Physicochemical characterization of D-mannitol polymorphs: The challenging surface energy determination by inverse gas chromatography in the infinite dilution region

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Physicochemical characterization of D-mannitol

polymorphs: The challenging surface energy

determination by inverse gas chromatography in the

infinite dilution region

María Graciela Cares Pacheco, G. Vaca-Medina, Rachel Calvet, Fabienne

Espitalier, Jean-jacques Letourneau, A. Rouilly, Élisabeth Rodier

To cite this version:

María Graciela Cares Pacheco, G. Vaca-Medina, Rachel Calvet, Fabienne Espitalier, Jean-jacques

Letourneau, et al.. Physicochemical characterization of D-mannitol polymorphs: The challenging

surface energy determination by inverse gas chromatography in the infinite dilution region.

Interna-tional Journal of Pharmaceutics, Elsevier, 2014, 475 (1-2), p. 69-81. �10.1016/j.ijpharm.2014.08.029�.

�hal-01611996�

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Physicochemical

characterization

of

D

-mannitol

polymorphs:

The

challenging

surface

energy

determination

by

inverse

gas

chromatography

in

the

inﬁnite

dilution

region

M.G.

Cares-Pacheco

a,

_*

_,

_G.

_Vaca-Medina

b,c

_,

_R.

_Calvet

a

_,

_F.

_Espitalier

a

_,

_J.–J.

_Letourneau

a

_,

A. Rouilly

b,c

_,

_E.

_Rodier

a

a_Université_de_Toulouse,_Mines_Albi,_UMR_CNRS_5302,_Centre_RAPSODEE,_Campus_Jarlard,_Albi_cedex₀₉_F-81013,_France b_Université_de_Toulouse,_{INP-ENSIACET,}_LCA,_Toulouse_310130,_France

c_INRA,_UMR₁₀₁₀_CAI,_Toulouse_310130,_France

Keywords: D-Mannitol Crystallization Polymorphism

Solid-stateanalyticaltechniques Surfaceenergy

Inversegaschromatography ABSTRACT

Nowadays,itiswellknownthatsurfaceinteractionsplayapreponderantroleinmechanicaloperations, whicharefundamentalinpharmaceuticalprocessingandformulation.Nevertheless,itisdifﬁcultto correlate surface behaviour in processes to physical properties measurement. Indeed, most pharmaceutical solidshave multiple surface energies because of varyingforms, crystal faces and impuritiescontentsorphysicaldefects,amongothers.

Inthispaper,D-mannitolpolymorphs(a,bandd)werestudiedthroughdifferentcharacterization techniqueshighlightingbulkandsurfacebehaviourdifferences.Duetothelowadsorptionbehaviourofb

and d polymorphs, special emphasis has been paid to surface energy analysis by inverse gas chromatography,IGC.SurfaceenergybehaviourhasbeenstudiedinHenry’sdomainshowingthat,for someorganicsolids,theclassicalIGCinﬁnitedilutionzoneisneverreached.IGCstudieshighlighted, withoutprecedentinliterature,dispersivesurfaceenergydifferencesbetweenaandbmannitol,witha mostenergeticallyactiveaformwithagd

sof74.9mJ!m"2.Surfaceheterogeneitystudiesshowedahighly heterogeneousamannitolwithamorehomogeneousb(40.0mJ.m"2₎_and_d_mannitol_(40.3_mJ_!_m"2_). Moreover, these last two forms behaved similarly considering surface energy at different probe concentrations.

1.Introduction

Active pharmaceutical ingredients, APIs, must comply with well-definedspecificationsin terms ofbioavailability, stability, toxicity, purity, morphology, stability, size, etc. Most of these substances can exist in several solid-state forms: polymorphs, pseudo-polymorphs, solvates/hydrates or amorphous forms depending on the generation, growth and formulation con-ditions. This diversity of solid forms requires a thorough understanding of solid-state phenomena that may occur in pharmaceuticalengineering.Eachoftheseformshasadifferent crystalline structure, and hence, different physicochemical properties. In the pharmaceutical field, the consequences related to polymorphism, habitus, surface state and particle size distribution does not relate only to APIs but also to

excipients.Moreover,excipientsplayakeyrolein manufactur-ability but also in API’s dissolution and bioavailability. Solid surfaceproperties suchas size, shapeandpowder agglomera-tionare alsoknowntoimpact dissolutionbehaviour, compact-ability, aerosol performance and surface energetics among others(Ho et al., 2012;Tang et al., 2009).

Thus, toensure a highquality to these organic solids, it is essentialcharacterizingthesolid-stateforms,bothinqualitative andquantitativeways.Characterizationcanbeapproachedbya wide varietyofanalytical techniques. Overthelast decade, the most frequently used solid-state techniques have been in decreasing order, X-ray powder diffraction (XRPD), differential scanning calorimetry (DSC), infrared spectroscopy (IR) and microscopy(Chienget al.,2011).Mostauthorsuseatleasttwo characterization techniques; however, all these methods give informationatdifferentlevelsordifferentdepthswithinthesolid andnotespeciallyonthesurface.Thesedays,itiswellknownthat surface interactions play a fundamental role in mechanical operationssuch as grinding, millingand compaction,processes

* Correspondingauthor.Tel.:+33563493226;fax:+33563493025. E-mailaddress:gcares@mines-albi.fr(M.G. Cares-Pacheco).

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commonlyusedinpharmaceuticalformulationsbutalsoinstorage stability.Indeed,animportantphysicochemicalpropertyofsolids is thesurface energy because it reﬂects interfacialinteractions betweenthe solid and its environment. It seems,therefore, of utmostimportancetoexamineandquantifythesurfaceproperties ofasolid.

Organicsolidsaredeﬁnitelycomplexsystems.Thecomplexity isrelatedtotheanisotropicnatureofcrystallinesolids.Infact,it has been demonstrated that each face of a crystal or defects present in the solid structure has different surface properties generally attributed to different proportions of the functional groupsexposedonit(Hengetal.,2006;Hoetal.,2010).Thus,a singlevaluethatrepresentsthesurfaceenergyofapowdermaybe atbest,ameanvalue.

A quite large number of methods have been used in the literaturetodeterminesurfaceenergyonpharmaceuticalssolids; contact angle, vapour adsorption techniques and atomic force microscopy (AFM). The most common methods are those that relate,directlyorindirectly,surfaceenergytothecontactangle formedbetween a liquid and a solid: spreading, capillary rise, Wilhelmyplateandheatofimmersion.Thelimitationsofthese methodshavebeenwellreviewedbut,evenifthesurfaceenergy valuesobtainedfromcontactanglemeasurementsaresomewhat inaccurate, the mean values obtained have been successfully correlatedtofunctionalityorend-useproperties(Buckton,1995;

BucktonandGill,2007).

Nowadays,thestudyoftheanisotropicsurfacepropertiesofa solidgoesthroughtheinvestigationofsolid–vapourinteractions. In fact, wettabilitymeasurements are based onthe interaction betweenaliquidandasolidsurface.Thisleadstoamacroscopic average of the surface energy, which is sensitive to surface roughness,porosity,packingstructureandtortuosityoftheporous material. On the contrary,gas–solid interactions give access to microscopicvariationsofthesurfacestructure.Indeed,thestudyof theinteractionsbetweenisolatedgasmoleculesandthesolidof interest willbe sensitive tolocalvariations of thesurface at a molecularscale.Differentcharacterizationtechniquesare imple-mentedbasedonvapouradsorption–desorptiononto/fromasolid, which are aimed to give information on speciﬁc surface area, porousstructure and distribution (Rouquerol et al.,1999).The mechanisms of surface coverage and/or pore ﬁlling can be describedbythestudyofasorptionisotherm.Indeed,theoverall shapeoftheisothermisgovernedbythegas–solidinteractions,the solid’sporestructureandtemperature.Asorptionisothermrelates the adsorbed vapour amount to the vapour concentration surroundingthesolidinequilibriumconditions.Different param-eterscanbemeasuredtodetermineanadsorptionisotherm:the vapourpressure,thesamplemassandtheretentiontime.Eachof these properties gives rise to a class of analytical techniques; manometric,gravimetricorchromatographic.However,veryfew are exploited to give surface energetic information; for that purpose,thetwomaintechniquescommonlyusedaredynamic vapoursorption(DVS)(Storeyand Ymén,2011)andinversegas chromatography(IGC)(HoandHeng,2013;Mohammadi-Jamand

Waters,2014).

