Polymer-plasticizer compatibility during coating formulation: A multi-scale investigation

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O

pen

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rchive

T

OULOUSE

A

rchive

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uverte (

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To link to this article : DOI : 10.1016/j.porgcoat.2016.08.008

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To cite this version :

Jarray, Ahmed and Gerbaud, Vincent and

Hemati, Mehrdji Polymer-plasticizer compatibility during coating

formulation: A multi-scale investigation. (2016) Progress in Organic

Coatings, vol. 101. pp. 195-206. ISSN 0300-9440

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Polymer-plasticizer

compatibility

during

coating

formulation:

A

multi-scale

investigation

A. Jarray

a,b,∗

_,

_V.

_Gerbaud

a,b

_,

_M.

_Hemati

a,b

a_Université_de_Toulouse,_INP,_UPS,_LGC_(Laboratoire_de_Génie_Chimique),₄_allée_Emile_Monso,_F-31432_Toulouse_Cedex_04,_France b_LGC,_INP,_ENSIACET,₄_Allée_Emile_Monso,₃₁₄₃₂_Toulouse,_France

Keyword: Plasticizer Miscibility Pharmaceuticalproducts Coating Moleculardynamics

a

b

s

t

r

a

c

t

Duringtheformulationofsoliddosageformscoating,plasticizersareaddedtothefilmformingpolymer toimprovethemechanicalpropertiesofthecoatingshellofthedrugproduct.Forthecoatingformulation tobesuccessfulandinordertoproduceflexiblecontinuousfilm,theplasticizershouldbecompatible withthefilmformingpolymer(i.e.highplasticizer-polymermiscibilityinsoliddispersion)(McGinity andFelton,2008).Thispaperproposesandcomparesdifferentmulti-scalemethodstopredictthe com-patibilitybetweenplasticizersandfilmformers.Themethodsarebasedon,i)Moleculechargedensity usingCOSMO,ii)SolubilityparametercalculationusingMoleculardynamics,iii)Mesoscalesimulation usingDPD,whereweproposeacoarse-grainmodel,andiv)experimentalDSCanalysisforvalidation. ThemethodsaretestedforvariousblendsincludingHPMC-PEG,MCC-PEGandPVP-PEG.Thedifferent methodsshowedsimilarresults;PEGplasticizerdiffusesinsideHPMCandPVPpolymerchains,thereby extendingandsofteningthecompositepolymer.However,MCCsurroundsPEGmoleculeswithout diffus-inginitsnetwork,indicatinglowPEG-MCCcompatibility.WealsofoundthatDPDsimulationsoffermore detailsthantheothermethodsonthemiscibilitybetweenthecompoundsinaqueoussoliddispersion, andcanpredicttheamountofplasticizerthatdiffuseinthefilmformingpolymernetwork.

1. Introduction

Polymeric film coatings are widely used for oral-controlled

orsustaineddrugrelease.Theygenerallyconsistof mixturesof

various materials that are added to confer or enhance specific

propertiestothefinalproduct.Typically,acoatingdispersionis

composedofwater,film-formingpolymer,plasticizerand other

additivessuchasfillersandstabilizers.

Today,importantdifficultiesinpolymericcoatingformulation

are; a)theassessment ofpolymer-plasticizerinteraction,b)the

selectionofasuitableplasticizercompatiblewiththefilm-forming

polymer,andc)understandingthemechanismbywhich

plasticiz-ersimprovetheflexibilityofcoatingfilmsatthemolecularand

mesoscales.

Variousstudieshavebeenreportedintheliterature,

investigat-ingtheeffectofplasticizersonthepropertiesofthefinalpolymeric

∗ Correspondingauthorat:UniversitédeToulouse,INP,UPS,LGC(Laboratoirede GénieChimique),4alléeEmileMonso,F-31432ToulouseCedex04,France.

E-mailaddresses:ahmed.jarray@ensiacet.fr(A.Jarray),

vincent.gerbaud@ensiacet.fr(V.Gerbaud),mehrdji.hemati@ensiacet.fr

(M.Hemati).

coating.Laboulfieetal.[1]studiedtheeffectofplasticizeronthe

mechanicalresistanceandthermalbehaviorofcompositecoating

films.Theyfoundthatadditionofaplasticizer(polyethyleneglycol

(PEG))enhancedtheplasticbehavioroftheHPMC-basedcoating

filmsandimproveditsmechanicalproperties.Jarrayetal.[2]also

studiedtheaffinitybetweenpolymersandcoatingadditivesindry

andaqueoussystems.Saettoneetal.[3]foundthatthedrugrelease

isinfluencedbythetypeandamountoftheplasticizer.

In this work, we propose and compare four multi-scale

approachesallowingtochoosetheadequateplasticizerandto

for-mulate therightaqueous polymericcoating; thefirstapproach

is based on the generation of s-profiles of the materials.

s-profilespresentamap ofthechargedensityoverthesurfaceof

the moleculeand provideinformation aboutthe moleculeand

an understandingof themutualsolubilitiesof solvents[4]. The

secondapproachisamolecularscaleapproach,basedonthe

sol-ubility parameterı (i.e.thesquare rootofthecohesiveenergy

density).Thisparameterdescribestheintramolecularand

inter-molecularforcesofa substance.Itisa measureofthetendency

of a moleculeto interactwith thesurrounding molecules. The

solubilityparameterisusedinthecoatingindustryforselecting

compatiblesolventsforcoatingsmaterials,andinsurface

charac-terizationoffillers(e.g.calculationofinterfacialenergyassociated

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Fig.1. Schematicrepresentationofatypicalfilmformationmechanismandplasticizereffectondrugrelease.

with stearic acid/water interface) [5]. The third approach is a

mesoscaleapproach, wheredissipative particledynamics(DPD)

simulationisusedtoinvestigatethestructureofpolymeric

coat-ingdispersion,wherewefollowthesameDPDparameterization

used by Jarrayet al. [6]. The last approach is an experimental

thermalanalysisusingdifferentialscanningcalorimetry(DSC).The

developedapproaches aretested forvarioussystems composed

of polyvinylpyrrolidone (PVP), microcrystalline cellulose (MCC),

hydroxypropyl-methylcellulose(HPMC),polyethyleneglycol(PEG)

andwater.

