixturetoa knownvolumeofdistilledwater,untilcrystalscannotbedissolved anymore.Smallamountsofsolid(about20mg)wereaddedeach timeandnoadditionwasperformedbeforethesolutionwasclear. Whentheequilibriumwasreached,solutionswerestirredfor24h. Theuncertaintyofsolubilitydetermination,1S,islowerthan 5%.

4. Results

4.1. Experimentalsolubilityandpurecompoundproperties

Concerning thethermodynamic properties ofthe solids,the experimentalresultsofthisworkandfoundintheliteratureare showninFig.2,andthemeanvaluesandstandarddeviationare presentedinTable1.

Table1

Meanvaluesandstandarddeviationofmeltingtemperatures,enthalpiesand1Cpofibuprofen,paracetamol,salicylicacid,benzoicacid,anthraceneand4-aminobenzoic

acidfromDSCexperiments(exceptthelasttwo)anddatatakenfromtheliterature[8,21,22,25,40–53].

Compound 1Hm(J/mol) Tm(K) 1Cp(J/(molK))

Ibuprofen[8,21,47,53] 25203.9(1577) 347.88(0.65) 48.8

Paracetamol[22,43,45–47,49,50] 27470.6(1720.3) 442.1(0.47) 87.4

Salicylicacid[25,47] 24626.12(2652.4) 431.37(0.12) None

Benzoicacid[40–42,44,48,51,52] 17350.34(774.7) 395.17(0.29) 58.43(0.81)

Anthracene[47,52] 28790(585.1) 489.18(0.89) 6.28

Fig.2.Meltingenthalpyof(a)ibuprofen,(b)paracetamol,(c)salicylicacidand(d)benzoicacidasafunctionofthemeltingtemperature.

Theexperimentalsolubilitydataobtainedinthisworkandfrom theliteratureare givenin Fig.3.The experiment errorsonthe solubilityarefrom1%to4%.

These solubility data will be used to test qualitatively and quantitativelythethermodynamicmodelsaccuracy.Thechosen criterionchosetoqualitativelyevaluatethemodelsisthe preserva-tionofthesolubilityrankingofanAPIinvarioussolvents(Table2). Thisscaleisdefined,inthiswork,asanorderedlistofsolvents fromthesolventinwhichtheAPIistheleastsolubletomost sol-uble.Quantitatively,themodelaccuracyisevaluatedbythemean squareerrorbetweenthemodelpredictionandtheexperimental molefractionsolubility.Thesensitivityofthemodelspredictionto thesolidstateproperties(1Hm,Tmand1Cp)havealsobeentaken

intoaccount.

4.2. OriginalUNIFACandmodifiedUNIFAC

Themeansquarerelativeerrorsobtainedforthesolubility pre-dictionusingUNIFACandUNIFACmodifiedforallthesolutesand solvents tested are reportedin Table 3. The experimentaldata usedarethesameasinFig.3.Foreachsolubilityprediction, stan-darddeviationwillbecomputedusingaMonteCarlomethodas explainedpreviously.Thesemeanrelativeerrorshavebeen calcu-latedusingthefollowingequation:

mse=1 n n

X

i=1



xi predicted−xi experimental xi experimental



2

Themeansquarerelativeerrors(mse)obtainedrangefrom0.07to 26.62forUNIFACandfrom0.137to322forUNIFACmod.Some pre-dictionsinparticularsolventsinducedhighmsevalues,sothatthe obtainednumbersdonottrulyrepresentthequalityofthe mod-els.For example,theupperpartoftherangesdecreasesto6.79 and18.04withoutchloroform.Despitetherelativegoodresults obtainedinthecaseofibuprofen,benzoicacidoranthracene,it canbestatedthatUNIFACseemsnotabletopredictquantitatively thesolubility.But,itisreallyinterestingtocomparethesolubility predictedordersofmagnitudetotheexperimental,andinthisway tocheckifthemethodsgivegoodapproximationsornot.

In addition, thepredictions obtainedat lower temperatures (20–25◦_{C)aremuchbetterthanthoseobtainedathigher}

tempera-tures.TheoriginalUNIFACsolubilitypredictionsoftheconsidered compoundsasafunctionoftheexperimentalaregiveninFig.4.The behaviourobservedforUNIFACmod.isroughlythesame.Inthis paper,weusethetermUNIFACtodiscussaboutboththese mod-els.Inthisfigure,foronesoluteinonesolvent,itcanbeobserved thatthemorethetemperatureincreases,theless thepredicted solubilityisaccurate.Inaddition,thetemperaturedependenceof thebinaryparametersisintroducedinUNIFAC,byapolynomial ij=aijT2+bijT+cij.Evenifthisapproachgivesgoodresultsforsmall

moleculesandforVLE,itcannotrepresentthecomplexityofthe evolution ofinteractions andvolumetric properties (densityfor example)withtemperature.