Nomenclature

A(m2) Surfaceareaofsolidincontactwiththe adsorbedphase

Aads(J) Helmholtzfreeenergyoftheadsorbed

phase

ag(m2/molecule) Area occupied by an adsorbed probe

molecule

as(m2/g) Speciﬁcsurfaceareaofthesolid

Fads(J) Freeenergyoftheadsorbedphase

Fs(cm3STP/min) Carriergas ﬂowrateattheexitof the

columnat273.15–Kandstandard pres-sure

D

Gads(J) Gibbsfreeenergyvariationfor

isother-maladsorptionofnadsmolesofprobe

fromngmolesingasphaseinitially

D

gads(J/mol) Molar free energy variation for an

isothermaladsorptionof probe mole-cules

D

gCH2 (J/mol) Molar free energy variation for an isothermaladsorptionof a methylene group

j_(") James–Martincorrectionfactor

K(m) Henry’sconstant

m(g) Samplemass

nads(mole) Adsorbedmolenumber

Na(molecules/mol) Avogadronumber

ng(moles) Numberofgasmoles

nm(moles) Monolayer capacity or number of

adsorbed moles corresponding to a monolayer

nsol(moles) Solidmolenumber

P(Pa) Vapourpressure

P2(Pa) Vapourpressureofa purecomponent

inequilibriumwithitsadsorbedphase ataspreadingpressure

p

2

R Perfect gas law constant, 8314JK"1

mol"1

Sads(J/K) Entropyoftheadsorbedphase

T(K) Temperature

Tc(K) Columntemperature

tN(min) Netretentiontime

t0(min) Deadtime

tR(min) Retentiontime

Vads(m3) Volumeoftheadsorbedphase

VN(cm3/g) Netretentionvolume

Wadh(J/m2) Work of adhesion when adsorption

occurs Greeksymbols

g

c(J/m2orN/m) Criticalsurfaceenergyofasolid(usedin

Zismantheory)

g

d

l (J/m2orN/m) Liquid surface energy (or surface

ten-sion)

g

d

s(J/m2orN/m) Dispersivecomponent of solid surface

energy

g

s(J/m2orN/m) Totalsurfaceenergyofasolid

g

ps(J/m2orN/m) Polarcomponentofsolidsurfaceenergy

g

d

CH2 (J/m

2_or_N/m) _Dispersive_component_of_surface_energy

ofamethylenegroup

u

(#₎ _C_angle_of_a_liquid_on_a_solid

u

s(") Surfacecoverage

m

ads(J/mol) Chemical potential of the adsorbed

phase

m

g(J/mol) Chemicalpotentialofthegasphase

p

(J/m2₎ _Spreading_pressure_of_the_adsorbate_per

unitsurfaceareaofsolid

p

2(J/m2) Spreadingpressureoftheadsorbatein

equilibriumwithitsvapourphaseatP2

’

(J/mol) Changeininternalenergypermoleunit of adsorbent due to the spreading of adsorbate

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Objectofawidenumberofpublicationsoverthelastdecade, IGCappearstobeapowerfultechniquetocharacterizethesurface properties of divided solids (Ho and Heng, 2013). In general, chromatographyis a separationtechniquebasedontheafﬁnity betweentwophases,stationaryandmobileone.Developedinthe latest50s,IGCisbasedonthephysicaladsorptionofgasmolecules on a solid surface. Unlike analytical gas chromatography (GC), whereaknownstationaryphaseisusedtoseparateandidentifyan unknownmixture,inIGCthestudiedsolidisthestationaryphase, andwellidentiﬁedvapourmolecules,calledprobes,areusedto determine the interaction capacities of the unknown material packedintothecolumn.Theproberetentionistheresultofsurface interactionsbetweenthesegasmoleculesandthesolid(Conder

andYoung,1977).Thesephysicalinteractionsaredominatedby

van der Waalsforces, whose magnitudedepends on theprobe nature for a ﬁxed solid, allowing then both chemical and morphologicalstudiesof dividedsolids. Inaddition, IGCallows tostudytheinﬂuenceonsolidsurfaceoffactorssuchashumidity

(Buckton and Gill, 2007), physical (Heng et al., 2006) and/or

chemicaltreatments(Hoetal.,2010).

As we already noticed, it is well known that solids are anisotropicsystems.Literature devotedtothesurface heteroge-neityassessmentfromadsorptionmeasurementsisexhaustively reviewedintheworksofJaroniecandMadey(1988)andRudzinski

andEverett(1992).Torepresenttheexistenceofadistributionof

energy siteson a solid surface exploiting IGC data,the energy distributionfunction,

x

(2),isgenerallyused.

Thisphysicalmodelsupposesanenergeticallyheterogeneous surface with a continuous distribution of adsorption energies, which can be described as a sumof homogeneousadsorption patches.ThisapproachhasbeenwellreviewedbyBalard(1997)

whohasfocusedhisworkonthestudyofinorganicsolids(Balard

et al., 2008; Papirer et al.,1991,1999; Boudriche et al., 2011).

Anotherwaytostudysurfaceheterogeneityhasbeenproposedby

Fafardetal.(1994)usingIGCininﬁnitedilutionconditions;this

willbedescribednext.

The firstapplications of IGC in thefield of pharmaceuticals began in thelatest 80s.The firstapproach was focusedonthe determinationofHansensolubilityparametersoflactose,caffeine, theophylline and methyl hydroxybenzoate (Phuoc et al., 1987, 1986).Ithadnotbeenuntil1994thatthetechniquewasusedfor thesurfaceenergycharacterizationofpharmaceuticalsolids.The studies conducted by (Ticehurst et al., 1994) on salbutamol sulphate and

a

-lactose put in evidence the sensitivity of the technique to detect small differences in crystallinity between batches,differencesundetectedbyothertechniquessuchasDSC

(Ticehurst et al., 1996). Nowadays, polymorphism remains a

challengingissueforIGC, maybeduetotheupstreamdifﬁculty obtainingthedifferentpurecrystallineformsofapharmaceutical solidand/orbecauseoftheinstabilityofthepolymorphicsystem duringanalysis.Inspiteofsuchdifﬁculties,amorphous pharma-ceuticals, which are of great interest because of their better solubility,andthus,betterbioavailability,havebeenthesubjectof severalstudies(BrumandBurnett,2011; Miyanishietal.,2013;

Suranaetal.,2003).

Mannitolhasbeenchosenforthecurrentstudy,inparticular because of the kinetic and thermodynamic stability of its polymorphicsystem. D-Mannitol, or

(2R–5R)-hexane-1,2,3,4,5,6-hexolaccordingtoIUPACnomenclature,is apolyhydric alcohol withthechemicalformulaC6H14O6.Itisoneofthemostcommon

excipientsinpharmaceuticalproductsduetoitschemicalstability andnon-hygroscopicity.Asanactiveingredient,ithasbeenused fortreatingrenalfailureandintracranialhypertensionandmore recently as a bronchoconstrictor (Tang et al., 2009). Several publicationsinrelationtoD-mannitolpolymorphscanbefound;

however, they are somewhat confusing and sometimes even

contradictory. D-Mannitol can exist as four crystalline forms,

threeanhydrousformsnamely

a

,

b

and

d

andahemihydrateone. The

d

formisenantiotropicallyrelatedto

a

and

b

forms.Themost stable form is

b

-mannitol, and the less stable at ambient conditions is the

d

form. Nevertheless, it has been observed thattheunstableform,

d

,canbestableforaperiodofatleast 5yearsatroomtemperature,ifstoredindryenvironment(Burger

etal.,2000).

Bothphysicochemicalpropertiesandpolymorphic transforma-tionbetweencrystallineforms ofD-mannitol thatmayoccurin

crystallization,mechanicalmillingandthermaltreatmentstudies have been successfully characterized by multiple solid-state analyticalmethods(Brunietal.,2009;Burgeretal.,2000;Caron etal.,2007).SurfaceenergyanalysesbyIGChavehighlightedthe acidic natureof the

b

form, attributed to the high density of hydroxyl groups at mannitol surface (Saxena et al., 2007). In addition,IGChasbeenusedtodifferentiatetwoopticalformsof mannitol,theracemic mixtureDLand D-mannitolcomposed of

onlyonestereoisomerinitsanhydrous

b

.Grimseyetal.(1999)

found that the dispersive interactions were stronger for the racemic mixture DL-mannitol. Using molecular modelling, the authors attributed this different behaviour to the different densities of the dispersive and acidic sites. More recently, investigationsconcerningD-mannitol havebeenfocused onthe

effect of milling or/and surface heterogeneity (Ho et al., 2010, 2012).Despiteitswidespreaduseinpharmaceuticalformulations, studies on the surface energetic properties of mannitol poly-morphshavebeenrarelyreported.

The current study focuses on the surface energetics of D

-mannitol polymorphsthroughdynamic contact angle measure-ments,DVSandIGCimplementation.Finally,thesolidanisotropyis studiedtoevaluatesurfaceheterogeneityatlowsurfacecoverage. Thedualaimofthisworkistohighlightthedifferencesbetween surfaceandbulkpropertiesofanhydrousformsofD-mannitoland

tocomparethesurfaceenergydeterminationtechniquesusedfor pointingouttheirrelevanceconsideringthephysicalsenseofthe measure.

