Comparison of predicted and experimental DSC curves for vegetable oils

O

pen

A

rchive

T

OULOUSE

A

rchive

O

uverte (

OATAO

)

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This is an author-deposited version published in :

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Eprints ID : 6277

To link to this article : DOI: 10.1016/j.tca.2012.07.007

URL : http://dx.doi.org/10.1016/j.tca.2012.07.007

To cite this version : Teles dos Santos, Moises and Gerbaud,

Vincent and Carrillo Le Roux, Galo Comparison of predicted and

experimental

DSC

curves

for

vegetable

oils.

(2012)

Thermochimica Acta, vol. 545 . pp. 96-102. ISSN 0040-6031

Any correspondence concerning this service should be sent to the repository

Comparison

of

predicted

and

experimental

DSC

curves

for

vegetable

oils

M.

Teles

dos

Santos

a,b,∗

_{, V.}

_Gerbaud

b

_{, G.A.C.}

_Le

_Roux

a

a_{LSCP/CESQ–DepartmentofChemicalEngineering,UniversityofSãoPaulo,Av.Prof.LucianoGualberto,380,05508-900SãoPaulo,SP,Brazil} b_{LGC–INPENSIACET,4AlléeEmileMonso,31030Toulouse,France}

Keywords: Triacylglycerols DSC Solid–liquidequilibrium Vegetableoil

a

b

s

t

r

a

c

t

Wecompareexperimentalandpredicteddifferentialscanningcalorimetry(DSC)curvesforpalmoil(PO), peanutoil(PeO)andgrapeseedoil(GO).Thepredictedcurvesarecomputedfromthesolid–liquid equi-libriummodellinganddirectminimizationoftheGibbsfreeenergy.ForPO,thelowerthescanrate,the bettertheagreement.ThetemperaturetransitionsofPeOandGOwerepredictedwithanaverage devi-ationof−0.72◦_Cand−1.29◦_{Crespectively,inrelationtoexperimentaldatafromliterature.However,}

thepredictedcurvesshowedotherpeaksnotreportedexperimentally,ascomputedDSCcurves corre-spondtoequilibriumhypothesiswhichisreachedexperimentallyforaninfinitelysmallscanrate.The resultsrevealedthatpredictedtransitionstemperaturesusingequilibriumhypothesescanbeusefulin pre-experimentalevaluationofvegetableoilsformulationsseekingfordesiredmeltingprofiles.

1. Introduction

Astheindustrialusageofvegetablesoilsincreases,the

knowl-edge of thermal profileof suchsystems becomes fundamental,

especiallyforproductdesignpurposes.Themeltingprofileofa

veg-etableoilplaysafundamentalroleonproductdevelopment,asthe

quantityofsolidfatinagiventemperaturestronglyinfluencesthe

suitabilityofthefatforaparticularapplication.Wehaverecently

usedapredictiveapproachbasedonsolid–liquidequilibrium(SLE)

modellingandoptimizationtoolstocomputethemeltingcurves

of vegetable oils and their blends. It was validated for a large

varietyofsystemscomposedbytriacylglycerols(TAGs)molecules

[1–4].Moreover,SLEproblemresolutionalsoallowscomputingthe

ExcessGibbsfreeenergyatagiventemperature,whichcanthenbe

usedtocomputethechangesinheatcapacityduetosolid–liquid

transitions.Thesetheoreticalchangesinheatcapacitycanbealso

comparedwithexperimentaldata,namelyDSCcurves.The

objec-tiveofthepresentworkisfurthercomparingthepredictedresults

withexperimentaldata,speciallythephase transition

tempera-tures,analyzingthecapabilityoftheequilibriumbasedmodelin

describeexperimentalDSCcurvesforvegetableoils.

Itis knownthatexperimentalDSCcurvesarestrongly

influ-encedbymanyfactors,suchasheat/coolingscanrates,thermallag

andsamplesize.ThepredictedDSCcurvesofthepresentapproach

∗ Correspondingauthorat:LGC–INPENSIACET,4AlléeEmileMonso,31030 Toulouse,France.

E-mailaddress:[email protected](M.TelesdosSantos).

are,however,basedonequilibriumhypotheses,whichwould

cor-respondtoaninfinitelylowscanrate.