UNIFACisapair-wiseadditivemodel,thusthetemperature evo-lutionofthespecificinteractions(likehydrogenbonds)cannotbe trulyrepresented.Moreover,evenifthebinaryinteraction

param-Table2

Experimentalsolubilitylogarithmrankingat30◦_{Candordersofmagnitude(insolubilitylogarithm)foribuprofen,paracetamol,salicylicacidandbenzoicacidinvarious}

organicsolvents.

Ibuprofen Paracetamol

Solvent Orderofmagnitude Solvent Orderofmagnitude

Heptane [−3;−2] Dichloromethane [−9;−8]

Cyclohexane [−2;−1.5] Ethylacetate [−6;−5]

Ethanol [−1.5;−1] Acetonitrile [−5;−4]

Toluene Dioxane

Ethylacetate Chloroform

Isopropanol Heptanol [−4;−3]

Acetone Methylethylketone

Octanol [−1;−0.5] Acetone Chloroform Butanol Propanol [−3;−2] Ethanol Methanol Dimethylsulfoxide [−1]

Benzoicacid Salicylicacid

Solvent Orderofmagnitude Solvent Orderofmagnitude

Hexane [−5;−4] Cyclohexane [−8;−7]

Cyclohexane Hexane

Heptane Chloroform [−7;−6]

Acetonitrile [−3;−2] Carbontetrachloride [−6;−5]

Carontetrachloride Xylene

Benzene Acetonitrile [−4;−3]

Heptanol [−2;−1.5] Aceticacid [−3;−2]

Acetone Methanol [−2;−1.5]

Octanol Ethylacetate

Isopropanol Ethanol

Butanol Octanol

N-Methylpyrrolidone [−1.5;−1] Acetone

Dioxane Ethylmethylketone

Table3

PredictionerrorsofUNIFAC,COSMO-SACandNRTL-SACforibuprofen,paracetamol,benzoicacidandsalicylicacidusingEqs.(4)and5,usingsolubilitydatainTable2..

Compound Model MSerrorEq.(5) Meanstandarddeviation MSerrorEq.(4)

Ibuprofen UNIFAC 0.07 11% 0.104

UNIFACmod. 0.137 15% 0.079

COSMO-SAC 1.150 8% 1.307

NRTL-SAClit. 0.201 12% 0.276

NRTL-SACthiswork1 0.202 10% –

NRTL-SACthiswork2 0.165 13% –

Paracetamol UNIFAC 2.306 31% 58.67

UNIFACmod. 1.165 30% 3.780(0.754b₎

COSMO-SAC 25.187 19% 309(166b₎

NRTL-SAClit. 0.367 26% 0.509

NRTL-SACthiswork1 76(0.9b_{) – –}

NRTL-SACthiswork2 0.805(0.250b_{) 27%}

-NRTL-SACthiswork3 9.034(2.750b_{) – –}

Salicylicacid UNIFAC 26.62(0.195a_{) 29% –}

UNIFACmod. 322(3.01a_{) 36% –}

COSMO-SAC 15.03(5.01a_{) 66%}

-NRTL-SAClit. 125(0.451a_{) 44% –}

NRTL-SACthiswork 361(0.436a_{) 49% –}

NRTL-SACthiswork 409(0.590a_{) 63% –}

Benzoicacid UNIFAC 0.180 9% 1.077

UNIFACmod. 0.439 8% 0.572

COSMO-SAC 1.136 33% 1.932

NRTL-SAClit. 0.107 9% –

NRTL-SACthiswork 0.114 9% –

4-Aminobenzoic UNIFAC 6.790 – –

acid UNIFACmod. 18.04 – –

COSMO-SAC 8.50 – –

NRTL-SACthiswork 0.672 – –

Anthracene UNIFAC 0.247 11% 0.506

UNIFACmod. 0.808 12% 1.388

COSMO-SAC 3.203 19% 3.80

NRTL-SACthiswork 3.631 19% –

a_{msewithoutchloroform.} b_{msewithoutdichloromethane.}

Fig.3.Experimentalsolubilityof(a)ibuprofen[20,21],(b)paracetamol[22],(c)salicylicacid[23–27],(d)benzoicacid[28–30],(e)4-aminobenzoicacid[31–34]and(f) anthracene[35–39]invarioussolventsasafunctionofthereversetemperature(van’tHoffplot).