2. Filmformersandplasticizer

2.1. Filmformers

Ingeneral,filmformersareorgano-chemical

macromolecule-formingsubstancesthat undergoapolymerizationreactionand

formcrystallineoramorphouscontinuousstructureasthe

coat-ingdries.Theroleofthefilmformeristoformacohesivecoating

filmonagivensubstrateand–whererelevant–toholdtogether

thecomponentsofthecoating[7].Filmformationistheresultof

theincreaseinpolymerconcentrationinthecolloidaldispersion,

leadingtotheformationofathree-dimensionalnetwork.

Theformationofapolymericfilmarisesfromthe‘coalescence’,

i.e. deformation, cohesion and polymer chain interdiffusion, of

theindividualcolloidalparticlesnormallyheldapartby

stabiliz-ingforces [8].Evaporationof theinterstitial waterupon drying

leadstothedeformationoftheparticlesofpolymeruntilcomplete

coalescence(Fig.1).Thismechanismrequiressufficientcolloidal

stabilitytoformclosepackinguponcoalescence;otherwise,poor

filmqualitymaybeobtained.Filmformationprocessalsorequires

thespreadingof thesolutionintoa thin-layer.Keddieetal.[9]

demonstratedthatvoidscouldremaininthefilmduringfilm

for-mationevenafterwaterevaporation.

Theobtainedfilmmustbesmoothanduniform.However,

typ-ically,filmcoatingpreparedfrompurepolymertendstobebrittle

andcrackupondrying.Toovercomethisproblem,onewayisto

addaplasticizertothecoatingdispersion.

2.2. Plasticizersincoatingformulations

Forpolymerswithlimitedfilm-formationability,aplasticizer

may be added to ease the deformation and to favor colloidal

particlescoalescence.Theplasticizerpartiallyeliminatesthe

inter-actions responsible for the mechanical cohesion between the

chains,andthereforeincreasestheirmobility.Asaconsequence,

therigidmaterialis transformedintosoft and flexiblematerial

[10].PlasticizersreducetheglasstransitiontemperatureTgand

theminimumpolymerfilmformingtemperature(MFT)atlevels

thatdependonthecoatingprocess.Plasticizersalsocreate

chan-nelsthroughwhichdrugdiffusesforpelletscoatedwithinsoluble

films[11](Fig.1).

Agoodchoiceofaplasticizerdependsonitscompatibilitywith

thepolymerandonthepermanenceoftheplasticizerinthefilm

during coating. Compatibility between a polymer and a

plasti-cizerproducesstableand homogeneouscoating film.Itis often

characterizedby a highmiscibility betweentheplasticizer and

thepolymerblend.Polymer-plasticizerincompatibilityinfluences

notonlythemechanicalpropertiesbutalsodrugrelease[12,13].

Permanenceofaplasticizermeansitstendencytoremaininthe

plasticizedmaterial;i.e.longtermcompatibility.Itdependsonthe

sizeofthemoleculeandonitsrateofdiffusion.

Bodmeier and Paeratakul [14,15] studiedthe distributionof

plasticizersbetweentheaqueousphaseand colloidalpolymeric

dispersions.Theyalsostudiedthefactorsinfluencingtherateof

diffusionofplasticizerthroughthepolymer.Duringsoliddosage

formscoatingpreparation,foroptimalmixingbetweenthe

plas-ticizer and the polymeric dispersion, Bodmeier and Paeratakul

recommendedtheintroductionofwater-insoluble plasticizerto

theaqueouspolymerdispersionbeforedilutionofthelatter.They

alsorecommendedalongerplasticizationtimeforwater-insoluble

plasticizersthanforwater-solubleplasticizers.Inhisworkonthe

coating of large Alumina particles, Ould-chikh [16] found that

addingaplasticizer(PolyvinylAlcohol(PVA))inaqueouspolymeric

suspensionreducesdramaticallythesegmentationorthecracking

ofthecoatingfilmsupondrying.

3. Materialsandmethods

3.1. Materials

Ourexperimentalstudyiselaboratedwithdifferentmaterials

widelyusedinfoodandpharmaceuticalindustries.Thepolymers

are;PVP:polyvinylpyrrolidone(K10),MCC:microcrystalline

cel-lulose(AvicelPH-101)andHPMC:hydroxypropyl-methylcellulose

(E19).ThechosenplasticizerisPEG400:polyethyleneglycol400.

AllthecompoundsarepurchasedfromSigma–Aldrich.

Polyvinylpyrrolidoneorpovidone(PVP)occursasafine,whiteto

creamy-whitecolored,describedasasyntheticpolymerconsisting

essentiallyoflinear1-vinyl-2-pyrrolidinonegroups[17].Although

PVPisusedinavarietyofpharmaceuticalformulations,itis

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Table1

Compositionofthedifferentformulationstudiedthroughoutthispaper. Formulationname Binder/coatingcomposition(w/w)

Polymer Plasticizer Solvent PEG10% – 10%PEG 90%water HPMC-PEG10%–10% 10%HPMC 10%PEG 80%water PVP-PEG10%–10% 10%PVP 10%PEG 80%water MCC-PEG10%–10% 10%MCC 10%PEG 80%water HPMC:hydroxypropyl-methylcellulose,PVP:polyvinylpyrrolidone,MCC: micro-crystalline.

cellulose,PEG:polyethyleneglycol.

wet-granulationprocesses[18,19]andasasolubilizerinoraland

parenteralformulations.

Microcrystalline cellulose (MCC)is purified cellulose,

practi-callyinsolubleinwaterandinmostorganicsolvents,producedby

convertingfibrous-cellulosetoaredispersiblegeloraggregateof

crystallinecelluloseusingacidhydrolysis[20].MCCishighly

cohe-sivecellulose[21].Itiswidelyusedinpharmaceuticals,primarily

asabinder/diluentinoraltabletandcapsuleformulationswhereit

isusedinbothwet-granulationanddirect-compressionprocesses

[22].

Hydroxypropyl-methylcelluloseorHypromellose(HPMC)isa

whiteorcreamy-whitefibrousorgranularpowder.It’savailablein

severalgradesthatvaryinviscosityandextentofsubstitution[17].

It’ssolubleincoldwater,formingaviscouscolloidalsolution;

prac-ticallyinsolubleinhotwater.Dependingupontheviscositygrade,

concentrationsof2–20%(w/w)areusedforfilm-formingsolutions

tofilm-coattablets.Lowerviscositygradesareusedin aqueous

film-coatingsolutions.ComparedwithMethylcellulose,HPMC

pro-ducesaqueoussolutionsofgreaterclarity,withfewerundissolved

fiberspresent,andisthereforepreferredinformulationsfor

oph-thalmicuse[17].