2. Polymorphsgenerationandcharacterization 2.1.Polymorphsgeneration

2.1.1.Materials

Analytical grade organic solvents, acetone and methanol (MeOH),werepurchasedfromFlukaandAcrossOrganic respec-tively,bothwithamassfractionpurityhigherthan99.5%.High puritydeionizedwater(18M

V

)wasobtainedfromalaboratory puriﬁcationsystem.

D-MannitolandsorbitolweregenerouslysuppliedbyRoquette.

Thebatch,Pearlitol160C,iscomposedof99%of

b

mannitolmass percentageandonly1%ofsorbitol.Thebatch,Pearlitol200SD,is composed of a mixture of

b

and

a

mannitol while the batch NeosorbP100Tiscomposedofsorbitolbutnoinformationabout polymorphic composition has been given. The solubility of D

-mannitolwasdeterminedforeachdissolutionmedium.Duetothe highsensitivityoftheHPLCHi-Plexcolumntoorganicsolvents,the solubilityvaluesweredeterminedbytwodifferentways.HPLCwas usedonlywhenthesolvent waspurewater,andclassicsolvent evaporation(dryextractmethod)wasimplementedwhensolvent waswater/acetoneormethanol.Thesolubilityofthecommercial batchPearlitol160C in waterwas foundtobe157mg pergof solutionat20#_C._For _the_mixture_{water/acetone}_with_a _volume

ratioof1:1,thesolubilityat20#_C_was_found_to_be₃₄_mg_per_g_of

solution.Forpuremethanolat60#_C,_the_solubility_was_found_to_be

5mg per g of solution.It has tobe notedthat the dry extract method is less precise than the HPLC quantiﬁcation method,

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becauseitdoesnotallowtoquantifysorbitolinﬂuence,butitwas theonlyonefeasible.

2.1.2.Protocols

Therecrystallizationofpure

b

and

d

polymorphswasobtained throughcrystallizationofanaqueoussolutionofD-mannitolusing

acetoneasanantisolventaccordingtothefollowingsteps:

$Dissolutionof9gofD-mannitolin50gofwaterunderstirringat

roomtemperatureforatleast2h.

$FiltrationofthesuspensionusingaBüchnerﬁlterequippedwith a2

m

mpolyethylenemembrane.

$Additionof50mlofacetoneatroomtemperature,maintaininga vigorousstirring.

To obtainthe

d

form,thecrystalswereallowed togrow for maximum4min.Forthe

b

form,longertimeperiodswereused, allowingthepolymorphictransformation.

Forthe

a

mannitolgeneration,acrystallizationprocedureby seedingandfastcoolingwasusedaccordingto:

$Dissolution of D-mannitol in methanolat 60#C for 2hunder

stirring(2gin250mlofMeOH).

$FiltrationofthesuspensionusingaBüchnerﬁlterequippedwith a2

m

mpolyethylenemembrane.

$Seedingwithapurephysical

a

formobtainedbyDSC,asfollow:

-Firstcycle:heatingrateof20#_C_min"1_from₂₀_to₂₀₀#_C_followed

byacoolingcyclewitharateof5#_C_min"1_until₂₀#_C. -Second cycle: heating rate of 20#_C_min"1 _from ₂₀ _to ₁₆₀#_C

followedbyacoolingcyclewitharateof5#_C_min"1_until₂₀#_C. $Fastcoolingoftheﬁltrateinanice–ethanolbathundervigorous

stirringfor30min.

For all samples, the same ﬁltration, drying and storage conditions were used,that is a Büchnerﬁltrationwitha 2

m

m polyethylene membranefollowedbyadrying inanovenunder vacuum,at30#_C_and₂₀₀_mbar_for_at_least₃_days._Finally,_all_solid

sampleswerestoredinadessiccatorundervacuum(6%relative humidity). In order to remove the sorbitol impurity from the commercial powder, at least two consecutive recrystallization processeshavebeenperformedperorganicsolid.

2.2.Characterizationtechniques

Thedifferentcrystallineformsofanhydrousmannitol

a

,

b

and

d

werecharacterizedbyHPLCtoquantifychemicalimpuritiesand bysolid-stateanalyticalmethodssuchasDSC,XRPD,TGA,SEM,IR, confocalRamanspectroscopy,DVSandIGCtoquantifyandqualify physicalproperties.

2.2.1.Polymorphsﬁngerprints

X-ray diffractograms were obtained using a PANanalytical X’Pert ProMPDdiffractometer(set-upBragg–Brentano). Diffrac-tiondataareacquiredbyexposingthepowderssamplestoCu-K

a

radiation,whichhasawavelengthof1.5418Å.Thegeneratorwas setto45kVandtoacurrentof40mA.Thedatawerecollectedover arangeof8–50#₂

_u

_with_a_step_size_of_0.03#₂

_u

_and_a_nominal_time

per stepof39.9s, usingthescanningX’Celeratordetector. Data analysiswasperformedusingX’PertDataCollectorsoftwareand phaseidentiﬁcationwascarriedoutbymeansofPANalyticalHigh Score Plus software in conjunction with the ICDD Powder DiffractionFile2databaseandtheCrystallographyOpenDatabase. Ramanspectroscopyanalyseswereperformedwithanatomic force microscope equipped with a confocal Raman imaging

upgrade,Alpha300fromWITec.Thepositioningaccuracyofthe scantableis 1.5nminXYdirection and0.3nminZdirection.A magniﬁcationof50%andawavelengthof532nmwasusedasthe excitationsource,Nd:YAGlaser.TheRamandatawereacquired usingWITecProjectPlussoftwarethathasa16bitsresolutionand asamplingrateof250Hz.

InfraredspectrawerecollectedonaThermoScientiﬁcNicolet 5700 FT-IR spectrometer equipped with an attenuated total reﬂectionmodule(ATR).

DSCmeasurementswereperformedwithaDSCQ200fromTA Instrument.Measurementswereperformedonsamplesof3–5mg placed in non-hermetic aluminium panels, in the temperature range of 20–200#_C _at _a _heating _rate _of ₅#_C_min"1_. _All _data

measurementsareaveragesofat leastthreemeasuresonthree differentsamples. Thermogravimetric analyses wereperformed usinganTGA-DSC111fromSetaramonsamplesof5–20mgplaced innon-hermeticaluminiumpanels,performingcyclesfrom25to 250#_C_at_a_heating_rate_of₅#_C_min"1_.

2.2.2.Sizeandparticleshapeanalysis

Particleshape analyseswereperformedbyscanningelectron microscopy,usingaXL30FEGfromPhilips.Particlesizeanalyses fortheanhydrousformsofD-mannitolweredeterminedbyimage

analysisusingaPharmaVisionSystem830(PVS830)fromMalvern Instruments.Theparticlesdispersionpressurewassetat6bar.The numberofanalysedobjectswasﬁxedat70,000.

2.3.Characterizationresults,polymorphsscreening 2.3.1.Powdercrystallinityandpurity

ThechemicalpurityofeachpolymorphwascheckedbyHPLC using a Hi-Plex Ca ligand exchange column coupled with a refractiveindexdetector(analysisconditions:mobilephaseHPLC gradewater,ﬂowrate0.3mlmin"1_,_column_temperature₄₅#_C).

XRdiffractogramsofD-mannitolpureformsareshowninFig.1

andtheIRspectra inFig.2.Bothresultsareinagreement with thosepublishedintheliterature(Burgeretal.,2000),evenifno informationonchemicalpuritywasgiven.Despitethefactthat eachtechniqueprovidesmeaningfulinformation,andnosample preparation is required, both techniques may not be sensitive enough and have their own limitations. Indeed, no signiﬁcant differencesbetweenthecommercialpowder(1%of

a

-sorbitol)and the recrystallized

b

formwere detected. Anyway, detection of smallquantitiesis complexand maydependonthelocationof sorbitolwithinthepowder,nearto(at)thesurfaceorwithinthe bulkofthecrystals.

TheRaman spectra of D-mannitol polymorphsare shown in

Fig.3.Theseareinexcellentagreementwiththosepublishedinthe

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literature(Burgeretal.,2000;Haoetal.,2010).ConfocalRaman spectroscopyseemstobeasensitivecharacterizationtechnique, andithasbeenusedtostudypolymorphmixtures.Nevertheless, noqualitativeorquantitativeanalysisofthesorbitolpresencein thecommercialpowderhasbeenrelevant,maybeduetothefact that D-mannitol and its isomer, sorbitol, differ only by the

stereochemistry of one hydroxyl group (inducing subtle intra-and inter-molecular behaviour differences) or due to the low samplemassusedintheanalysis(somemicrograms).Finally,the chemical purity of the samples was conﬁrmed by thermal methods.