etersaretemperaturedependent(9mn),themoleculargeometry

andisomerismarenottakenintoaccount.Asmentionedinthe literature[5,8], thepredictedsolubilityof organicmolecules in nonpolarsolvents(heptane,cyclohexane,andtoluene)areingood agreementwiththeexperimentaldata.Inthecase ofpolar sol-vents,capableofforminghydrogenbonds,wefoundthesolubility to bealways underestimated for the chosen solvents. In

addi-tion,inthecaseofsolubilityinalcohols,theordersofmagnitude ofthepredictedsolubilitiesareveryclose.Thisprobablymeans thatinUNIFAC,thepair-wiseinteractioncoefficientsinvolvingthe OHgroupispredominantovertheinteractioncoefficientsofthe aliphaticchains(–CH2–CH3,-CH3groups).Thesolubilityordersof

magnitude,shown inTable4,seemstoconfirmthis statement. Fromaqualitativepointofview,theobtainedsolubilityranking

Fig.4.UNIFACpredictionsof(a)ibuprofen,(b)paracetamol,(c)salicylicacid,(d)benzoicacid,(e)4-aminobenzoicacidand(f)anthracenewithEq.(5)asafunctionofthe experimentalsolubility.

ofthestudiedmoleculesaregiveninTable4.Thistableshowsthat forlargesolubilityvalues(x>0.05),UNIFACgivessatisfactory qual-itativeresultsforpredictingsolubilityorderofmagnitudeandthe solubilityrankingisalmostpreserved.Forparacetamol,original UNIFAChasdifficultiestopredictsolubilitylowerthan0.05.The predictedordersofmagnitudearenotinagreementwith experi-mentaldata.

4.3. COSMO-SAC

Fromtheresults,presentedinFig.5andTable5,itcanbestated thatCOSMO-SACgivespoorresultsinthesolubilitypredictionof thedrugstested.Themeansquareerrorsrangefrom1.15to25, dependingonthemoleculeandonthepurecomponent proper-tieschosen.Notsurprisingly,therelativedeviationisparticularly

Table4

OriginalUNIFACsolubilityrankingatCor30◦_{Candordersofmagnitude(insolubilitylogarithm)foribuprofen,paracetamol,salicylicacidandbenzoicacidinvarioussolvents.}

Ibuprofen Paracetamol

Solvent Orderofmagnitude Solvent Orderofmagnitude

Heptane [−3;−2] Dichloromethane [−9;−8] Cyclohexane [−2;−1.5] Dioxane [−5] Ethanol Heptanol Isopropanol [−1.5;−1] Acetonitrile [−5;−4] Octanol DMSO Toluene Methanol

Ethylacetate Butanol

Acetone Ethylacetate

Chloroform Propanol

Methylethylketone Ethanol

Acetone [−4;−3]

Chloroform [−3;−2]

Benzoicacid Salicylicacid

Solvent Orderofmagnitude Solvent Orderofmagnitude

Hexane [−5;−4] Hexane [−9;−8]

Heptane Cyclohexane

Cyclohexane Carbontetrachloride

Carbontetrachloride [−4;−3] Xylene [−7;−6]

Benzene [−3;−2] Chloroform [−3]

Octanol Aceticacid

Isopropanol Acetonitrile

Acetonitrile Octanol [−3;−2]

Butanol Ethylacetate

Heptanol Ethylmethylketone

Dioxane [−2;−1] Acetone [−2;−1.5]

Acetone Ethanol

N-Methylpyrrolidone Methanol

Table5

COSMO-SACsolubilityrankingat30◦_{Candordersofmagnitude(insolubilitylogarithm)foribuprofen,paracetamol,salicylicacidandbenzoicacidinvarioussolvents.}

Ibuprofen Paracetamol

Solvent Orderofmagnitude Solvent Orderofmagnitude

Heptane [−3;−2.5] Dichloromethane [−6;−5]

Cyclohexane [−2] Chloroform [−5;−4]

Toluene [−1.5;−1] Acetonitrile [−3;−2.5]

Chloroform Ethylacetate

Ethylacetate [−1;−0.5] Heptanol

Octanol Butanol [−2.5;−2]

Ethanol Methanol

Isopropanol Propanol

Acetone Dioxane [−2;−1.5]

Ethanol

Methylethylmketone Acetone

Dimethylsulfoxide [>−1]

Benzoicacid Salicylicacid

Solvent Orderofmagnitude Solvent Orderofmagnitude

Heptane [−5.5;−5] Hexane [−6;−5]

Cyclohexane Cyclohexane

Hexane Carbontetrachloride

Isopropanol [−5;−4] Xylene [−4]

Carbontetrachloride [−4;−3] Chloroform [−4;−3]

Benzene [−3;−2] Aceticacid [−3;−2]

Acetonitrile [−2;−1] Acetonitrile [−2;−1.5]