2. Models

2.1. DSCcalculations

DSCcurvesrecordthechangesinheatcapacityofamaterialas

thetemperaturechanges.Theapparentheatcapacity(duetophase

transitions)isgivenby:

Cpap= ∂qL ∂T + ∂qS ∂T + ∂qSL ∂T (1)

whereqLandqSare,respectively,thespecificheatconsumedin

raisingthetemperatureofthesolidandtheliquidphaseand∂qSL

isthelatentheatofmeltingatT+1/2∂T(averagemelting

temper-ature).Asweareinterestinginevaluatingthetemperatureswhere

occurthesolid–liquidtransitions,wemustevaluatethethirdterm

onrighthandsideofEq.(1).Therefore:

CSL≡∂qSL ∂T =C ap p − ∂qL ∂T − ∂qS ∂T (2)

CSLrepresentstheheatcapacityduetothemeltingofTAGsandwe

areinterestedinitsprediction.Consideringthatthereferenceliquid

enthalpyiszero,theenthalpyofapuremoleculeionsolidphase

j(H_i,0j )isequaltothemeltingenthalpyonthiscrystallinestatej

ofthesolidmixtureoftriacylglycerolsmusttakeintoaccountan

Excessenthalpy.Theseconsiderationsleadto:

Hmix= np

X

j=1 nc

X

i=1 nj_i
Hj_melti+HE (3)

wherenj_iisthenumberofmolesofcomponentionsolidj,npisthe

numberofphasesandncthenumberofcomponents(TAGs).Eq.(3)

representstheheatthatmustbeprovidedtothesolidsampleto

meltit(latentheatofmelting).

Bydefinition:

GE=HE−TSE (4)

Considering the solid mixtures of triacylglycerols as regular

solutions(SE_{=0)andusingEq.(4)onEq.(3),thefinalexpressionfor}

theapparentheatcapacityduetosolid–liquidtransitionsbecomes:

CSL= ∂G E ∂T + np

X

j=1 nc

X

i=1
H_meltj _i∂n j i ∂T (5)

Eq.(5)showsthatforeachpointinaDSCcurve,theapparent

heatcapacityduetosolid–liquidtransitionscanbecalculatedusing

numericalderivativesofExcessGibbsfreeenergyandthenumber

ofmolofeachmoleculeineachsolidphase,evaluatedatTiand

Ti+
T.ThosearecomputedfromtheSLEproblem.

2.2. Solid–liquidequilibriumproblem

Inthepresentwork,foragiventemperature,aSLEproblemis

solved.Then,anincrementintemperatureisgiven,andtheSLE

problemissolvedagaininthenewtemperature.Thevariationin

ExcessGibbsenergyandthenumberofmolofeachTAGthatmelt

arerecorded.TheirnumericalderivativesarefinallyusedinEq.(5)

topredictapointinthecalculatedDSCcurve.

2.2.1. SLEmodelling

TheintensiveGibbsenergyforaphasej(gj_{)istheweightedsum}

ofthepartialGibbsenergyofallcomponentspresentinthatphase.

Bydefinition,thepartialGibbsEnergyofacomponentinamixture

isthechemicalpotentialofthatcomponentinthemixture(j_i).

Therefore: gj₌ nc

X

i=1 xj_i(j_i)=>gj₌ nc

X

i=1 xj_i(j_i,0+RTln _ijxj_i) (6)

where _ijandx_ijaretheactivitycoefficientandmolarfractionof

componentionphasej,respectively,andj_i,0isthechemical

poten-tialofpurecomponentiatthesameconditions(T,P)ofthemixture.

Forj=liquid:

Considering,asinourpreviouswork[3],thattheliquidphaseis

ideal,Eq.(6)issimplifiedto:

gliquid=RT nc

X

i=1 (xliquid_i lnxliquid_i ) (7) Forj=solid:

Thechemicalpotentialofapurecomponentiinthesolidstatejin

thetemperatureofthemixture(T)isgivenby[5]:

solid(j)_i,0 =T
Hsolid(j)_m,i 1 T_m,isolid(j)

−1

T

!