ThermogravimetricanalysesbyTGAwereusedtoensurethat no residual solvent was present in the samples. DSC analyses allowed differentiating the commercial powder Pearlitol 160C fromthe

b

pureform.Indeed,sorbitolpresenceinthecommercial powder decreases both heat of fusion and melting point of

b

polymorph.Theﬁrstendothermicpeakat81.4#_C,_found_during_the

analysisofthecommercialpowder,isconsistentwiththemelting point of

a

sorbitol (Nezzal et al., 2009). The endothermic/ exothermic event observed in

d

form was attributed to a transformationofthiscrystallineformintoamorestable

b

form. Closevaluesofmeltingpointsbetween

a

and

b

mannitolindicate smallvolumeenergeticdifferences.Alltheseresultspresentedin

Table1areinagreementwiththosefoundintheliterature(Bruni

etal.,2009;Burgeretal.,2000).

Forthedeterminationsoftheheatoffusion,usingasigmoid baseline,astandarddeviationoflessthan5%wasestimatedwhile

meltingpointsvaluesaremoreaccuratewithastandarddeviation oflessthan0.5%(sixmeasuresaverage).

2.3.2.Particlesizeandmorphology

AsshowninFigs.4and5,themorphologyofeachpolymorph andthecommercialsamplesisdifferent.Importantdifferencescan bealsofoundintheliterature,mostlyattributedtothedifferences inrecrystallizationprocedures(Brunietal.,2009;Hoetal.,2012). Asexpected,since

b

and

d

mannitolaregeneratedbythesame method,bothformsarealikewiththinnersticksfor

d

mannitol. Sizedifferencesarelinkedtocrystalgrowthduration.The

a

formis theﬁnestonewithaneedle-shapemorphologyandaD[

v

,0.5]of 25.3

m

mandD[v,0.9]of42.4

m

m(Fig.4b).Thecommercialsample Pearlitol160Cisformedbyirregularstickswithamedianvolume diameterD[v,0.5]of64

m

mandaD[v,0.9]of250

m

m(Fig.5a).

b

Mannitol is composed of better deﬁned sticks with smoother surfaces(Fig.4a),andithasaD[v,0.5]of26.7

m

mandaD[v,0.9]of 81.7

m

m.Inbothcases,itseemsthatsmallparticlesgetstuckon thesurfaceoflargerones.

3. Surfacebehaviour

Thesurfaceenergyofasolid,

g

s,canbedeﬁnedasthehalfofthe

energyofcohesion,whichistheenergyrequiredtoseparateand thencreatetwointerfacesofunitofsurfaceareafromaprimarily monolithic material and furtherdisplaceone separated partto inﬁnity(inadiabatic,reversibleconditions)(Lee,1991).Thisenergy ofcohesionisalsotheenergyofinteractionbetweenmolecules and atoms under consideration. The surface energy can be approached through the interactions of the solid with its environment,andthenthroughthenatureoftheintermolecular forces involved in the physisorption process. Indeed, surface energy can be divided into dispersive,

g

d

s, and non-dispersive

components,

g

ps.Thestudyofnon-polarmoleculesasn-alkanes

willgiveaccess to

g

ds valuewhile thestudy ofmolecules with

permanent dipolemoments, electricalcharges,which maygive risetoacid–base,ionicormetallicinteractionsamongothers,will giveaccessto

g

psvalues.

Whatever the system probe–solid, dispersive interactions alwaysoccur,theyarethefocusofthepresentwork.

3.1.Theoreticalbasis

Thisstudyislimitedtothemostwidespreadtechniquesand speciﬁcattentionwillbepaidtotheisothermsectionexploitation. Gravimetricadsorptiontechniques suchasDVS (dynamicvapor sorption) are based on the gravimetric measurement of the amountofvapouradsorbedonthesurfaceofasolid.Thistechnique allowstodetermineameanvalueofthesurfaceenergyofapowder basedonthewholeisotherminformation(StoreyandYmén,2011). Indeed,duringDVSanalysisacompletesurfacecoveragecanbe reached.

While wettabilityand DVS measurements providea macro-scopic average of the surface, techniques such as inverse gas chromatography, IGC, can be sensitive to local microscopic variations of the surface structure depending on the injection size. In practice, IGC experiments are generally performed accordingtotwoimplementations, whichdiffer bytheamount of probe molecules injected. The first implementation, called infinitedilution,IGC-ID,isdefinedbytheinjectionofverysmall quantities of molecules. Experimentally, is expected that the retention time or volume remains constant in function of the injection size; thus, probe molecules behaves independently (condition of linear chromatography). The second one, called finite concentration,IGC-FC, is based on higher solute concen-trations (non-linear chromatography), and some degree of

Fig.2.IRspectraofD-mannitolpolymorphs.

500 1000 1500 2000 2500 3000 3500 200 300 400 500 600 700 800 Raman shift [cm−1] Intensity β form α form δ form

(7)

interaction betweenprobe molecules is expected (Conder and

Young,1977).

However,whilestudyingD-mannitolpolymorphsthatarelow

speciﬁcsurfaceareaorganicsolids,someconcernsandquestions had arisen to actually differentiate these two domains of implementation: at which relativepressure, P/Psat, rangeis the

IGC-IDzone limited?Howsmallshouldbetheinjectionsizeto actuallyobtainretentiontimesindependentofthegasmolecules concentration? Moreover, is the linear part of the adsorption isothermdeﬁnedbysymmetricorslightlyasymmetrical chroma-togramsasadmittedinliterature?

Totrytoanswerthesequestions,surfaceenergyvalueswere estimated exploiting only the linear part of the adsorption isothermatverylowsurfacecoverage.Thiswillbepresentednext but, above all, preliminary bases of IGC theory need to be presented.Inparticular,thermodynamicapproachof physisorp-tion on a solid surface is reminded so as to point out the speciﬁcities of solid-adsorbed vapour system underlying the classicalresultsusedwheninterpretingIGCresults.

3.1.1.BasicIGCtheory

The time spent for a probe molecule to pass through the column,tR,reﬂectstheinteractionsbetweenthevapourmolecules

and the solid;it is then the key measure in IGC analysis. The strength of theseinteractions depends onthesolid nature and structure(surfaceheterogeneities),thenatureandquantityofthe probemolecules.

AsshowninFig.6,afractionofthisresidencetime,calleddead time,t0,correspondsonlytothetimeforaprobemoleculetoﬂow

throughthesolidwithoutanyinteractionandcanbedetermined

byanon-adsorbedmoleculesuchasmethane.Then,netretention timeisdeﬁnedas:

tN¼tR"t0 (1)

Takingintoaccountthepressuredropalongthecolumnusing theJames–Martincorrectionfactor,j,itispossibletorelatetNto

thenetretentionvolumepersamplemassunit,VN,through:

VN¼_mjFstN_273:15Tc (2)

wheremisthesolidmass,Fsisthecarriergasexitﬂowrateat

standard temperature and pressure, and Tc is the column

temperature.

Relatingaretentiontimeorvolume,toasurfaceenergyvalue needs to introduce some additional concepts. First of all, it is assumed that thesolid onwhich adsorptionoccurs, adsorbent, remainsunchangedinstructureandischemicallyinert.Theprobe moleculesintheadsorbedstatecalledadsorbatemayberegarded as a distinct phase whose volume is considered negligible comparedtotheprobemoleculesinthevapourphase,alsocalled adsorptive. The diminution of the surface tension, due to physisorption, is called the spreading pressure,

p

, and is the intensivevariablethatcharacterizestheadsorbedphase. Accord-ing to Ruthven approach (Ruthven, 1984), a new free energy thermodynamicfunctioncanbedeﬁnedas:

Fads¼Aadsþ

’

nsol (3)

wherensolisthemolenumberofadsorbentwhile

’

representsthe

change in internal energy per mole unit of adsorbent due to thespreadingoftheadsorbateovertheadsorbentsurface,Aadsis

theHelmholtzfreeenergyofthesystemadsorbate–adsorbent.

Fig.4.SEMmicrographsofD-mannitolpolymorphs;(a)bform,(b)/formand(c)dform. Table1

Summaryofphysicalsolid-statecharacterizationobtainedbyDSC.

Pearlitol160C NeosorbP100T Pearlitol200SD b-Form a-Form d-Form

Heatoffusion[Jg"1_] _300.20.4 _179.7 _292.10.2 _304.5 _294.4 _0.9/"2.1_{Melting/recrystallization} Meltingpoint[#_C]_(onset) _165.6_81.4 _96.8 _165.1_68.6 _166.7 _165.3 _146.8/156.2_{Melting/recrystallization}

(8)

Foradsorptiononatwo-dimensionalsurface,thesurfaceareaAin contactwiththeadsorbedmoleculesisdirectlyproportionaltonsol.