Octanol [−1;−0.5] Ethylacetate [−1.5;−1]

Butanol Methanol

Dioxane Octanol

Acetone Ethanol [>−1]

N-Methylpyrrolidone [>−0.5] Acetone

Fig.5.COSMO-SACpredictionof(a)ibuprofen,(b)paracetamol,(c)salicylicacid,(d)benzoicacid,(e)4-aminobenzoicacidand(f)anthracenewithEq.(5)asafunctionof experimentalsolubility.

highinsolventsinwhichsolubilityisverylow,e.g.paracetamolin ethylacetate.AsinthecaseofUNIFAC,themodelgives satisfac-toryresultswithaproticandapolarsolvents(hexane,heptane,and chloroform).Ontheopposite,inpolarsolventscapableofforming hydrogenbonds(alcohols,ketones,esters,...)withthesolute,the predictedsolubilityissystematicallyoverestimated.Inaddition,it canbenoticedthatthepredictedsolubilityvaluesofamolecule

inalcoholsarealwaysnearlythesame,whateverthesizeofthe alcoholmolecule(seeordersofmagnitudesinTable5).

AspreviouslyachievedfortheUNIFACmodel,thepredictions obtainedatthelowertemperatures (20–25◦_{C) aremuch better}

thantheoneobtainedathighertemperatures(Fig.5).Inthismodel, theelectrostaticandhydrogenbondsparametersarenot temper-aturedependent.

Fromaqualitativepointofview(Table5andFig.5), COSMO-SACisquitereliableforthesolubilitypredictionofthemostsimple molecules,likealkanes.Thismodeloverestimatessolubilityin alco-holsandketonesand leadstoanonreliable solubilityscale. In addition,theordersofmagnitudearetwicetheexperimentalin mostcases.Consideringsolubilityranking,thismodelisnotasgood asUNIFAC.Toevaluatetheinfluenceofhydrogenbondonthe pre-dictingcapabilitiesofCOSMO-SAC,thehydrogenbondisexcluded fromthemodel,setting theconstantfor thehydrogenbonding interaction(c_hb)tozero.Thisconstantappearsinthecalculation ofthesegmentactivityŴ,in theexpressionof theelectrostatic interactions.

Theresults areshown in Fig. 6 and it canbe seenthat the predictedsolubilitiesare underestimatedin polarsolvents. The modelpredictionsarein goodagreementwiththesolubilityof polarmoleculesinpolarsolvents,whichishigherthanideal,mainly resultsfromspecificinteractionslikehydrogenbonds.Inaddition, theresultsobtainedwithandwithouthydrogenbondsalsosuggest thatinCOSMO-SACthehydrogenbondcontributionis overesti-mated.Thechbconstantisanadjustableparameterwhichhasbeen

optimizeduponmanyVLEdataofsmallorganicmolecules. How-ever,theorganicmoleculesinourstudyaremuchlarger,flexible, andcontainh-bondingsurfacesthatareburriedorhinderedsothat h-bondscannotform.Then,itislikelythatsuchsurfacesshallnotbe includedintheh-bondterminthemodel.Itwouldbevery interest-ingtore-optimizethistermforlargeorganicmoleculesusingSLE data(providingthatenoughexperimentaldataareavailable).Even ifEq.(4)isconsidered,thisdoesnotimprovetheresultsasthe1Cp

termincreasesthepredictedsolubility(seeSection4.5).Inaddition, evenifstereoisomerismcanbetakenintoaccountinCOSMO-SAC (eachisomerhasitsownsigmaprofile),molecularselfandcross associationsarenotconsidered.It iswellknownthatibuprofen formshydrogen-bondeddimerinsolution:twocomposedofthe sameenantiomersofR–RandS–SandtheracemateofR–S.The self-associationofdrugmoleculesmaydecreasethenumberoffree molecularsitesavailabletoformhydrogenbondswiththesolvent, whichmayexplaintheoverestimationofthecontributionof hydro-genbondstothecalculationoftheactivitycoefficient.Sucheffects arealsofoundforbenzoicacid(Self-associationandhydrationof

Fig.6.COSMO-SACpredictionofparacetamolinethanolandmethanolwith hydro-genbonds(straightlines),andnohydrogenbonds(dashedlines)asafunctionof thetemperatureusingEq.(5).

benzoicacidinbenzene[54]orinalessextentforcarboxylicacid likeaspirin).