(8)

where
Hsolid(j)_m,i andT_m,isolid(j)are,respectively,themeltingenthalpy

andmeltingtemperatureofTAGionsolidstatej.UsingEq.(8)on

Eq.(6),onehaveforthesolidphases:

gsolid(j)=RT nc

X

i=1 xsolid(j)_i
H solid(j) m,i R 1 T − 1 T_m,isolid(j)

!

+ln( _isolid(j)xsolid(j)_i )

!

(9)

Threemainpossiblesolidstates(polymorphicforms)are

consid-eredforTAGs:˛,ˇ′_{orˇ.Activitycoefficientsareneededtocompute}

Gibbsfreeenergyonsolidstates(Eq.(9)).Thedefinitionofactivity

coefficientisgivenby:

RTln i(T,P,x)=¯giE=



∂ngE ∂ni



T,P,nj=/i (10)

So,anExcessGibbsenergymodelmustbeused.The2-sufixe

Mar-gulesmodelwaschosenforthreemainreasons:(1)itissuitablefor

mixtureswherethecomponentshavesimilarmolarvolume,shape

andchemicalnature[5];(2)anexperimentaldatabaseinTAGsis

availableallowingcomputethemodelparameters[6]anditallows

flexibility/simplicityrequiredintheoptimizationstep.The2-sufixe

Margulesequationformulticomponentmixturesisgivenby:

gE₌ nc

X

i=1 nc

X

j=i+1 Aijxixj (11) Aij=2qaij (12)

Theparameterqisameasureofmolecularsizeintheconsidered

pair(i,j)andxiisthemolarcompositionofTAGi.Theparameters

aijarerelatedtointeractionsbetweenTAGsiandj[5].

Thenecessarybinaryinteractionparameters(Aij)arecalculated

usingcorrelationswiththeisomorphismbetweenthetwo

triacyl-glycerolsiandj[6].Oncetheactivitycoefficientsarecalculated,

theGibbsenergyineachphasecanbecalculatedusingEq.(7)or

(9).Moreover,weusecorrelationstocomputethemelting

temper-atureT_m,isolid(j)andmeltingenthalpy
Hsolid(j)_m,i ofeachTAGineach

crystallinestate(j=˛,ˇ′_{orˇ)[6,7].AstheTAGcompositionofthe}

vegetableoilisaninput,computingtheGibbsfreeenergyofeach

phasebecomesfullypredictive.

2.2.2. MinimizationofGibbsfreeenergyfunction

Solid–liquidphaseequilibriumproblematagiventemperature

and pressure isthe solutionof a nonlinearprogramming (NLP)

problemsearchingfortheglobalminimizationofthetotalGibbs

freeenergysubjecttomaterialbalanceconstraints.Results

pro-videtheequilibriumdistributionofeachTAGamongthesolidand

liquidphases.Theproblemcanbestatedas:

min G(n)= nc

X

i=1 np

X

j=1 nj_ij_i(n)= np

X

j=1 nj_gj ₍₁₃₎ s.t.: ni= np

X

j=1 nj_i i=1...nc (14) 0≤nj_i≤ni i=1...nc; j=1...np (15)

Foragivencompositionineachphase,theactivitycoefficientsare

calculatedandthen,usedtocalculatethetotalGibbsenergy.The

objectiveoftheoptimizationstepisdeterminingthecompositions

ina giventemperature.For solvethisNonLinearProgramming

problem,itwasuseda programdevelopedinGAMS[8]usinga

GeneralizedReducedGradient(GRG)-basedmethod.

3. Experimentaldata

3.1. PalmoilDSC

TheDSCanalysiswascarriedoutusingaDSG60equipment

coupledwithaFC-60-A(Shimadzu)andliquidnitrogenas

cool-ingmedium.TheDSCinstrumentwascalibratedwithindium,zinc

andlead.Apalmoilsampleof9.7mgwasloadedintoastandard

aluminumpanandcoverwashermeticallysealedusing

manufac-turer’scrimpingtool.Anemptyandhermeticallysealedaluminum

panwasusedasreference.Firstly,thepalmoilsamplewasheatedto

80◦_{Candheldfor5minatthistemperature.Thisis2timesthefinal}

meltingpointofpalmoil(approximately40◦_{C)anditallows}

even-tualcrystalmemorytobedestroyed.Thesamplewasthencooled

from80◦_Cto−50◦_{Candheldatthistemperaturefor10min.The}

samplewasthenreheatedfrom−50◦_Cto80◦_{Candthemelting}

peakswererecorded.Thesampleswerecooledand/orheatedat

twoscanningrates:5◦_Cmin−1_and10◦_Cmin−1_.