Polyethyleneglycols(PEG’s)ormacrogolsareproducedby

poly-merizationofethyleneoxideinthepresenceofwater.PEGsare

widelyusedinavarietyofpharmaceuticalformulationsandcan

beusedtoenhancetheaqueoussolubilityordissolution

charac-teristicsofpoorlysolublecompounds[23].Theyarealsousefulas

plasticizersinmicroencapsulatedproductstoavoidruptureofthe

coatingfilmwhenthemicrocapsulesarecompressedintotablets.

WhenaddedtomixturesofHPMC,PEGimprovesthemechanical

propertiesofthefinalcoatingproduct[1,24,25].

3.2. Preparationprotocolofthesamples

Polymer-plasticizer-watersamples(PVP-PEG,HPMC-PEGand

MCC-PEG in water) were prepared by adding the polymer in

deionizedwaterpreviouslyheatedto80◦_C._The_mixture_was_then

homogenizedbymoderateagitationfor30–60minusinga

rotor-statorhomogenizer(UltraturraxT25,JankeandKunkel,Germany)

at85◦_C._The_plasticizer_was_then_{progressively}_added_under

agi-tationuntilitwasevenlydispersed.Themixturewasthencooled

usinganicebathunderagitationfor30min.Solutionswere

there-afterdegassedat50mbarfor2h.Toattainmaximumstabilization,

thereadilypreparedsolutionswerestoredimmediatelyat5◦_C_for

atleast24h.

Thesampleswereafterward spread onaglass plateusinga

CAMAG handcoater(Manufactured by CAMAG, Switzerland) to

produceathinfilmof5mm.Theliquidfilmsarethenplacedfor

24hatambienttemperatures.Table1presentsthedifferent

for-mulationsusedthroughoutthisstudy.Typically,thepercentageof

plasticizerinthecoatingdispersionislessthan10%(w/w).The

rea-sonwechoseahighpercentageofPEGequaltothepercentageof

thedifferentpolymersisdouble;i)Tobeabletoseethemixingof

PEGwiththepolymersintheDPDsimulations,andii)Toclearlysee

theeffectofaddingPEGinthecoatingwhenusingDSCanalysis.

3.3. Methods

3.3.1. MethodA:sigmaprofile

COSMO(Conductor-likeScreeningModel)[26]isapredictive

modelforthethermodynamicpropertiesoffluidsandsolutions

thatcombinesquantumchemistryandstatisticalthermodynamics.

Inthismodel,thesolventisregardedasahomogeneous

conduct-ing medium but affected by a finite dielectric constant arising

fromalargenumberofelectrostaticchargesenvelopingthe

sur-faceofthesolutemolecule.Thesurfaceofthismoleculebearsa

polarizationchargedensity.Todeterminethis density,quantum

mechanicscalculationbasedonthedensityfunctionaltheory(DFT)

arelaunchedinordertooptimizethegeometryofthemoleculeand

toestablishitselectronicstructure.Then,calculationsbasedonthe

COSMOmodelareusedtoconstructthechargedensitycurvecalled

sigma-profile.Thisprofileistheprobabilityp()offindingsurface

segmentwiththechargedensity[4]:

p()=Ai()/Ai (1)

withAi()thesurfaceareawithachargedensityofvalueand

Aithetotalsurfaceofthemateriali.COSMOemploysmolecular

shapedcavitiesthatrepresenttheelectrostaticpotentialby

par-tial atomic charges.The resultsdepend mainlyon thevan der

Waalsradiiusedtoevaluatethecavitysurface.Thecavitysurface

isobtainedasasuperimpositionofspherescenteredattheatoms,

discardingallpartslyingontheinteriorpartofthesurface[26].

MoredetailsaboutCOSMOcanbefoundinRef.[26].

Conductor-like Screening Model (COSMO) implemented in

Dmol3moduleasapartofMaterialStudio7.0packageof

Accel-rys was used to generate the sigma-profiles of the molecules.

Wateris chosen asthe solventenvironment (relativedielectric

constant=78.54).Aglobalorbitalcutoffradiusof3.7Åwasused

throughoutthecalculations.Wehaveusedthegradient-corrected

functionals(GGA)ofPerdewandBecke[27,28]forthegeometry

optimization and the COSMO calculations. It has been

demon-stratedbyPerdewandWangthatthistechniqueproducesmore

reliablepredictionsthantheVosko-Wilk-Nusair(VWN)technique

[29].Forbestaccuracy,weusedthetriple-numericalpolarization

(TNP)basisset[30].InDmol3-CSOMO[31],theradiiofthespheres

thatmakeupthecavitysurfacearedeterminedasthesumofthe

vanderWaalsradiioftheatomsofthemoleculeandoftheprobe

radius.First,geometryoptimizationwasperformedtobringthe

energytoobtainthemoststableconformationandtoadjustthe

coordinatesoftheatoms.Thesigmaprofileswerethereafter

gener-ated.Complementarysigmaprofilesofapolymerandaplasticizer

indicategoodmiscibilitybetweenthem[4].

Fig.2showsthesigmaprofileofwateraswellasitsCOSMO

surface.WatercanacteitherasH-bonddonororH-bond

accep-tor.The s-profile ofwater spansintherange of±0.02eÅ−2.It

isdominatedbytwomajorpeaksarisingfromthestronglypolar

regions;thepositiveregion(H-bondacceptorregion)isduetothe

polaroxygenandthenegativeone(H-bonddonorregion)isdue

tothepolarhydrogenatoms.Thenegativelychargedsurfacesof

thewatermoleculesappearblueandthepositivelychargedones

appearred.Non-polarpartsofthesurfaceofthemoleculearegreen.

Thepeakarisingfromthepositivelypolarhydrogensislocatedon

theleftside,atabout−0.015eÅ−2_._Most_parts_of_the_surface_of

water moleculesareabletoformmoreorlessstronghydrogen

bond.Hydrogenbondingisconsideredasweakupto±0.01eÅ−2_.

Outside this limit, moleculescan beregarded asstrongly polar

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Fig.2.s-profileofwater.(Forinterpretationofthereferencestocolourinthetext,thereaderisreferredtothewebversionofthisarticle.)