Sotheproduct

’

nsolisequivalentto

p

A.Hence,Eq.(3)turnsinto:

Fads¼Aadsþ

p

A (4)

Incaseofgasadsorption,thegastransferwilloccurlowering thefreeenergyofthesystemuntilequilibriumisreached(Fadsis

minimum).Theequilibriumoftheadsorbateisrepresentedbythe followingfundamentalthermodynamicequation,whichcombines theﬁrstandsecondlaws:

dFads¼"SadsdT"PdVadsþAd

p

"

mads

dnads (5)

ThankstotheEuler’shomogeneousfunctiontheorem,Fadscan

alsobeintegratedas:

Fads¼"PVadsþ

mads

nads (6)

SubtractingEq.(5)tothedifferentialofthefunctionsixleadsto anequilibriumrelationliketheGibbs–Duhemone:

"SadsdT"VadsdPþAd

p

"nadsd

mads

¼0 (7)

Giventhattheadsorbedphasevolumeisgenerallynegligible,the relationthatlinksvariablesalonganisothermaladsorptionisthen: A

@p

_@

_P ! " T" nads

@mads

@

P ! " T¼ 0 (8)

Equilibriumconditionsbetweentheadsorbedphase andthe adsorptiveoneimplytheequalityoftheirchemicalpotentials.In addition,adsorptivephaseisassumedtobehaveasanidealgas.In thiscase,Eq.(8)leadstotheGibbsadsorptionisotherm: A

@p

_@

_P ! " T¼ nads

@mg

@

P ! " T¼ RT Pnads (9)

Dependingontheprobemoleculesconcentration,theadsorbed phase may obey to different equations of state. At very low concentrations, it is supposed to obey an equation of state equivalenttoidealgaslawaccordingto:

p

A¼nadsRT (10)

Inthiscase,theGibbsadsorptionisothermbecomes:

@p

@

P ! " T¼

p

P (11)

IntegrationofEq.(11)leadstotheHenry’slaw,thatisalinear relation between adsorptive pressure and adsorbate spreading pressurethroughaconstantK:

K_¼

p

Por nads A ¼K P RT (12)

Weconsidernowtheisothermaladsorptionofnadsmolesof

adsorbateataspreadingpressure

p

2inequilibriumwithng"nads

moles of gas phase at a pressure P2 from a gaseous phase

comprisinginitiallyngmolesatapressureP1.Thevariationoffree

enthalpyofadsorptioncanbeexpressedas:

D

Gads¼nadsmadsðT;

p2

Þþðng"nadsÞ

mg

ðT;P2Þ"ngmgðT;P1Þ (13)

where

p

2istheequilibriumspreadingpressureatP2,bothbeing

relatedbyK=

p

2/P2.

Finalconditionsofthis adsorptionareequilibriumones.The chemicalpotentialoftheadsorbedphasecanthenbeexpressedas thatadsorptiveidealgasone.Eq.(13)turnsinto:

D

gads¼

D

G_nads g ¼RTln P2 P1¼"RTln P1K

p2

(14)

Asit wasalreadyenlightened,themeasuredvaluethatgives accesstotheequilibriumconditionsistheretentionvolumeVN,

anditcanbedirectlyrelatedtotheequilibriumconstantKfrom Eq.(12):

VN¼nads_PRT¼KA¼Kasm (15)

Takingintoaccount, allthehypothesespreviouslydescribed andrelatingEqs.(14)and(15),thevolumeVNcanberelatedtothe

changeinmolarfreeenergyofadsorptionby:

Fig.6.Principleofinversegaschromatography.

(9)

D

g_ads_¼_"RTlnP1VN

p2

asm (16)

Experimentally,Tistakentobethecolumntemperature,Tc.

Theﬁrstapproachtoquantifysurfaceenergyovercomingthe unknownarbitraryvalues,

p

2andP1dilemma,wassuggestedby

DorrisandGrayin1979.Theirmodelisbasedontheobservation

thatinachemicalfamilyofhomologues,theretentiontimeisan exponentialfunctionofthenumberofcarbonatoms(Derminot, 1981).Experimentally,itisnecessarytoinjectaseriesofn-alkanes andplotthevariationoftheterm"RTlnVNversusthenumberof

carbon atoms.Theslope ofthis lineisthevariationof thefree energyofthesystemduringtheadsorptionofamethylenegroup,

D

gCH2;

D

gCH2¼"RTln V_Nþ1

VN (17)

In addition,the changein free energy of adsorption canbe understoodastheadhesionoftwophasesduetotheinteraction forcesbetweenthemanddescribedbytheenergyofinteractionor itsopposite,theworkofadhesion(thatistheworknecessaryto overcometheinteractionsforces).Iftheprobemoleculesare n-alkanesandtheadsorptiontakesplaceonanon-polarsolid,the interaction forces are dominated by dispersive interactions (London type). Applying the model of Fowkes for Lifshitz-van derWaalsinteractionsrepresentingtheworkofadhesion,Wadh,

theGibbs freeenergy ofadsorption,

D

gads,canbeexpressedas

follows:

D

g_ads_¼NaagWadh¼Naag2 ffiffiffiffiffiffiffiffiffiffiffi

g

d l

g

ds q (18) FinallyEqs.(17)and(18)leadsto:

D

gCH2¼NaaCH22 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

g

d CH2

g

d s q ¼"RTlnV_VNþ1 N (19)

whereaCH2isthesurfacearea,6%10"18m

2_,_and

_g

d

CH2isthesurface energyofamethylenegroup,(35.6mJm"2_at₂₀#_C).

3.1.2.Surfaceenergyproﬁle

The SEA analysis software, Cirrus Plus from SMS company, proposestostudysurfaceheterogeneityusingIGC-IDbasis,andit istheoneusedinthisresearchwork.Surfaceheterogeneitystudies usingIGC-IDbasishavebeenproposedbyFafardetal.(1994)and describedbyYlä-Mäihäniemietal.(2008).Ascanbedepictedfrom

Fig.7,the

g

d

sproﬁleisdeterminedbyinjectingaseriesofalkanesat

differentconcentrations.

Theaimistorelatedifferentprobemoleculesconcentrationsto a surfacecoverage of thesemolecules over thesolid, toﬁnally correlatethesurfacecoveragetoasurfaceenergyvalue.

In our case, ﬁrst order method (FM) was used to study adsorptionisothermsfromIGCelutionchromatograms.IntheFM

method as in the peak maximum method (PM), different

concentrationsofprobemolecules(correspondingtodifferentP/ Psat)areinjectedintothecolumn(Fig.7–step1).

The net retention volume, VN, can be determined for each

injectionconcentrationusingthenetretentiontimeobtainedfrom ﬁrstordermoment(Eq.(2))oftheelutionpeak.TorelateVNto

surface coverage, n/nm, the software calculates the desorbed

amount,n,frompeakareaanalysis.Sincemonolayercapacity,nm,

for each alkane is calculated from the BET adsorption model, surfacecoveragecanbecalculatedfromthedesorbedamount,n,at eachprobeconcentration(Fig.7–step2).AsillustratedinFig.7, foreachalkaneataparticularsurfacecoverage

g

d

scanbecalculated

classically using IGC-ID theory via Dorris–Gray and/or Schultz approaches. Finally, each

g

d

s value can be related to a surface

coveragevalue(Fig.7–step4). 3.2.Surfaceanalysestechniques 3.2.1.Materials

Analytical grade organic solvents such as ethanol, toluene, dichloromethane,diiodomethane,formamide,ethyleneglycol33% and1,4-dioxanewerepurchasedfromFlukaorAcrossOrganicallof themwithamassfractionpurityhigherthan99.5%.Thenon-polar probesoctane,nonane,decaneandundecanewerepurchasedfrom Sigma,assay>99%.

3.2.2.Protocols

DynamiccontactangleswereobtainedwithaKrüssprocessor tensiometerK12in combinationwithaKsoftware.Thepowder sampleswereplacedinastainlesssteelholderwithholesinits bottomsmallenoughtoavoidthepowderﬂowingthroughthem. The samples, previouslypacked with a centrifuge at 1000rpm during5min,weresuspendedfromthemicrobalanceplacedinthe processortensiometerjustabovethesurfaceofthetestliquid.The liquidreservoirwaskeptat20#_C₍₂₉₃_K)_with_a_thermostated_bath

(HaakK20/DC5).

Gas adsorption manometry was performed in an ASAP

2010instrumentfromMicromeritics.Eachsamplewasdegassed undervacuumat50#_C₍₃₂₃_K)_during_at_least₇₂_h._For_comparison

purpose,argonwasusedastheadsorptiongas.Theanalyseswere carriedoutatatemperatureof"196#_C₍₇₇_K)_(liquid_nitrogen).

Gasadsorptionanalyses bygravimetrywerecarriedoutin a dynamic vapour sorption (DVS-2) instrument from surface

measurement systems SMS. The DVS measures sample mass

evolution using a Cahn microbalance with a resolution

(10)

experimentallydeterminedat5

m

g.Duringtheanalyses,avapour flowconstitutedofamixtureofprobe-saturatedanddrycarrier gas(nitrogen)surroundsthesample.Thepartialpressureofthe probe iscontrolled using mass flowcontrollers, and thewhole systemiskeptisothermalbyanenclosedcabinetfixedat25.0#_C

(297K).Isothermsweremeasuredusinganalyticalgraden-nonane asnon-polarprobeanddifferentpolarprobessuchasisopropanol andethanolwerealsotested.Thesamplesizewastypically70mg, and atleast onecycleof adsorption–desorptionwas studied: a cycleconsistsofmassmeasurementsversustimeuntilequilibrium isreached, performedatﬁxed increasing(decreasing)valuesof partial pressure vapour probe (P/Psat). The sorption isotherms

valuescalculatedarethen,theequilibriummassvaluesobtainedat each partial pressure with an equilibrium criterion of mass variationlowerthan5

m

gduring5min.