At last, even if the predicted solubilityis quantitatively far fromtheexperimentaldata,Fig.6showsthat themodel nicely predictsthesolubilitytemperaturedependence.Fordesigning a crystallizationprocess,theoneofthemostimportantparameter isthesupersaturation:thedrivingforceoftheprocess,definedas theratiobetweentheinitialandfinalconcentration(S=C/C*).For instance,asshowninFig.6,theexperimentalsupersaturationfor paracetamolinmethanolfrom30◦_Cto0◦_{CisS=1.54andthe}

pre-dictedisS=1.5(similarresultsareobtainedforallthemolecules testedinthepaperinsmallalcoholmolecules).

Table6

NRTL-SACsegmentswhen1Cpisneglected(Eq.(5)).

Compounds X Y− Y+ Z mse Numberofsolvents

Ibuprofen[55] 1.038 0.051 0.028 0.318 1.055 19

Ibuprofen(thiswork1)a _{0.507 0.297 0.350 0 0.005 6}

Ibuprofen(thiswork2)b _{0.484 0 0.267 0.210 0.0188 9}

Paracetamol[56] 0.498 0.487 0.162 1.270 – 8

Paracetamol[7] 0.416 0.016 0.168 1.86 – 5

Paracetamol(thiswork1)c _{0.265 0.576 0.668 0.717 0.029 6}

Paracetamol(thiswork2)d _{0.369 0.618 0.521 1.095 0.859 14}

Paracetamol(thiswork3)e _{0.275 1.036 1.159 0.777 0.033 6}

Salicylicacid[55] 0.726 0.176 0 0.749 0.774 18

Salicylicacid(thiswork1)f _{0.911 1.762 0.129 0.329 0.182 6}

Salicylicacid(thiswork2)g _{1.006 2.29 0 0.451 0.0617 6}

Benzoicacid[17] 0.524 0.089 0.45 0.405 0.160 7

Benzoicacid[55] 0.494 0 0.336 0.468 0.292 26

Benzoicacid(thiswork)h _{0.576 0 0.121 0.543 0.144 6}

4-aminobenzoicacidi _{0 0 4.229 2.321 0.222 5}

Anthracenej _{1.486 0 0 0.564 0.180 5}

a_{Inacetone,cyclohexane,chloroform,ethanol,octanolandethylacetateat30}◦

C.

b_{Inallthesolventconsideredinthisstudy(seeFig.3)at30}◦_C.

c _{Inacetone,ethylacetate,chloroform,toluene,ethanolandwaterat30}◦_C. d _{Inallthesolventsofthiswork(seeFig.3)at30}◦_C.

e_{Inethanol,propanol,acetone,methylethylketone,waterandtolueneat30}◦_C. f _{Inethanol,ethylacetate,cyclohexane,acetone,acetonitrileandxyleneat30}◦_C. g_{Inethanol,ethylacetate,acetone,xylene,acetonitrileandwaterat30}◦_C.

h _{Incyclohexane,acetonitrile,1-butanol,benzene,n-methylpyrrolidoneandwater,at30}◦

C.

i _{Inethylacetate,ethanol,dimethoxyethane,THFanddioxane,at30}◦_C.

4.4. NRTL-SAC

TotestthepredictionabilitiesofNRTL-SAC,thesegments val-ues(X,Y−_,Y+ _{andZ)weretakenfromtheliterature[7,55,56].It}

canbenoticedthatsegmentvaluesfoundintheliteraturecan sig-nificantlydifferforthesamecompound.Forinstance,asshownin Table6,ChenandCrafts[56]andMotaetal.[7]havepublished differentsegmentvaluesforparacetamol.Thesedifferencescanbe notonlyduetothevaluesusedforthepurecomponent parame-ters(1Hm,Tm,and1Cp)determinedexperimentallyorregressed

simultaneouslywiththesegments,butalsoduetothenatureand thenumberofsolventsusedintheregression.

Inordertotestthemodelsensitivitytothequadruplet[XY−

Y+_{Z],calculationswereperformedwithdifferentsolventsforall}

thesolutesinordertoobtainnewvalues.Allthesenewvaluesand thecorrespondingmeansquareerrorsaregivenin Table6.The sensitivityofthemodeltotheexperimentalsolidstateproperties isperformedusingtheMonteCarlomethod.

Fromaquantitativepointofview,themodelgivesresultswith a mserangingfrom0.107to409or3.63 when neither chloro-formnordichloromethaneareconsidered(seeTable3).NRTL-SAC predictionsusing[55]segmentvaluesversusexperimental solu-bilityisrepresentedinFig.7,andusingsegmentfromthisworkin Fig.8(quadruplet1foribuprofen,quadruplet2forparacetamoland

quadruplet2forsalicylicacid).Duetotheempiricalnatureofthe model,NRTL-SACseemstobelessaffectedbyerrorsonthe ther-modynamicpropertiesthantheothermodels.Theresultsobtained areingoodagreementwiththeexperimentaldata,andmostofthe resultsarebeneathamseof4.However,themserrorsseemquite hightodoquantitativepredictions.