3.2. PeanutoilandgrapeseedoilDSC

TheexperimentalDSCforthesetwosystemswasgatheredfrom

literature[9].Thetemperaturetransitionspredictedbythepresent

workarethencomparedwiththeexperimentalpeaksrecordedat

literature.

3.3. Triacylglycerolscomposition

Forpalmoil,thecompositionintermsofTAGswastakenfrom

theliterature[10].Forpeanutoilandgrapessedoil,theTAGs

com-positionwascomputationallypredictedinthisworkusingthefatty

acidsdataavailable[11],followingtherandomdistributionoffatty

acidsonglycerolstructuretoformtriacylglycerols.Table1

sum-marizestheTAGcomposition.

4. Resultsanddiscussion

4.1. Palmoil

Fig.1showsthetwoexperimentalcurvesandthepredictedone

forpalmoil,allofthemcarriedoutforthepresentwork.Asthe

out-putsignaloftheDSCexperimentsisinmWunitsandthepredicted

onesarekJmol−1_K−1_{,the3curveswerenormalizedtoobtainfor}

Fig.1.PredictedandexperimentalDSCcurvesforacommercialpalmoilsample. Pam:palmiticacid(C16:0).

Table1

Triacylglycerolcompositionofvegetableoils(%mass).

TAG Palmoila_{(%) Peanutoil}b_{(%) Grapeseedoil}b_(%)

POO 22.43 6.85 – POP 21.87 – – PPO 7.82 1.73 – PPP 7.55 – – PLO 7.2 4.72 2.69 PLP 6.95 – – OOO 5.88 13.48 – POS 3.82 – – POL 3.7 4.72 2.69 OPO 2.03 3.42 – SOO 1.98 1.38 – OOL 1.92 18.56 6.11 OLO 1.87 9.28 3.05 PPS 1.32 – – PPL 1.28 1.20 – PLS 1.21 – – PLL 1.18 3.25 9.21 OLL – 12.78 20.87 LOL – 6.40 10.44 OPL – 4.72 – LLL – 4.40 35.65 LPL – 1.62 4.6 OOB – 1.48 – SLL – – 4.68

Atriacylglycerol(TAG)isrepresentedbyits3fattyacids.P(palmiticC16:0);S(stearic C18:0);O(oleicC18:1),L(linoleicC18:2)andB(behenicC22:0).

a_{Fromliterature.} b_{Predictedinthiswork.}

the3casesanareaunderthecurveequalto1(thetemperatures

transitionsandshapesofthethreecurvesremainingunchanged).

Thesolidphaseisassumedtobeincrystallinestateˇ′_,aspalmoilis

aˇ′_{-tendingfatbecauseofthepresenceofasymmetricmixed-acid}

TAGs,suchasPOOandPPO[12].

Thepredicteddistributionamongtheliquidandsolidphasesof

thepredominantmoleculescanbeobservedinFigs.2–5.

Fig.1showsthatthemodelwasabletopredictthetwo

temper-atureranges(0–10◦_Cand15–25◦_{C)wherethemostpronounced}

phasetransitionsoccur.Thesetworegionscorrespondtothepalm

stearin(highmeltingfraction)andpalmolein(lowmelting

frac-tion), usually separated in industrial processing of palm oil. In

addition,thereisasteepdecreaseinheatcapacityaround12◦_C

revealedbythetwoexperimentalcurvesandalsocorrectly

pre-dictedbythepresentwork.

However, two main differences arise from Fig. 1: the peak

around39◦_{Cnotpresentintheexperimentalcurvesandtherange}

−15◦_Cto0◦_C.

Thepeakaround39◦_{CcorrespondstotheTAGPPP.Aliterature}

work[13]presentsanexperimentalDSCforthepalmoilwitha

heatingrateof1◦_Cmin−1_,5◦_Cmin−1_,10◦_Cmin−1_and20◦_Cmin−1_.