SpeciﬁcsurfaceareaandsurfaceenergyanalysesofD-mannitol

polymorphs were carried out using the IGC-surface energy analyser(IGC-SEA)fromSMS.Eachpolymorphsamplewaspacked intopre-silanisedcolumnsof300mmlengthand4mminternal diameter,pluggedwithsilanisedglasswool.Priortoanalysis,each columnwasconditionedat50#_C_for₂_h_at_0%_RH._Helium_was_used

asacarriergasat10sccm,andthecolumntemperaturewasﬁxed at 30#_C ₍₃₀₃_K) _during _the _analysis, _all _experiences _were

undertaken in identical conditions. Due to the progressive spreadingof theprobe molecules withthemigration time,the adsorption isotherms and the net retention volume, VN, were

determinedusingpeakcenterofmass,whichcorrespondstothe FM method (Giddings, 1965). The retention times of probe moleculesandmethaneweredeterminedusingaﬂameionization

detector (FID). Dead volume was determined by methane

injections and dispersive surface energy determination by a homologousseriesofvapourn-alkanes(undecane,decane,nonane and octane).Dispersive surface energy proﬁles werecalculated usingCirrusPlussoftware(version1.2.3.2SMS,London)following Dorris–GrayandSchultzapproaches.

Forallspeciﬁcsurfaceareaandsurfaceenergydeterminations, astandarddeviationoflessthan5%wasestimated.Forcomparison purposes, all columns were ﬁlled with a mass of powder correspondingtoasurfaceareaof0.5m2_._The_idea_was_to_study

similarsurfacecoveragevaluesobtainedexperimentally. UnlikeothersIGCequipments,IGC-SEAhasaninjectiondevice thatallows tocontroltheinjection size,and soit worksﬁxing speciﬁc surface coverage values. The corresponding surface coverage,

u

s,ateachinjectionconcentrationistheratiobetween

the desorbed amount, n, determined from peak area and the monolayercapacityofthesolid,nm(

u

s=n/nm).Inourexperiments,

nmwasdeterminedfromthespeciﬁcsurfaceareavalueobtained

byIGC-SEAusingn-nonaneasprobemolecule. 3.3.Resultsanddiscussion

3.3.1.Surfaceenergeticscharacterizationbywettingforce:capillary penetrationmethod

Theﬁrstapproach todetermine surfaceenergy wasthrough dynamic contact angle studies. The aim was on one hand, to evaluate the wettability of mannitol using different liquids, allowingustodeterminewhichsolventsshouldbeusedforDVS analyses,ontheotherhandtotestthesurfaceenergyestimationby thisapproach.To undertakethis, twocommercialbatcheswere used. In fact, this type of analysis involves high quantities of powder, so the batch Pearlitol 160C was used to evaluated

b

mannitol,andthebatchPearlitol200SDwasusedtoevaluate

a

mannitol behaviour. Contact angle measurements on bulk powdersusingthecapillarypenetrationarepresentedinTable2. The geometric factor C, linked to packing characteristics, was determinedusing n-hexane, and theerrorassociated toallthe

measures was evaluated as the standard deviation of four measurements.

Severaltheoriescanbeusedtoconvertcontactangledatainto surfaceenergyvalues.Theobjectiveistoﬁndapropercombination oftestsolventsknowingthatthesurfaceenergyvaluedependson theliquidsthatareusedandthetheorythatischosen.Thesurface energyresultsobtainedbycapillaryrise,usingOwens–Wendtand Fowkesmodels,aregatheredinTable3.

ThemodelproposedbyOwens,Wendt,RabelandKaelbledefines surfaceenergyasa sumof a dispersivecomponentanda polar component(OwensandWendt,1969).Thesurfaceenergyvalues were evaluatedwithout usingwaterand ethanolassolventsfor improvingthefitconfidence(R2160C=0.956andR2200SD=0.909).For

water,itseemsthatthehydrophiliccharacterofmannitoldoesnot ensurethatthemechanismofliquiduptakeisonly adsorption,anda partialdissolutionofthepowdercouldoccur.Fowkesmodelhas similar basis as the model above but determines the two components,dispersiveand non-dispersive,takingintoaccount the spreading pressure,

p

(Fowkes, 1964). In contact angle measurements,Fowkesmodelisgenerallyappliedonlywithtwo liquids, wateranddiiodomethane. Inourcase, weused diiodo-methanetoevaluateddispersiveinteractionsandethyleneglycol 33%ratherthanwatertoevaluatedpolarinteractions.

Contactangleanalysisallowstochoosethesolventsneededfor DVS studieshighlightingthedifﬁcultiesof solvent choicefor

b

mannitol analysis, for which acceptable wettability behaviour (

u

!0)islimitedton-hexane.For

a

mannitol,n-nonanewasused asprobemoleculetostudy

g

d

s andpolarmoleculesas

dichloro-methaneandethanol,tostudy

g

pscomponent.

As a conclusion, capillary rise measurements give a global approachofthesolidsurfaceenergy,beingawareofthelimitations and therelativityof theaccuracy(lowR2 _results)_of_the_values

gatheredinTable2,wehaveshownconsistencybetweenOwens– WendtandFowkesmodels.

3.3.2.Surfaceenergeticscharacterizationbyadsorptiontechniques: solid–vapourinteractions

Alltheresultsobtainedfromsolid–vapouradsorption techni-quesare gatheredinTable 4.Speciﬁc surfaceareavalues were determined by three different techniques such as manometry

Table2

DynamiccontactanglemeasurementsonD-mannitolcommercialpowdersby capillaryrise.

Solvant Contactangleu[#_] Pearlitol160C C=3.4%10"5_[cm5_] Pearlitol_C₌_1.75_%10200SD"5_[cm5_] n-Hexane 0.0 0.0 n-Octane 38.0*4.0 – n-Nonane 38.6*3.2 0.0 Ethanol 43.1*4.1 26.1*2.5 Toluene 41.5*2.8 0.0 Dichloromethane 43.1*4.1 21.0*2.0 1,4-Dioxane 47.3*1.6 0.0 Diiodomethane 76.4*0.7 55.7*2.3 Formamide – 58.5*2.6 Ethyleneglycol33% 84.2*1.5 75.6*1.7 Water 79.1*0.3 61.3*3.4 Table3

Surfaceenergy[mJm"2_]_analysis_determined_by_capillary_rise_and_different_models approach.

Solid/model OwensandWendt Fowkes

gd

s gps gs gds gps gs Pearlitol160C 18.7 4.8 23.5 19.5 4.7 24.2 Pearlitol200SD 27.6 6.1 33.7 31.1 4.2 35.3

(11)

usingargon(ASAP),gravimetryusingDVSandIGCwithalkanesas probemoleculesforbothlastones.Alldataexploitationisbasedon theBETadsorptionmodel.

For the DVS analysis, the baseline instrument stability was especially important due tothefact thatthe absolutelevelsof vapouruptakewereinthedetectionlimitsatlowP/Psat.Infact,the

absolutevapouruptakeswerelow,typicallylessthan0.3%.Asan exampleforthecommercialform,Pearlitol160C,anadsorptionof 0.025% at P/Psat close to one was obtained, while for

b

and

d

-mannitolamassuptakesmallerthan0.3%wasobtainedatthe samepressureratio.

Tostudysurfaceenergyfromagravimetrictechniquesuchas DVS,thesurfacetensionofthesolventhastobetakenintoaccount tohaveaccuratevalues(n-hexane

g

d

s= 18.4mJm"2andn-nonane

g

d

s= 22.7mJm"2). Indeed, the probe molecules must have a

surfacetensionlowerthanthesolidsurfaceenergy(i.e.liquidmust wet thesurfacesolid,

u

!0#_)._Also, _the_vapour_uptake _must_be

adsorptionandthermodynamicequilibriumatallpartialpressures must be reached. So, as expected from dynamic contact angle results(Table2),DVSstudieshavebeensuccessfullyperformedfor the batch 200SD and the pure

a

form. Moreover, despite the physicalcompositiondifferences,theobtainedisothermsshowed aclassictypeIIBETshaperevellingsimilaradsorptionbehaviour (+50mJm"2_).