3.3.2. MethodB:solubilityparameterviamolecularsimulations 3.3.2.1. Solubility parameter. Thesolubilityparameter,ı (i.e.the

square root of the cohesive energy density), describes the

intramolecularandintermolecularforcesofasubstance.Itisa

mea-sureofthetendencyofamoleculetointeractwiththesurrounding

molecules.Solubilityparameterhasbeenprovedusefulforseveral

pharmaceuticalapplicationsandhasbeencorrelatedtoavarietyof

properties[32]suchasthesurfacetension,refractiveindex,workof

adhesionandtensilestrength.Solubilityparameterwasalsousedin

thecoatingindustryforselectingcompatiblesolventsforcoatings

materialsandalso,insurfacecharacterizationoffillers[5].

Inmolecularsimulation,theHildebrandsolubilityparameter

canbecalculatedfromthepairpotentialbysummingthepairwise

interactions[33].Thecohesiveenergydensityisequaltominus

theintermolecularenergy,i.e.theintramolecularenergyminusthe

totalenergy: ı2_k= < n

X

i=1 Ek i-E k c> Nav<Vcell> (2)

withnthenumber ofmolecules inthesimulation cell,Navthe

Avogadronumber,k=1,2,arethevanderWaalsenergy

(disper-sion)andthecoulombianenergy(polar)respectively. ¨<> ¨denotes

atimeaverageoverthedurationofthedynamicsinthe

canoni-calensembleNVT,Vcellthecellvolume,theindex“i”referstothe

intramolecularenergyofthemoleculei,andtheindex“c”

repre-sentsthetotalenergyofthecell.

AsshownintheworkofHildebrandandScott[34],the

compat-ibilitybetweenaplasticizerandapolymercanbedeterminedby

themiscibilitybasedonthesolubilityparameter.Theenthalpyof

thepolymer(1)−plasticizer(2)mixturecanbedeterminedby:

H=

v

_mix((E2

v

₁ ) 1/2 -(E1

v

₂ ) 1/2 ) 2 x1x2-

v

_mix(ı₁-ı₂)x₁x₂ (3)

where

v

_mixisthemolarvolumeofthemixture,v₁andv₂aremolar

volumesofthepolymerandtheplasticizerrespectively,E1and

E2aremolarenergiesofvaporization,x1andx2arevolume

frac-tions.

Aplasticizer(1)andapolymer(2)aremiscibleinallproportion

whenı1=ı2[35],whichgivesapositivevalueoftheenthalpyofthe

mixture.ThisassumesthattheGibbsfreeenergyofmixingGis

negative(G=H-TS)toallowsolutionformation.Inthiscase,

alltheinteractionsbetweenthemoleculesoftheplasticizerand

thepolymerareofthesameorderofmagnitude.Thedegreeof

miscibilitybetweenaplasticizer(1)andapolymer(2)increases

asthesquareofthedifferencebetweenthesolubilityparameters

ı=(ı1-ı2)2decreases.

AsimilarapproachwasadoptedbyPrice[36]topredictthe

com-patibilitybetweenpolymersandplasticizers, butheusedgroup

contribution methodto calculate the solubilityparameter, and

foundthattheobtainedvalues areunderestimated.Inthis

arti-cle,we willusemolecularsimulationtocalculatethesolubility

parameterratherthangroupcontributionmethods.Jarrayetal.[2]

andBenali[37]usedmolecularsimulationstocalculatethe

solu-bilityparameterandfoundgoodagreementwiththeexperimental

solubilityparametervalues.

3.3.2.2. Computationofthesolubilityparameter. Forthe

computa-tionofthesolubilityparameters,werunmolecularsimulationsin

thecanonicalensembleNVTwiththeForcite®_module_of_the

Mate-rialStudioSuiterelease7[31].Simulationsarerunover500pswith

atimestepof1fs.ThetemperatureissetatT=298Kandcontrolled

byaNoseHooverthermostatwithaQratioequalto0.01.Energy

andpressurestabilitywaschecked.Thelast50psareusedfor

aver-agingpotentialenergycomponents.Theaveragecohesiveenergy

iscomputedtoderivethesolubilityparameterbyusingequation

(2).Thestandarddeviationmethodcanbeevaluatedbytheblock

averagesmethod[38].FollowingtheworkofJarrayetal.[2],we

estimatedtheaveragestandarddeviationastentimesthestandard

errorgivenbyForcite[31].

COMPASSII(Condensed-phaseOptimizedMolecularPotentials

forAtomisticSimulationStudiesII)[39]forcefieldwasusedwith

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Fig.3.“Coarse-grained”compounds;moleculesandmonomerconversionintoequallysizedbeads.

was truncated by a spline function after 15.5 angströms. For

theCoulombianinteraction,partialchargeswereassignedbythe

predefinedforcefieldequilibrationmethod,whiletheEwald

sum-mationwasusedtoaccountforthelong-rangeinteractions.

3.3.3. MethodC:DPDmethod

3.3.3.1. Overview of the DPD method.The dissipative particle

dynamics method (DPD) is a particle mesoscopic simulation

methodwhichcanbeusedforthesimulationofsystemsinvolving

colloidalsuspensions, emulsions, polymersolutions, Newtonian

fluidsand polymermelts.Thismethodenablesaccessinglarger

spatiotemporalscalesthanthoseinthemoleculardynamics.

Recently,anumberofworkershaveusedtheDPDmethodfor

thesimulationofpolymersystemsincludingSchulzetal.[40,41],

Schlijperetal.[42],TomasiniandTomassone[43],Jarrayetal.[6]

and Caoetal. [44].Also, GamaGoicochea[45] usedit tostudy

polymeradsorption.

IntheDPDmethod,thecompoundsarecomposedofmolecules

described as a setof soft beads that interact dynamically in a

continuousspaceandmovealongtheNewtonmomentum

equa-tion.Theseinteractionsbetweenthesoftbeadsgoverntheaffinity

betweenthecompoundsandtherefore,controlthefinalstructure

builtbythebeadsintheDPDsimulation.

AnimportantparameterintheDPDmethodistheterm ¯aijof

theconservativeforce,whichrepresentsthemaximumrepulsion

betweentwounlikebeads;itencompassesallthephysical

infor-mationofthesystem.Itcanbedeterminedaccordingtoalinear

relationshipwiththeFlory-Hugginsparameterij:

¯aij(¯=3)=¯aii+

ij

0.286 (4)

The number density ¯ is equal to 3 DPD units, for which

therepulsionparameter/Flory-Hugginsparameterrelationshiphas

beendefined[46].TheFlory-Hugginsvaluescanbecalculatedfrom

theHildebrandsolubilityparameter[34]usingtheformula:

ij=

(ıi-ıj)2(Vi+Vj)

2kBT (5)

withVthevolumeofthebeads,ıjandıiarethesolubility

param-etersofbeadsiandjrespectively.