The model accuracy of the resultsstrongly depends onthe quadruplets[XY−_Y+_{Z]usedasparameters.Infact,thechoiceof}

theseparametersisacriticalsteptousethismodel.

Thesegmentsvaluescanbeunderstoodasaweightgiventoeach moleculebehaviour:hydrophilic,hydrophobic,polarattractiveand repulsive.Theyrepresenta“meanbehaviour”ofthemoleculein solutioncomputedusingexperimentaldata.Thesevaluesdepend onthequalityandquantityofthesolubilitydatausedtoregress thefourparameters.Theywillnotrepresenttherealbehaviourof theAPIinallthesolventsiftheexperimentaldataarenottaken judiciously.However,thechoiceoftheexperimentaldataisnot obvious.NRTL-SAC using segmentscalculated in somealcohols willnotnecessarilygivegoodpredictionsinotheralcoholsandit givesevenworseresultsinothersolventlikeketonesoralkanes. Sometestsperformedonparacetamolshowedthatthepredictions obtainedusingtheparametersregressedusingfoursolubilitydata inpropanolandbutanol(twotemperatures)gavethesameresults asthoseobtainedwithquadruplet3ofthiswork.Infact,allalcohols

Fig.7.NRTL-SACpredictionof(a)ibuprofen,(b)paracetamol,(c)salicylicacid,(d)benzoicacid,(e)4-aminobenzoicacidand(f)anthracenewithEq.(5)usingsegmentsfrom theliteratureasafunctionofexperimentalsolubility.

Fig.8.NRTL-SACpredictionof(a)ibuprofen,(b)paracetamol,(c)salicylicacid,(d)benzoicacid,(e)4-aminobenzoicacidand(f)anthracenewithEq.(5)usingsegmentsfrom thiswork(thiswork1foribuprofen,2forparacetamol,1forsalicylicacidand1forbenzoicacid)asafunctionofexperimentalsolubility.

donothavethesameweightoneachsegmentnumber.Eveniftheir quadrupletsmayindicateaclosebehaviourtendency,theycanalso bequitedifferent.Inaddition,theuseofalargeexperimentaldata setincreasesthemodelperformanceandreliability.

Inordertoshowtheinfluenceofthesegmentvaluesusedinthis study,fourtypesofibuprofensolubilitypredictionsinethanolare reportedinFig.9.

Toendwiththesolventselectionandinordertogetthemost reliableregression, theidea is toselectthesolventso thatthe weightofeachsegmentisthesame:

X

i Xi=

X

i Y+ i =

X

i Y− i =

X

i Zi (17)

Fig.9.NRTL-SACpredictionofparacetamolinethanolusingfourdifferentsegment quadrupletsasafunctionofthetemperature.

withithesubscriptforthesolvent.Inthisway,allthebehaviourof thesolutemoleculeswillbeinvestigatedwiththesameweight.

Thismethodisstillinstudy,butwetriedtofindthebest sol-ventsfortheparacetamolregression.Todothat,wetakeallthe solventsinvestigatedby[17]andweforcedthissumtobegreater than1(tohaveeachsegmentnumberrepresentedwithenough weight).Thecalculation,madewithversion23.6.5ofGAMS soft-ware,gaveatotalof10solvents(chloroform,1,2-dichloroethane, 1,4-dioxane, ethanol, formamide, formic acid, isobutylalcohol, nitromethane,1-propanolandwater)toreachamaximum devi-ation of 0.002. If we regressed the segment numbers of these solvents, themeansquare errorwould behigherthan themse obtainedinTable6becauseofthediversityofthesolventused. But,theobtainedquadrupletshouldbemoresuitableasthemean behaviourshouldbebetterrepresented.Furtherstudiesarestill inprogress.

Evenifthepredictiondiffersquantitativelyfromaquadruplet totheother,NRTL-SACgivesgoodordersofmagnitudewhatever thesegmentsused(seeTables7and8).Moreoverthesolubility rankingispreserved.

Asshown in Figs. 7 and8 in thecase of ibuprofen, solubil-itypredictionsfortemperaturesabove25◦_{Carelessaccurate.In}

thismodel,theinfluenceoftemperatureonsolubilityis underes-timated,especiallywhenhydrogenbondsareinvolved.Thiscould beexplainedbythefactthatthesolubilitydependenceon tem-peraturebeingrelatedtothesolidstateproperties,andnotonthe possibleevolutionofmolecularinteractions(hydrogenbond,Van derWaals,dispersionforces,...)betweenmoleculesinsolution.