For allIGCexperiences,anexperimentalvalueoftNfor each

probemolecule,ateachsurfacecoveragevalue,wasfundamental inordertoavoidanymeaninglessextrapolation.Thus,duetothe limitations of SEAinjection system,n-heptanewas not usedas probe molecule because it cannot be injected at low surface coveragevalues(

u

s<0.01).Concerningn-undecane,itcannotbe

injected at

u

s>0.01,but,even ifitcanbeinjectedat reallylow

u

s+0.0001,noisysignalswereobtained,andproblemsofreturnto

thebaselineafterinjectionwereobserved.Also,forn-undecane, strong differencesbetweenpeak maximum and peak center of

mass werefound, showingimportant asymmetryof theoutlet pulsepeaks,whichinducedagreaterrorintheR2_values_obtained

forthealkanesline(step3onFig.7).Thus,tostudysurfaceenergy of D-mannitol polymorphs, C₈, C₉ and C₁₀ were used as probe

molecules.Nevertheless,forC8,alinearapproximationwasusedto

obtainlowsurfacecoveragevaluessinceitcannotbeinjectedat

u

s<0.001.

Incaseofpolarinteractionsstudies,allvapourprobescouldnot be injected at low surface coverage values (

u

s<0.02), and

asymmetrical chromatograms were obtained. As it was not possibletodetermineHenry’sregion,onlyn-alkanesarethefocus ofthiswork.

InIGC-ID,averylowconcentrationofvapourprobeisinjected. Thus, no probe-probe molecular interactions are expected to occur and the adsorption follows Henry’s law. The chromato-grams have a Gaussian shape, and the retention time is independentoftheamountofprobeinjected.Forsomeorganic solids,thisregionmaybedifﬁculttoobserve,thespeciﬁcsurface areaandtheintensityoftheinteractionsseemtoplayakeyrole. Indeed,in thecaseoflowsurfaceareasamples,themonolayer capacityofthesolidiseasilyreached(

u

s=1).Thereby,aprecise

controloftheinjectedamountiscrucialtostudysurfaceenergyat the“zeroconcentrationregion”.

MostauthorsdeﬁnetheIGC-ID zoneat lowvapour concen-trations, typically for P/Psat<0.03. To verify this statement for

organicsolids,inourexperiments,theHenryregionwasdeﬁned foreachprobemolecule.Thechosencriterionwaslinearityofthe adsorptionisotherm,withacorrelationcoefﬁcientR2_>_0.999._For

almostallsolidsstudied,thesodeﬁnedHenry’sregionrevealedto becomposed of two zones. Theﬁrst onewas characterized by chromatogramshavingaGaussianshapeandbythefactthatthe retentiontimewasindependentoftheamountofprobemolecules injected,asshowninFig.8a.ThisIGC-IDregionwasfoundtobe limitedtoreallylowsurfacecoveragevalues:for

b

,

d

mannitoland

Table4

SpeciﬁcsurfaceareasanddispersivesurfaceenergiesofD-mannitolpolymorphs. Solids Speciﬁcsurfaceareaas

[m2_!_g"1_]

Dispersivesurfaceenergygd s [mJ!m"2_]

ASAP-Ar DVS IGC-C9 DVS CGI

us=0.04% CGI us=0.6% CGI us=8% Pearlitol160C 0.41 – 0.37 – 70.7 61.6 44.9 Pearlitol200SD 1.59 C7-0.9 1.68 49.5 81.1 80.2 54.9 NeosorbP100T 1.16 – 4.40 – 45.4 45.1 42.4 b-Form 0.39 – 0.37 – 40.0 39.6 38.2 a-Form 8.40 C9-5.61 8.54 51.4 74.9 74.0 45.5 d-Form – – 1.01 – 40.3 40.4 38.4

(12)

Pearlitol160C,thiszonewaslimitedto

u

s<0.001.Thesecondzone

wascharacterized byadecrease ofthenetretentiontime with increasingsurfacecoverage(Fig.8b).For

a

,mannitoltNwasnever

independentoftheinjectedamount,sotheﬁrstzonewasnever reached. Thisdifference canbe attributedtohighsolid surface heterogeneity (Fig. 9) and to the strength of the interactions involved.

AsshowninTable4,the

a

formisthemostenergeticallyactive formwith

g

d

sof74.9mJm"2at

u

s=0.04%.Thesefoundinghighlight

thepotentialof pure

a

polymorphin drypowderinhaler(DPI) formulations.Nowadays,itiswellknownthatsurfaceproperties playafundamentalroleinthedrug-carrierinteraction.Tangetal.

(2009)studiedsurfaceenergyofdifferentD-mannitolbatchesto

explainaerosolperformance.Theauthorsconcludedthathigher surface energy powders can lead to an improvement of the respirablefractionoftheactiveingredient.Ithastobenotedthat surface energy analysis must to be performed together with particles dynamics studies (packing, contact area and detach-ment).Indeed,particlesshape is animportantfactorin aerosol performance.Itseemsthatneedle-likeparticlesreacheasierdeep lungsdepositionwithoptimumtherapeuticbeneﬁt(Tangetal., 2009).Thehighersurfaceenergybatchobtainedbytheauthorsis composedofamixtureof

a

and

b

mannitol.Fromourresults,this highvalueisattributedtothepresenceof

a

form,whichgenerates morecohesiveandadhesivepowders.Indeed,thepresenceof

a

mannitol in the commercial powder 200SD seems to highly inﬂuencethemixturebehaviour(Table4).

Themostcommonlyusedcarrieris

a

lactosemonohydratewith a

g

dsof+40mJm"2atP/Psat+0.04(Hengetal.,2006).Nevertheless,

ithasbeenshownthatlactosecanpromotechemicaldegradation of some active pharmaceutical ingredients when used in formulations as an excipient (Guenette et al., 2009). Thus,

a

mannitolhavingahighsurfaceenergy,stabilityandwelldeﬁned needle-shape morphology is a possible candidate for useas a bronchoconstrictorinDPIformulations.

Thestable

b

formislessactivewith

g

d

sof40.0mJm"2andnot

muchdifferentof

d

formwith

g

d

sof40.3mJm"2.AfterDVSanalysis,

wherevapour uptakelevelswerein thedetectionlimitsrange, doubtsaboutisothermtype(IIor III)havearisenforthesetwo forms.Unfortunately,theadsorptionbehaviourcannotbestudied at

u

s>1withIGC-SEAequipmenttoconﬁrm(disconﬁrm)isotherm

type.Besides,signiﬁcantdifferenceshavebeenfoundbetweenthe commercialpowderandthe

b

pureformobtainedby crystalliza-tion. These differences could be mostly attributed to particles morphology; the recrystallized

b

mannitol seems to be more “homogeneous”(Fig.4a)thanthecommercialpowder(Fig.5a). Anisotropiesinthemorphologyofthecommercialformcanbe

seenashighenergeticsitesthatinﬂuencethesurfaceenergyvalue obtainedatlowsurfacecoverage.

Sorbitolinﬂuenceon

b

mannitol,throughPearlitol160Cbatch, was not quantiﬁed. Indeed, sorbitol surface behaviour was evaluatedviathecommercialbatchNeosorbP100T.Nevertheless, DSCanalysishighlightedthatthisbatchisconstitutedmostlyof

g

-sorbitol(45mJm"2₎_while_the_polymorphic_form_present_in_the

batch Pearlitol160C may mostlikely be

a

-sorbitol, which is a metastableformnot availablepurecommercially(Nezzaletal.,

2009).

Thesurfaceenergyvalueobtainedforthestable

b

formisin agreement, but lower,withthose obtainedinthe literature via contactangleonasinglemacroscopiccrystalusingOwens–Wendt model(Hoetal.,2010).Indeed,crystalline

b

mannitolobtainedin thisresearchisclosertothelessenergeticallyactivefacet(011) thantothemoreenergeticallyactiveone(010)determinedbythe authors(44.0mJm"2_)._Saxena_et_al.₍₂₀₀₇₎_studied_surface_energy

bydynamicmolecularmodellinganddetermineda

g

d

sof56.2mJ

m"2_for_the_plan₍₀₂₀₎_and_a

_g

d

sof55.3mJm"2fortheplan(110).

Nevertheless, these high values were never obtained in this researchwork.

The results obtainedvia IGC at

u

s= 3% for the commercial

powderPearlitol160CaresimilartothoseobtainedbyHoetal.

(2010)witha

g

d

s of49.5mJm"2.Moreover,thesevaluesarealso

similar tothose obtainedby Saxena et al.(2007) using IGC-ID classicalapproach(P/Psat+0.03),witha

g

ds of48.2mJm"2.

Dorris–GrayandSchultzmodelshavebeenusedtodetermine

g

d

s.Nevertheless,SchultzmodelshowedslightlylowerR2values

foralmostallpolymorphsatalmostallsurfacecoveragevalues. TheseresultsareinagreementwiththeresultsofYlä-Mäihäniemi

etal.(2008).Theauthorsattributedthisfacttotheuncertaintyof

thecross-sectionalareaofmoleculesinvolvedinSchultzequation (inﬂuence of molecular shape and temperature). Nevertheless, thesedifferenceswerenotthatcriticalinthiswork.