Forpolymers,thenumberofbeadsthatcomposesonepolymer

chaincanbeestimatedwiththenumberofDPDnDPD:

nDPD= Mw

MmCn

(6)

Mw is themolecular weightof thepolymer,Mm themolecular

weightofthemonomerandCnthecharacteristicratioofthe

poly-mer.AdetaileddescriptionoftheDPDmethodisbeyondthescope

ofthisarticlebuthasbeendescribedinourpreviouswork[6]and

intheworkofGrootandWarren[46].

3.3.3.2. DPDsimulation parameters. In ourDPD simulations,we

usedthesameapproachproposedbyJarrayetal.[6].Polymerand

plasticizersmoleculeswerecoarse-grainedintobeads(seeFig.3);

A waterbeadrepresents6water molecules(volumeofawater

molecule≈30Å3),whichroughlycorrespondstoasinglemonomer

ofPVP, andtoahalfmonomerofMCC. PEG400iscomposedof

threesimilarbeads;eachonecontainsthesamefragmentwhich

wecalledPEG1.Inthesameway,HPMCrepeatingunitis

coarse-grainedinto4beads(oneHL,twoHOandoneHC)(Fig.3).

ThenumberofbeadsusedtodescribetheHPMCpolymerin

theDPDsimulationsisdeterminedbytheDPDnumbernDPDwhich

wascalculatedusingEq.(6).Theratiocharacteristicwascomputed

usingMaterialStudio’s[31]Synthiamodule[47].Wefoundthatthe

HPMCpolymerchainiscomposedof10repetitions(nDPD=10),and

theMCCpolymeriscomposedof44beads(nDPD=44).The

conser-vativeforceparametersaijbetweeneverycoupleofbeadsisthen

calculatedusingtherelationship(4).Theresultsaresummarized

inTable2.

AllDPDsimulationswereperformedwithinMaterialsStudio7

softwarepackage[31].A30×30×30rc3(i.e.24.4×24.4×24.4nm)

simulationcellboxwasadoptedwhereperiodicboundary

condi-tionswereappliedinallthreedirections.Initially,thebeadswere

randomlydispersedinthesimulationcell.EachDPDsimulationran

for1000DPDunits(i.e.5374.17ps)whichwassufficienttogeta

steadyphase.Theintegrationtimewastakenast=0.02DPDunits

(i.e.107.48fs).DPDsimulationswereruninthecanonical

ther-modynamicNVTensembleatatemperatureofT=298K.TheDPD

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Fig.4.s-profileofwater,PVP,HPMC,MCCandPEG400.

Table2

Theconservativeforceparameters ¯aij.

¯aij PVP MCC HL HO HC PEG1 Water

PVP 157.00 MCC 170.85 157.00 HPMC HL 157.00 170.5 157.00 HO 161.14 159.85 161.12 157.00 HC 159.09 179.56 158.82 167.56 157.00 PEG1 157.38 167.64 157.43 159.26 161.33 157.00 Water 256.78 198.64 252.37 222.05 260.48 253.79 157.00 PVP:polyvinylpyrrolidone,MCC:microcrystallinecellulose,HPMC:hydroxypropyl-methylcellulose,PEG:polyethyleneglycol.

Table3

ListofparametersusedinDPDsimulations.

Numberofmoleculesofwaterinonebead 6

Simulationboxsize 24.4×24.4×24.4nm Cut-offradiusrc 8.314Å

Dissipationparameter 4.5DPDunits(i.e. 0.09043gmol−1_fs−1₎

DPDsimulationtime 1000DPDunits(i.e. 5374.17ps) Integrationtime 0.02DPDunits(i.e.

107.483fs) TemperatureT 298K

3.3.4. MethodD:differentialscanningcalorimetry(DSC)

Differential scanning calorimetry (DSC) performs

measure-mentsofheatflowbyvaryingthethermalenergysuppliedtothe

sample.Thistechniqueisparticularlyusefulfordeterminingthe

glasstransitiontemperatureTgandthemeltingtemperatureTm.

Meltingisaphasetransition,characterizedbythemelting

tem-peratureTm,thatoccurswhenthepolymerchainsfalloutoftheir

crystalstructuresandbecomeadisorderedliquid.

Inthiswork,theDSCtestswerecarriedoutwithadifferential

scanningcalorimetryanalyzerDSCQ2000.Thesoftwareusedfor

analysisofDSCdatawasUniversalAnalysis2000softwareanalysis.

IntheDSCinstrument, thesamplesweresealedinDSC

alu-minumpanandscannedbetween25–300◦_C_with_a_heating_rate

of20◦_C_mn−1_._An_empty_aluminum_pan_served_as_reference._Each

panisincontactwithathermocoupleconnectedtoacomputer.

Theregistrationofasignalproportionaltothedifferenceinthe

heatflowbetweenthesetwopansisusedtodeterminethemelting

temperatureTmandthemeltingenthalpyH.Thepeak

tempera-tureofthemeltingendothermintheDSCcurveswastakentobe

themeltingtemperatureTmofthepolymer.Hwascalculatedby

integratingthemeltingpeak’sareaforeachsample.

InourDSCanalysis,westudiedmorepreciselythecrystalline

meltingpointsofthefilmsassociatedwiththeappearanceofan

endothermicpeakintheDSCcurves.Thismeltingpeakprovides

accesstothemeltingtemperatureTm,andtotheenergyrequired

formeltingdifferentmorphologiescrystals.

Toestimatetheinteractionbetweenthematerialsintheblend,

weusedtheFlory-Hugginstheory[48].TheFlory-Hugginstheory

hasprovidedagoodempiricaldescriptionofthemixingbehaviorof

polymer-diluentsystemsandpolymer–polymersystems[49,50].

Caoetal.[51] andMarsacetal.[52,53]usedtheFlory-Huggins

theoryfortheestimationofpolymer-solventinteractionusingthe

meltingpointdepression dataobtainedfromDSCthermograms.