ToconcludeonNRTL-SAC,thismodelcanbeusefultogivean estimationofthesolubilityofAPIsinvarioussolvents.Butitneeds reliablesegmentvaluesforquantitativepurposeandneeds exper-imentaldata.

4.5. Therightmeltingenthalpyortemperatureandtheuseof 1Cp

In the case of SLE, equilibrium equation can be Eq. (4) or Eq.(5).Eq.(4)isthemostrigorous,but,usually, the1Cp term

Fig.10.UNIFACpredictionofparacetamolusingdifferentthermodynamic prop-erties[23,34,35,37]inethanol(upperside)andethylacetate(downside)with (a)1Hm=27,100J/mol,Tm=443.6K,(b)1Hm=27,100J/mol,Tm=443.15K,(c)

1Hm=28,100J/mol,Tm=441.15K,(d)sameas’b’with1Cp=99.8J/molK,(e)same

as’c’with1Cp=99.8J/molK,(f)sameas’a’with1Cp=75J/molK.

is neglected and Eq. (5) is used. Evenif Gracin et al. [5] have found a small influence of the 1Cp term with UNIFAC model,

the two equations willbe compared usingall the models pre-sented previously.In addition, thesignificance of thevalues of thepurecompound propertieshastobeunderlined.Measuring accuratelythemeltingtemperatureandenthalpymaybedifficult, sinceitreliesonproductcrystallinity,purityandonthe analyt-icalmethodused.AspresentedinTable1manydifferentvalues havebeenreportedintheliterature.InFigs.4,5,7and8, stan-darddeviations ofthemodelscausedbypropertieserrors have been presented. So, when a model is used for predicting solu-bility,itserrorhastobetakenintoaccount,and themeasured Tm,1Hm and1Cp havetobeasaccurateaspossible.

Neverthe-less,prediction errorsinducedbythemodelsareusually larger then the ones induced by the solid state property uncertain-ties.

As shown in Fig. 10, it can be seen that a higher melting enthalpyimpliesahigherpredictedsolubility.Thesamebehaviour isobservedforhigher1Cp.Moreover,inthecaseofpolymorphism

(likeparacetamol),theuseofthewrongmeltingenthalpy, tem-peratureor1Cpcancausebadpredictionsormisinterpretations (paracetamolpresentsatleasttwopolymorphswithclosemelting temperatureandenthalpy).

Table7

NRTL-SACsolubilityrankingat30◦_{Candordersofmagnitude(insolubilitylogarithm)foribuprofen,paracetamol,salicylicacidandbenzoicacidinvarioussolventsusing}

segmentsfromtheliterature.

Ibuprofen Paracetamol

Solvent Orderofmagnitude Solvent Orderofmagnitude

Heptane [−2] Dichloromethane [−8;−7]

Acetone [−2;−1.5] Chloroform

Cyclohexane Ethylacetate [−6;−5]

Toluene Methylethylketone

Octanol Acetonitrile

Ethanol Acetone [−5;−4]

Ethylacetate Dioxane

Isopropanol [−1.5;−1] Propanol [−3;−2.5]

Chloroform [3×10−1_to4×10−1_{] Methanol}

Butanol Ethanol

Dimethylsulfoxide [−2.5;−2]

Benzoicacid Salicylicacid

Solvent Orderofmagnitude Solvent Orderofmagnitude

Heptane [−5;−4] Hexane [−8;−7]

Hexane Cyclohexane

Cyclohexane Carbontetrachloride [−7;−6]

Carbontetrachloride −3 Xylene [−6;−5]

Benzene [−2.5;−2] Acetonitrile [−4;−3]

Acetonitrile Ethylmethylketone

Butanol [−2;−1.5] Ethylacetate

Octanol Acetone [−4;−3]

Isopropanol Octanol

Acetone Methanol

Dioxane [−1.5;−1] Aceticacid [−3;−2]

N-Methylpyrrolidone Ethanol

Dimethylsulfoxide [>−1] Chloroform

Table8

NRTL-SACsolubilityrankingat30◦_{Candordersofmagnitude(insolubilitylogarithm)foribuprofen,paracetamol,salicylicacidandbenzoicacidinvarioussolventsusing}

segmentscalculatedinthisstudy(thiswork1foribuprofen,2forparacetamol,1forsalicylicacidand1forbenzoicacid).