However,theauthorsobservedapeakaround41.51◦_Conlywhen

usingthelowestscanrate(1◦_Cmin−1_{).Thatreinforcedtheprevious}

discussion: the lower the scan rate, the closer to the

equilib-riumconditions,whicharetheonesusedforpredictions.Atthe

equilibriumlimit,thereisapeakat39◦_{Cnotdetectedusingthe}

higherheatingscanrates(5◦_Cmin−1_and10◦_Cmin−1_)usedinthis

work.

ThepredictedDSCcurvesrelyuponanequilibrium

hypothe-sis,whichmeansthatchemicalpotentialsareequalforallspecies

inallphases.Saiddifferently,thechemicalpotentialdifferenceis

zeroandthereisnodrivingforceformasstransferbetweenthe

liq-uidandsolidphases.Experimentally,thatwouldrequireinfinitely

lowscanratessothatthesystemcanreachequilibriumateach

Fig.2. Molarfractioninthesolidphase(a)andliquidphase(b)ofpalmoiltriacylglycerols.POO(—),POP(----)andPPO(***).

betweenthepredictedandexperimentalcurvesattherange−15◦_C

to0◦_C.

Also,it must bepointed outthat thetypicalcomposition of

palmoilusedforDSCpredictions(Table1)and thatfrom

com-mercial oil used in DSC experiments (Fig. 1) can show some

deviations.

TheshapeofthecalculatedcurveinFig.1istypicalofmixtures

withalargenumberofcomponents:thenumberofpeaksdoesnot

correspondtothenumberofchemicalspecies(17),asTAGsmelting

overthesamerangeleadtooverlappingpeaks.Inordertobetter

analyzethisaspect,thetemperaturerangeofFig.1wasfurther

ana-lysedover4intervals:T<0◦_C,0◦_C≤T≤10◦_C,10◦_C<T≤25◦_Cand

25◦_C<T

≤40◦C.ThefractionofeachTAGonsolidandliquidphases

isshowninFigs.2–5.Onecanobservethefollowingsolid–liquid

transitions:

•T<0◦_{C(12TAGsinsolid–liquidtransitions):POO,OOO,PLO,PLP,}

POL,OPO,SOO,OOL,OLO,PPL, PLSand PLL.Allof themhave

massfractionlowerthan10%.Theexceptionis POO(22.43%).

However,thisTAGis onlyatthebeginning ofitssolid–liquid

transition (Fig. 2). As all of the 11 others TAGs correspond

to only 35.20% of palm oil, the 4 peaks at this range have

relativelowintensity.Figs.2–5showthatmostofthose

tran-sitions occur over a temperature range, especially for POO,

which starts melting at −16◦_{C and ends at +9}◦_{C. One may}

attribute the first peak at −18◦_{C to thecombined and fairly}

sharptransitionsofOOO(−19◦_Cto−14◦_{C,Fig.3),OOL(Fig.4)}

andPLL (Fig.5).Theotherthree peaks(at−14◦_C,−10◦_{C and}

−4◦_{C) are less easily assigned because thesynergic effect of}

different solid–liquid transitions at this temperature ranges

(Figs.2–5).

Fig.4.Molarfractioninthesolidphase(a)andliquidphase(b)ofpalmoiltriacylglycerols.POL(—),OPO(----),SOO(***),OOL(◦_)eOLO(1).

•0◦_C≤T≤10◦_{C(10TAGsinsolid–liquidtransitions):POO,POP,}

PPO,PLP, PLO, POS, OPO, SOO, POL and PLS. Sometransition

startsbelow0◦_{C,likethatofPOO,buttheyend inthisrange.}

Theseexplainthetwopeaksat+1.8◦_Cand+6.5◦_{C.Theintensity}

isstrongbecausethe10TAGsmeltinginthisrangeaccountfor

79.01%inmassofthepalmoil.

•10◦_C<T≤25◦_{C(5TAGs insolid–liquidtransitions):POP,PPO,}

PPP,POSandPPS.TheseTAGsareresponsiblefor42.38%ofpalm

oil,correspondingtothesecondlargerpeak.Asmallbumpat

+12◦_{CcanberelatedtothetransitionendingforPOS.POP(21.87%}

inmass)andPPO(7.82%inmass)meltoverthisrange.Astheir

massfractionissignificant,aDSCpeakoccursaround+20.5◦_C.