The surface energetics proﬁles obtained using Dorris–Gray approachareshowninFig.9.AcriterionoftheﬁtR2_>_0.999_for_the

lineformedbythealkaneswasusedtoensurethequalityofthe data(Fig7–step3).Thisrestrictioncorrelatesquitewellwiththe Henry’szone determined byisotherms analysis, but itwas not exclusive.Indeed,itwasfoundthatforsomesolidsthiscriterion couldbecheckedforlargersurfacecoveragevalues,whichwere not related toisotherm linearity. As an example, in case of

b

mannitol, Henry’s domain is limited to

u

s<10% while a ﬁt of

R2_>_0.999_were_obtained_for

_u

s<40%.

It seemsimportanttohighlightthedifﬁcultiestodetermine Henry’sdomain.Indeed,forsolidswithhighsurfaceinteractions, as

a

mannitol, isotherm shape can be quite well described at

u

s<30%. For solids with low surface interaction, as

b

and

d

mannitol,ahighprecisionandcontroloftheinjectedamountis fundamental to determinelinearity domain; so is an adequate numberofexperimentalpoints.

AsitcanbenotedfromFig.9,

b

and

d

formsseemtobemore energetically homogeneous than the

a

form. Moreover non-signiﬁcantdifferencesbetween

b

and

d

havebeenfound.These resultscanbeinagreementwiththestatementsofHoetal.(2012), wheretheauthorspropose thatthesurfaceenergy distribution does not depend on total surface area of the sample but is dependentonthecontributionofenergeticsitespresentonthe solid.

DifferencesobtainedbetweenDVSandIGC-IDanalysesfor

a

mannitol are attributed to the physical sense of each surface energydetermination.TheDVSresultrepresentstheaverageofall energeticssites present in thesolid. Indeed, in DVS analyses a complete coverage of thesolid surfacewas reached and so an averagevalueofthesurfaceenergeticsisexpected.Contrariwise,in IGC-IDstudiesthedispersivesurfaceenergyisgenerallyattributed

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 35 40 45 50 55 60 65 70 75 80 Surface coverage Dispersive Surface Energy [mJ/m 2] β form α form δ form

Fig.9.SurfaceheterogeneityanalysisofD-mannitolpolymorphsusingDorrisang Graymodel.

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tothehigherenergeticsitesofthesurface.Ifthestudiedsolidis homogeneous, energeticallyspeaking,bothtechniquesare com-parable.Whenthesurfaceheterogeneityisstudied(Fig.9)using IGC-IDtheoryintheHenry’sdomain,wecanseethatthesurface energeticsof

a

mannitolgoesfrom75.7to45.5mJm"2_._This_last

value is closer but lower than the results obtained by DVS, 51.4*2.9mNm"1.TheseresultsaredifﬁculttoexplainbecauseIGC analyses were made at really low surface coverage,

u

s<12%,

showing a highly heterogeneous surface, for which energetics proﬁle is more inﬂuenced by the higher energy sites. Indeed, retentiontimedistributioncanbedescribedas:

tN¼

X

niti¼Xinit0eEi=RTc

with

t

i the residence time on the site i,Ei interaction energy

betweentheprobeandthesitei,and

t

0aconstant.

Thus,IGCvaluesshouldneverbesmallerthanthoseobtained by DVS. To get more conclusivesurface analysis, heterogeneity should be studied by IGC-FC using the adsorption energy distribution model (Balard, 1997)or/and by contact angle in a macroscopiccrystal.

Fromacriticalpointofview,theinjectionsystemoftheIGC-SEA equipment allows to control the injected amount of vapour molecules, andmoreover,allowstoinjectsmallquantitiesof it. Theseassetshavebeenextremelyimportantinthisworkbecause theywerethekeytodetermineHenry’sdomaininlowspecific surfaceareasolids.However,therearesomepointsthatcannotbe neglectedwhile usingtheSEAequipment todetermine surface energy.Thefirstoneisthatthesurfacecoverageratiodefinedby SMS,n/nm,isameanvaluebasedonthehypothesisthatmolecules

areequallydistributedoverthesurfacesolid.Thisdoesnotreﬂect reality because of the nature of the chromatographic elution process(Giddings,1965).

ThesecondoneisthattheDorris–GrayorSchultzapproaches have to be applied in the Henry’s law region where lateral molecular interactions arenegligible,andthe thermodynamics functionsdependonlyonadsorbate–adsorbentinteractions(for isothermstypeII,IVandV).Hence,thedeterminationofHenry’s region of the adsorption isotherm should be performed with care, experimental data points should be numerous enough (Fig.7–step1).Anotherpointthatshouldbetakenintoaccount is thatthese methodsare also based on surface homogeneity assumption,soonlyoneenergysiteisexpected.Assumingthat solids are heterogeneous and that the variation of the net retentiontimeinHenry’sregionisduetoamulti-sitessurface,it seems necessary tonoticethatthe

g

d

s valueattributedtoeach

surfacecoveragedoesnotcorrespondtoanaverageenergyvalueof thesites“visited”bytheprobesmoleculesandisspeciﬁctoagiven surfacecoverage.Carefulinterpretationofthesenumericalvalues hastobemade.

4. Conclusions

The results obtained enlightened signiﬁcant differences be-tween bulk and surface properties of D-mannitol polymorphic

system. As each technique provides speciﬁcinformation of the solid, the combination of these techniques allows a good understanding of the solid-state form. The combined set DSC and IGC solid-state techniques highlight both surface-bulk energetic differences. Moreover, DSC solid-state analyses were found tobea reliable techniquetodetermineboth polymorph physicalpurityandsorbitoldetectionwithinthesamples.

Surfaceenergyanalysisthroughdynamiccontactanglestudies gives a global idea of solids wettabilityand sohelps todeﬁne solvents of interest for studies by DVS and IGC. Nevertheless, surface energy valuesobtainedfor thecommercialpowdersby

dynamic contact angle were substantially lower than those obtainedbyDVSandIGC.Thesedifferencescanbeattributedto thelowerﬁtconﬁdencevalues,R2<0.96,obtainedforallmodels studiedOwens–WendtandFowkes.

DVSanalysiswasnonexploitableformostofthestudiedsolids. Infact,duetothelowadsorptionatlowpressures,

b

and

d

forms wereinthedetectionlimits,anditwasnotpossibletoanalyses them.ItseemsthatDVSanalysisisnotsuitablefortheanalysisof solids with low speciﬁc surface area and weak adsorbent– adsorbate interactions (adsorption behaviour). Nevertheless, it givesa globalviewof theadsorptionbehaviourbetweenprobe moleculeandthesolid,allowingtodetermineisothermtypeandto quantifythespreadingpressure.

IGCstudieshighlighted,withnoprecedentinliterature,surface energy differences between the forms

a

and

b

mannitol:

a

mannitolrevealed tobemoreenergeticallyactive witha

g

d s of

74.9mJm"2₍

_u

s!0)while

b

mannitolshowedavalueof40.0mJ

m"2 ₍

_u

s!0) similarto

d

mannitol (40.3mJm"2). These results

explainandcorroboratedtheuseof

a

polymorphasadrypowder inhaler(DPI),increasedbyitsneedle-shapemorphology.

To study surface heterogeneity by IGC-ID basis, it seems fundamentaltodeterminethezonewhereHenry’slawholds,due tothe fact that all thermodynamics assumptions are based on linear chromatography. Indeed, it seems that for low specific surface areasolids this region is almost not observable,so for reliablesurfaceenergyestimation,aprecisecontroloftheinjected amountiscrucialinordertoobtainverylowsurfacecoverage.It shouldtobenotedthatlowspecificsurfaceareaseemsnottobe theonlyrestrictiontothelimitedHenry'sregion;theinteractions strengthandsurfaceheterogeneityseemtohaveamoresignificant impact.

Thewell-knowninﬁnitedilution,orlinearchromatography,is deﬁnedbyHenry’sregion.IncaseofD-mannitol,thewordlinearin

thesensethat theHenry’scoefﬁcient, K, is independentof the probeconcentrationwasneverobtainedforthe

a

form.Inpractice, theobservedpeaksarequiteasymmetricalanddependentofthe injection size (forboth peak maxima and firstorder moment). Thus,inthewholesenseofitsdefinition,thissodefinedIDregion revealstobeabsentoralmostnon-observable.

Surfaceheterogeneityanalysis, in Henry'sdomain,showed a highly heterogeneous

a

mannitol (74.9 to 45.5mJm"2₎ _with _a

quitehomogeneous

b

and

d

mannitol.Moreover,nosigniﬁcant differences between these last two forms have been detected (+40–38mJm"2_).

The inﬂuence of size and morphology in surface energy behaviourof D-mannitol polymorphs is the subject of separate

papercurrentlyinpreparation. Acknowledgments

The authorswould like toacknowledge Sylvie delConfetto, Severine Patry and Veronique Nallet for technical support. GratefullyacknowledgestoRoquetteFrancefortheprovisionof thepharmaceuticalssolidsusedinthiswork.

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