Ibuprofen(thiswork2) Paracetamol(thiswork2)

Solvent Orderofmagnitude Solvent Orderofmagnitude

Heptane −2 Dichloromethane [−7;−6]

Cyclohexane Ethylacetate [−6;−5]

Ethanol [−1.5;−1] Ethylmethylketone

Toluene Acetonitrile [−5;−4]

Acetone Chloroform

Isopropanol Acetone [−4;−3]

Ethylacetate Dioxane

Chloroform Propanol −3

Octanol Butanol

Ethanol [−3;−2.5]

Methanol

DMSO [−2.5;−2]

Benzoicacid(thiswork2) Salicylicacid

Solvent Orderofmagnitude Solvent Orderofmagnitude

Heptane [−4.5;−4] Hexane [−9;−8]

Cyclohexane Cyclohexane [−8;−7]

Hexane Carbontetrachloride [−6;−5]

Carbontetrachloride [−4;−3] Xylene [−5;−4]

Benzene [−3;−2] Acetonitrile [−4;−3]

Acetonitrile Ethylacetate [−3;−2]

Acetone [−2;−1.5] Acetone

Octanol Ethylmethylketone

Dioxane Methanol [−2;−1.5]

Butanol Octanol

Isopropanol Aceticacid

N-methylpyrrolidone [−1.5;−1] Ethanol

Fig.11. CoefficientBasafunctionofTm/T.

Toevaluatetheimpactofneglectingthe1CptermintheSLEon

solubilityprediction,relativevalueofthetwoparts,constituting Eq.(4),canbecomparedusingthefollowingequation:

1hm(Tm) T1m− 1 T

1Cp(Tm) ln(TTm)−TTm+1

(18)

Then,wewillrewrite: 1Hm 1CpTm × 1− Tm T



ln(Tm T )− Tm T +1



=A×B (19)

If|AB|≪1,thenthesecondpartofEq.(4)cannotbeneglected, andiftheratioishighenough,itmaybeneglected(seeexample inFig.11).TheAtermisconstantandonlydependsonthe ther-modynamicpropertiesofthesolidstate.TheBtermisafunctionof temperatureasshowninFig.11.

Considering that for a standard crystallization operation, the runningtemperature is around 290K. At this temperature, B=−11.33andA=1.48foribuprofen,and B=−5.10,A=0.71 for paracetamol.Thedefinitionofarelativeerrorenablestoestimate theeffectbyneglectingthe1Cpterm:

relativeerror(%) = 1

AB−1 (20)

Inthecaseofthesetwomolecules,thiserrorisabout6%forthe ibuprofenand22%fortheparacetamol.Wecanconcludethatthe 1Cptermisnegligibleinthecaseofibuprofen,andnotinthecase

ofparacetamol. 5. Conclusion

Toconclude,noneofthemodelspresentedinthispaperisableto predictpreciselythesolubilityofthestudiedmolecules(containing variouscommonfunctionalgroupslikealcohols,ketones,amines) invarioussolvents.Evenconsideringthemodelerrorsmostofthe timestakenbytheimprecisiononthepuresolidproperties,the predictedsolubilityaregenerallyinagreementwithexperimental data(IbuprofenwithOriginalUNIFAC,somesolutes with NRTL-SAC).COSMO-SACpredictionsusuallyproducehighervaluesthan theexperimental,especiallywhenhydrogenbondsmayoccur.

UNI-FACismoreaccuratethanCOSMO-SACfortheAPIinthisstudy andgivesgoodresultsforsimplemolecules(anthracene). How-ever,evenifthesolubilityordersofmagnitudearepreserved,it isnotgoodenoughforperformingquantitativepredictions.Inthe caseofNRTL-SAC,predictionsareverydependentonthe parame-tersused(segmentvalues).Iftheseparametersdonotrepresentthe correctbehaviouroftheAPIinthesolventchosen,theresultswill notbesatisfying.Finally,UNIFACandNRTL-SAC,whichpreservethe solubilityordersofmagnitudecanbeagoodcomplementof exper-imentaltechniquestoguidethechoiceofacrystallizationsolvent. Butintheend,experimentsarestillrequiredtoobtainquantitative results.

Inaddition,allthemodelstestedfailtocorrectlydescribethe solubilitydependencewithtemperature.Theuseofanequationof stateseemstobemoreappropriateforpredictingtheevolutionof solubilitywithtemperature[57,58].

Resultspresentedinthispaperalsoshowthattheuseofthe mostpreciseequilibriumequationdoesnotsignificantlyinfluence thequalityoftheresults.Asthemodelsarenotaccurateenough, theuseofthemostaccuratethermodynamicpropertiesvaluesis notnecessary.Moreover,the1Cptermcanbeignoredaslongas

thegeneratederrorisnegligibleregardingthemodelerror.But,in thehypotheticalcaseofaperfectmodel,themostprecisevalues shouldbeused.

Acknowledgements

Theauthorswant toacknowledge ProSimCompanyfor their collaborationintheuseofSimulisThermodynamicssoftware,and Pr.FlorentBourgeoisforenlighteningdiscussions.

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