Meltingpointdepressionisthereductionofthemeltingpointofa

polymerwhenmixedwithanothermaterialandoccurswhenthe

twocomponentsaremiscibleorpartiallymiscible[53].Also,Nishi

andWang[54]usedtheFlory-Hugginstheoryfordrug–polymer

interaction.For theestimation of theFlory-Huggins interaction

parameter between the plasticizer and a polymer, we have

decidedtousethesameconceptandwecalculatedusingthe

followingequation: 1 Tm -1 Tm0 =- R Hm(lnxplast+ (1-1 mr)(1-xplast) +(1-xplast)2) (7)

(8)

Fig.5.Dmol3-COSMOsurfacesofHPMC,PVP,MCCandPEG400.

whereHmisthemeltingheatofthepureplasticizer,TmandT0m

arethemeltingtemperaturesoftheplasticizerinthe

plasticizer-polymermixturesandinthepureplasticizerrespectively,Risthe

gasconstant,xplastisthevolumefractionoftheplasticizerandmr

istheratioofthevolumeofthepolymerrepeatingunittothatof

thepureplasticizer.

A negative means that the attraction between

a polymer–plasticizer pair is stronger than the

aver-age attraction between a polymer–polymer pair and a

plasticizer–plasticizer pair (i.e., plasticizer–polymer attraction

>½(plasticizer–plasticizer+polymer–polymer)attraction).Inthis

case,plasticizermoleculesprefertobein contactwithpolymer

segmentsthanwiththeplasticizermolecules.Themorenegative

thevalueof,thestrongertheattractionbetweentheplasticizer

and the polymer, the higher the miscibility, and vice versa; a

positive value of indicates that the polymer and plasticizer

moleculestendtobeincontactwiththeirownkind,leadingto

repulsionbetweentheplasticizerandthepolymer[55,56].

Fig.6.MiscibilityofHPMC,PVPandMCCwithPEG400predictedfromthesolubility parametercalculations.

Table4

Solubilityparameterscalculatedbymoleculardynamicsandexperiments. Solubilityparameterı(Jcm−3₎1/2

Moleculardynamics Exp.

PVP 21.12±0.16 –

MCC 29.98±0.24 29.3[57]

HPMC 20.68±0.13 22.8[58] PEG400 22.88±0.24 – Water 47.78±0.59 47.9[32] PVP:polyvinylpyrrolidone,MCC:microcrystallinecellulose

.HPMC:hydroxypropyl-methylcellulose,PEG:polyethyleneglycol400.

4. Resultsanddiscussions

4.1. MethodA:-profiles

Fig.4showsthes-profileofPVP,HPMCandPEG400,and

com-paresthemtothatofawatermolecule.Fig.5showstheCOSMO

surfaceofMCC,PVP,HPMCandPEG400.

HPMChasanasymmetricprofile.Anasymmetricprofilemeans

thatthematerialdoesnotfeelcomfortableinitspurestate[4],i.e.

thereisanamountofelectrostaticmisfit.HPMChasadominant

peak inthenon-polarregionat−0.0029eÅ−2 _and_a_small_peak

around0.011eÅ−2_arising_in_the_positive_polar_region,_and_another

smallershoulderextendingfrom−0.01toabout0.015eÅ−2

corre-spondingtothepositivelychargedatoms.ThissuggeststhatHPMC

moleculesprefertobeincontactwithasolventshowinghydrogen

bonddonorcharacteristicsuchaswater.

PVPs-profile,showninFig.4,isalsoasymmetric,ithasamajor

non-polarpeakat−0.0028eÅ−2_and_a_smaller_peak_in_the_positive

regionofs-profile,meaningthatPVPcanonlyactasH-bond

accep-torandislookingforaH-bonddonor.ThepolaroxygeninPVPdoes

notfindapartnerwithareasonablynegatives;hence,when

mix-ingwithwater,thismisfitcanbeadjusted,andthepolaroxygen

maypairupwiththepolarhydrogenofwater.PEGhasavery

simi-larcurveshapetoHPMC,suggestingsolubilityinwater.FromFig.4,

wealsonoticethatHPMC,PVPandPEGhavesimilars-profile,this

indicatesasimilarbehaviorinwaterand,consideringthattheyare

alllookingforaH-bonddonor,maysuggestthattheyaremiscible

witheachotherifweconsidertheoldchemicalaphorism“similia

similibussolvuntur”or“likedissolveslike”.MCCmoleculeispolar

(9)

Fig.7. ImagesofDPDsimulationofPVP-PEG400,HPMC-PEG400andMCC-PEG40010%–10%(w/w)inwateratthefinalsimulationstep.

Fig.8.Distributionofpolymerbeads(PVP,HPMCandMCC)aroundandthroughPEG.

Inthenegatives-profileregion,thepositionoftheMCCpeakis

clearlyshiftedtothenon-polars-profilerangeandbothpeaksare

strongerthanthoseexhibitedbythewatermolecules.BothMCC

andwaterhaveasimilarsymmetricals-profile,whichmeansthey

feelcomfortableintheirpurestate.

The conclusionsobtained fromCOSMO aremostly

interpre-tationsbased oncharge distributions, and theydo not provide

a quantitativeor a substantialqualitative methodfor assessing

polymer-plasticizercompatibility.Nevertheless,theresultscanbe

comparedtotheremainingmethodsofthisarticle.

4.2. MethodB:solubilityparameterı

Table 4 compares experimental solubility parameters with

thosecalculatedbymolecularsimulations.Wefollowedthesame

calculationmethoddescribedaboveandproposedbyJarrayetal.

[2].Theaveragevalueofthecohesiveenergydensityisobtained

forallcompoundsfromthelast50picoseconds(ps)ofthe500ps

dynamicsimulation,spanning500000timesteps.

Table4showsthatexperimentalHildbrandsolubility

param-etersvaluesareclosetothemolecularsimulationresults.Jarray

etal.[2]calculatedthesolubilityparameterfordifferentmaterials

andalsofoundthatmolecularsimulationgivessolubilityparameter

valuesclosetotheexperimentalones.

Calculation of 1ı for PVP, MCC and HPMC with a

plas-ticizer (PEG400) indicates the likelihood of miscibility

between them (Fig. 6). PEG400 gives 1ı (PEG400-PVP)=10.7<1ı

(PEG400-HPMC)=17.5<1ı (PEG400-MCC)=22.4Jcm−3, showing that

the miscibility decreases in the following order:

PEG400-PVP>PEG400-HPMC>PEG400-MCC. This suggests that PVP

andHPMCaremorecompatiblewithPEG400asaplasticizerthan

MCC.