Moreover,atthistemperaturerange(10◦_C<T≤25◦_C),PPPand

PPSstarttheirtransitions.

•25◦_C<T

≤40◦C (2TAGs in solid–liquidtransitions): Over this

range, only PPP and PPS are still in solid–liquid transitions

(Figs.3and5).ADSCriseoccursaround+28◦_Cto31◦_C,likely

duetothetransitionendingofPPSat+30◦_{C.Atlast,PPPendsits}

transitionat+39◦_{Candcausestheobservedpeakatthis}

temper-ature.

ThefirstcompoundamongPOO,POPandPPOtocompletely

melt is POO (Fig. 2). This predicted result is in agreement

with the fact that this is the compound with the lowest

melting point,due toitshigher degreeofunsaturation(2oleic

chains).

Anotherinterestingfeaturearisingfromthepredictedresults:

there is a sharpdifference onmelting curves of POPand PPO,

althoughthesetriacylglycerolsareformedbythesamefattyacids

(palmiticandoleic).Thishighlightsthatthestereo-positionoffatty

acidsmustbetakenintoaccountwhenaccessingpropertiessuch

asmeltingenthalpyandmeltingpoint.

Fig.6. PredictedDSCcurveforpeanutoil(fullline)andgrapeseedoil(dashedline).

Table2

ExperimentalandcalculatedphasetransitionsDSCtemperaturesforpeanutandgrapeseedoil.

Transitiontemperatures(◦_C)

Exp. Calc. Exp. Calc. Exp. Calc. Exp. Calc. Exp. Calc.

Peanutoil −51.7 nc −29.7 −28 −14.57 −11 0.83 2 8.26 7

Grapeseedoil −39.32 −40 −31.62 −30 −22.82 −21 −15.12 −15 – –

nc:Notconverged;Exp:experimentalfrom[9];Calc:calculatedfromthiswork.

4.2. Peanutandgrapeseedoil

ThepredictedDSCcurvesforpeanutoilandgrapeseedoilare

showninFig.6.Theseoilshavecosmetic,pharmaceuticalandfood

applications.

It can be noted from Fig. 6 that the final melting point of

grapessedoilislowerthanthatofpeanutoil.Thisisduetothe

higheramountofunsaturatedfattyacidsingrapessedoil,which

canbenotedbyitshigheriodinevalue:140.58forgrapessedoil

and95.23forpeanutoil[9].Inbothoils,asharppeakaround−40◦_C

isobserved.FurtheranalyzingthefusionofeachTAGseparately,it

correspondstotheTAGLOL.Theotherpeakscannotbe

unequivo-callyrelatedtoeachTAG,becausethetransitionsforeachTAGdo

notoccurinsharplydistinguishedtemperaturerangesandpeaks

overlap.

Table2showsthecomparisonofthetransitiontemperatures

observed in Fig. 6 and experimental ones from literature [9].

An average deviation of −0.72◦_{C and −1.29}◦_{C were observed}

for peanut oil and grapeseed oil respectively. However, the

predicted curves show other peaks not reported

experimen-tally,duetothepreviouslydiscussedreasons(equilibriumbased

model).

UnlikepureTAG,thepolymorphicformofoilsandfatscannot

beestablishedunequivocallybyDSCanditcanonlybeachievedby

X-raydiffractionanalysis.Therefore,polymorphictransformations

inthesetwo oilswere notreportedin theexperimental

litera-turestudy[9].Forcalculations(Fig.6),theoilisassumed tobe

crystallizedontheˇ′_form.

5. Concludingremarks

Solid–liquidphasetransitionstemperaturesforpalmoil,peanut

oiland grapeseed oilcould bepredictedusing thermodynamic

equilibrium approach based onthe optimization of Gibbs free

energy.Asthepresentmethodispredictive,itcanbefurtherusedto

pre-experimentalevaluationofthermalprofileofothervegetable

oilsandtheirblends.However,theshapeofpeaksonpredictedDSC

curvescanbedifferentfromthoseofexperimentalones,as

exper-imentalDSCisinfluencedbyscanrate.Inthefirststepsofproduct

development,ausefultaskistoidentifythetemperaturesinwhich

themainphasetransitionsoccuranddeterminetheoverall

melt-ingprofile,ratherthana detaileddescriptionofcrystals.Taking

intoaccountthisobjective,theproposedapproachtotheproblem

revealedtobeuseful,despitethelimitationsofthemodelinnot

considernon-equilibriumstates.