MethodBbasedonthesolubilityparametercalculations can

predictthecompatibilitybetweenthefilm-formingpolymerand

theplasticizer;however,itdoesnotprovideinformationrelated

tothestructureoftheblend,nordetailsregardingtheinteractions

betweenthepolymerchainsandtheplasticizer(i.e.diffusionof

plasticizerinthepolymerchains).Inthenextsubsections,wewill

useDPDsimulationstovisualizethestructureoftheblendandwe

willcomparetheresultstothoseobtainedbymethodB.

4.3. MethodC:DPDsimulations

Inthissection,weexaminethestructureofPVP,HPMCandMCC

inthepresenceofaplasticizer(PEG400)usingDPDsimulations.

Polymerandplasticizercontentineach mixtureisfixedto10%

(w/w).

Foracompoundtobeeffectiveasaplasticizer,itmustbeable

todiffuseintothepolymer.Theplasticizer willdiffuseintothe

film-formingpolymerwiththerateandextentofdiffusionbeing

dependentonitswatersolubilityandaffinityforthepolymerphase

[35].Plasticizersmoleculesactbyinsertingthemselvesbetween

thepolymerchainstherebyextendingandsofteningthepolymer.

Thiswillimprovethemechanicalpropertiesofthefinalfilm[35].

InFig.7(a)and(b),PVPandPEGaswellasHPMCandPEGarewell

mixed,andPVP-PEGformsatubularstructure.InFig.7(c),MCCand

(10)

Fig.9.MiscibilityofHPMC,PVPandMCCwithPEG400predictedfromtheDPD simulationsbasedonthepercentageofpolymerthatdoesnotmixwithPEG400.

Fig.8showsthedistributionofpolymerbeads(PVP,HPMCand

MCC)aroundandthroughPEGplasticizer.

Thepercentage ofbeadsofpolymerthat coverPEGnetwork

Noutside

beads,polymercanbecalculatedbyusingthefollowingequation:

Noutside beads,polymer= 100 NBeads,polymer (NBeads,polymer−

X

i (

Y

j 1 (|ro− ri|+|ri−rj|−|ro−rj|±2rwater))) (8)

Where ri denotes the position vector of the ith polymer bead,

i=1...NBeads,polymer.NBeads,polymer isthetotal numberofpolymer

beads(HPMC,PVPorMCCinourcase),r_jdenotestheposition

vec-torofthejthPEGbead,roisthepositionvectorofthebeadatthe

geometriccenteroftheblend,rwateristheradiusofawaterbead

whichisroughlyequaltotheradiusoftheotherbeads,and1is

theDiracfunction.

Table5

Meltingtemperature(Tm)andmeltingenthalpy(1Hm).

Tm(◦_C) _1Hm_(J_g−1₎

PEG 24.7 140.6

PEGinHPMC-PEG 6.3 32.5 PEGinMCC-PEG 16.8 38.1 PEGinPVP-PEG 9.61 37.2

InFig.8(a),PVPshowsthehighestpercentageofbeadsinside

PEGnetwork(97%ofPVP),meaningthatPEGisasuitable

plasti-cizerforPVP.PEGalsomixeswellwithHPMC(Fig.8(b))with82%of

HPMCbeadsthatdiffusesthroughPEGand18%ofHPMCthat

sur-roundPEGbeads.MCChowever,completelysurroundsPEGwith

89%ofMCCbeadsoutside PEG,formingathickerexternallayer

comparedtothelayersformedinalltheothermixtures.This

sug-geststhatMCCisnotcompatiblewithPEGasaplasticizer.Fig.9

summarizesthemiscibilityofthedifferentblendsbasedonthe

amountofPEGthatdoesnotmixwiththepolymer.PVPismore

compatiblewithPEGthanHPMC,andMCCshowstheleast

com-patibility.DPDconclusionsare qualitativelysimilartosolubility

parameterresults(obtainedusingMethodB).

4.4. MethodD:DSCresults

Fig.10showsphotographsoftheappearancesofthesamples

usedinthisstudyandpreparedusingtheprotocoldescribedin

theprevioussection.PEGissolubleinwaterandformsa

homoge-noustransparentsolution(Fig.10(a)).HPMCisalsosolubleinwater

andHPMC-PEGformsatransparentsolution(Fig.10(b)).MCC-PEG

formsawhitesolution(Fig.10(c)).PVP-PEGformsatransparent

yellowishmixture(Fig.10(d)).Inallthemixtures,nophase

sepa-rationcanbeobservedbythenakedeye.

DSC thermogramsof thePEG400 and the films(HPMC-PEG,

MCC-PEG, andPVP-PEG)wererecorded usingDifferential

Scan-ningCalorimeterandarepresentedin Fig.11.Theminimumof

theDSCmeltinggraphisthemeltingpointthatwedenotedearlier

byTm.Table5presentsthemeltingtemperature(Tm)andmelting

enthalpy(Hm)obtainedfromtheDSCanalysis.

The thermal behavior of HPMC-PEG blend presents a

low-temperature peak at 6.36◦_C _(enthalpy: _32.5_J_g−1_). ₍_Fig. ₁₁_).

A decrease in the melting peak may indicate miscibility in

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Table6

Resultssummarytable.

Mixture DSCanalysis Thedifferentmethods HPMC-PEG • HPMCformsmoreorderedcrystalstructure

withfewerimpuritiesthanMCC • PartialmiscibilitybetweenPEGandHPMC.

• PVP,HPMCandPEGhavesimilarbehaviorin water(i.e.possiblemiscibilitywitheach other)A_.

• HPMCandPVParemorecompatiblewith PEG400asaplasticizerthanMCCB

• PartialmiscibilitybetweenPEGandHPMCC. PVP-PEG • PEGisagoodplasticizerforPVP(i.e.

miscibility).

• HighpercentageofPVPdiffusesinPEG networkC_.

• PVPmixeswithPEGinaqueoussystems

BandC_.

MCC-PEG • MCCandPEGmoleculesshowrepulsion. • MCCislesscompatiblewithPEGthanPVP

andHPMC.

• MCCsurroundsPEGinaqueoussystemsC. • MCCisnotcompatiblewithPEGasa

plasticizerB and C_.

A:COSMO,B:SolubilityparameterandMD,C:DPDsimulation.

Fig.11.DSC curvesofPEG 10%(w/w), HPMC-PEG10%–10%(w/w), MCC-PEG 10%–10%(w/w)andPVP-PEG10%–10%(w/w).

drug–polymersystem.Severalresearcharticlesusedthisdecrease

ofthemeltingtemperatureasanindicatorofsoliddosageforms

polymermiscibility[59,60].MixingHPMCwithPEGreducedthe

meltingtemperatureofPEGfrom24.7to6.3◦_C_(i.e._melting_peak

depression),indicatingasubstantialdegreeofmixingand

misci-bility.AddingPEGtoHPMCenhancesthechainmobility inthe

amorphousphaseofHPMC,andHPMC-PEGblendcrystallizeswith

moreeaseatlowertemperatures.

MCC-PEG, ontheotherhand, presentsanenthalpy eventat

16.8◦_C_(enthalpy:_38.1_J_g−1_)._The_melting_peak_temperature_of_PEG

generatedintheMCC-PEGblendishigherthantheonegenerated

intheHPMC-PEGblend,suggesting betterinteractions between

HPMCandPEGthanbetweenMCCandPEG.

PVP-PEGDSCcurveshowssimilartrendstotheHPMC-PEGcase

witha slightlyhigher endothermicpeakat 9.61◦_C _and _melting

enthalpyequalto37.2Jg−1_,_suggesting_miscibility_between_PVP

andPEGthatisslightlylowerthanthatofHPMC-PEG.However,as

indicatedbyMengetal.[56],themeltingtemperaturedecreaseis

notenoughtoclaimthataplasticizeriscompatiblewitha

poly-mer.Intheremainingofthissection,wewillusetheFlory-Huggins

theorytoevaluatethepolymer-plasticizermiscibilitywhichisthe

sameapproachusedbyCaoetal.[51],Marsacetal.[52,53]and

NishiandWang[54].

Themeltingtemperatureandtheenthalpyextractedfromthe

DSCthermogramsareusedforthecalculationoftheFlory-Huggins

Fig.12. MiscibilityofHPMC,PVPandMCCwithPEG400predictedfromtheDSC resultsbasedontheFlory-hugginsparameter.

parameter.Asemphasizedintheprevioussection,a negative

valueofindicatesthatthepolymerandtheplasticizerare

mis-cibleinthemelt,andthepolymer–polymerinteractionbecomes

strongerwiththedecreaseofthevalueof[55,56].Fig.12presents

theFlory-Huggins interactionparameterofthedifferent blends

calculatedusingEq.(7).

InthecaseofMCC-PEG,thepositivevalueof=1.07indicates

repulsionbetweenPEGandMCCmolecules.Thisindicates

immis-cibility(Fig.12)andthereforeMCCisnotcompatiblewithPEGand

mayresultinalessflexiblefilm.Liewetal.[61]alsofoundthat

MCCreducesthetensilestrengthandelasticityofthecoatingfilm

containingPEG.Thenegativevalueof=−1.79intheHPMC-PEG

blendindicatesattractionbetweenHPMCandPEGmolecules.An

attractionindicatesmiscibilityandresultsinaflexiblecoatingfilm.

ThisisinadequacywiththeexperimentalfindingofLaboulfieetal.

[1]whofoundthatmixingPEGplasticizerwithHPMCimproves

themechanicalpropertiesofthecoatingfilm.Liewetal.[61]found

thataddingPEGtoHPMCimprovestheelasticityoftheresulting

coatingfilm.RegardingPVP-PEGblend,alargernegativevalueof

=−3isobtainedsuggestinghighattractionbetweenPEGandPVP

molecules,andconsequentlyhighmiscibility.Barmpalexisetal.

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addi-tion,Liewetal.[61]foundthataddingPVPtoacompositecoating

filmcontainingPEGincreasesbothtensilestrengthandelasticity.

Similarly,Dana etal.[63]alsoshowedthattheadditionof PEG

resultedinanincreaseinelasticityandadhesivenessofPVP-based

hydrogels.

DSCresults(MethodD)aresimilartoDPD(MethodC)and

solu-bilityparameterconclusions(MethodB)obtainedpreviously.DSC

analysisshowedpartialmiscibilityofHPMCandPVPwithPEGin

theblend,butPVPinteractsbetterwithPEGthanHPMC.Inaddition,

thereisrepulsionbetweenMCCandPEGindicatinglow

compat-ibility.Similarly,fromDPDsimulationsandsolubilityparameter

calculation,weconcludedthatPVPismorecompatiblewithPEG

thanHPMCandMCC.

5. Conclusion

Inthisstudy,differentmethodsfortheassessmentof

polymer-plasticizerscompatibilitywereproposedandcompared.Wehave

usedDmol3andCOSMOmodeltogenerates-profilesofthe

com-pounds.We haveseenthats-profilesgivevaluableinformation

regarding polarities,hb-donorsand hb-acceptors,wichallowto

guessthesolubilityofcompounds.MCChasadifferents-profile

shapethantheotherpolymer(HPMC,PVPandPEG)andthecurve

suggestsalowsolubilityinwater.Butthes-profileresultswere

notsufficienttopredictthecompatibilitybetweenPEGandthe

dif-ferentpolymers.Weusedmolecularsimulationratherthangroup

contributionmethodforthecalculationofthesolubilityparameter,

andwefoundgoodagreementwiththeexperiments.Calculation

ofsolubilityparameterıusingmolecularsimulationsshowedthat

PVPandHPMCaremorecompatiblewithPEG400asaplasticizer

thanMCC.

DPDsimulationsshowedthatPEGplasticizermixwellwithPVP

indicatinggoodcompatibilitybetweenthem.Partialdiffusionof

PEGthroughHPMCisobtainedshowingthatthereispartial

mis-cibilitybetweenHPMCandPEG.However,PEGandMCCarenot

miscible,andMCCtendstocoverPEGinwaterwithaspherical

shell.TheexperimentalresultsobtainedbyDSCaresimilartothe

DPDsimulationresults.Itshowedthatthereisabetter

interac-tionbetweenHPMCandPEGthanbetweenMCCandPEG,andthat

HPMCshowsahigherdegreeofmiscibilityandmoreattractionto

PEGmoleculesthanMCC.Inaddition,PEGisagoodplasticizerfor

PVP.

Each methodhasits own advantage compared tothe other

methods;Forexample,theDPDmethodgivesinsightsonthe

struc-tureoftheblendsand predictstheamountofpolymerdiffused

insidetheplasticizer.COSMOmethodisfasterbutdoesnotpredict

theextentofthecompatibility.TheDSCmethodistime-consuming

andmoreexpensivethantheothermethods.

Table6summarizestheresultsobtainedbythedifferent

sim-ulationmethodsandcomparesthemwiththeresultsobtainedby

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