Acknowledgements

AuthorswouldliketothankMr.OmarJ.G.Fernandézforthe

valuablehelpduringthedevelopmentoftheoptimizationcode.In

addition,wewouldalsoliketothankthefinancialsupportreceived

fromTheNationalCouncilforScientificandTechnological

Devel-opment(CNPq–Brazil),andtheALFA-II-400FIPHARIAprogram

(EuropeanUnion).

References

[1]M.TelesdosSantos,G.A.C.LeRoux,X.Joulia,V.Gerbaud,Solid–liquid equi-libriummodellingandstabilitytestsfortriacylglycerolsmixtures,in:R.M.B. Alves,C.A.O.Nascimento,E.Biscaia(Eds.),Comput.Aid.Chem.Eng.27(2009) 885–890,http://dx.doi.org/10.1016/S1570-7946(09)70368-2.

[2]M. Teles dos Santos, G.A.C.Le Roux, V. Gerbaud, Computer-Aided Lipid Design: phase equilibrium modelling for product design, in:S.Pierucci, G. Buzzi Ferraris (Eds.), Comput. Aid. Chem. Eng. 28 (2010) 271–276,

http://dx.doi.org/10.1016/S1570-7946(10)28046-X.

[3]M.TelesdosSantos,G.A.C.LeRoux,V.Gerbaud,Phaseequilibriumand opti-mizationtoolsapplicationforenhancedstructuredlipidsforfoods,J.Am.Oil Chem.Soc.88(2011)223–233, http://dx.doi.org/10.1007/s11746-010-1665-z.

[4]M.TelesdosSantos,V.Gerbaud,G.A.C.LeRoux,Simulationofchemical inter-esterificationandmeltingcurvesforvegetableoilsblends,in:9thEuroFed LipidCongress,Rotterdam2011:LectureAbstracts,Eur.J.LipidSci.Technol. 113(S1)(2011)1–46,http://dx.doi.org/10.1002/ejlt.201100363.

[5]J.W. Prausnitz, R.N.Lichtenthaler, G.E.de Azevedo, Molecular Thermody-namics of Fluid Phase Equilibria, 3rd edition, Prentice-Hall, New York, 1998.

[6]L.H.Wesdorp,etal.,Liquid-multiplesolidphaseequilibriainfats:theoryand experiments,in:A.G.Marangoni(Ed.),FatCrystalNetworks,MarcelDekker, NewYork,2005,pp.481–709.

[7]C.K.Zéberg-Mikkelsen,E.H.Stenby,Predictingthemeltingpointsandthe enthalpiesoffusionofsaturatedtriglyceridesbyagroupcontributionmethod, FluidPhaseEquilib.162(1999)7–17.

[8]R.E.Rosenthal,GAMSRelease23.2.AUser’sGuide,GAMSDevelopment Corpo-ration,Washington,DC,2008.

[9]C.P.Tan,Y.B.CheMan,Differentialscanningcalorimetricanalysisofedibleoils: comparisonofthermalpropertiesandchemicalcomposition,J.Am.OilChem. Soc.77(2000)2,143–155.

[10]R.Sambanthamurthi,K.Sundram,Y.-A.Tan,Chemistryandbiochemistryof palmoil,Prog.LipidRes.39(6)(2000)507–558.

[11]R.D.O’Brien,FatsandOils–FormulatingandProcessingforApplications,2nd edition,CRCPress,2003.

[12]K.Sato,S.Ueno,Crystallizationtransformationandmicrostructuresof poly-morphicfatsincolloidaldispersionstates,Curr.Opin.ColloidInterfaceSci.16 (2011)384–390.

[13] C.P.Tan,Y.B.CheMan,Differentialscanningcalorimetricanalysisofpalmoil, palmoilbasedproductsandcoconutoil:effectsofscanningratevariation,Food Chem.76(1)(2002)89–102.