Procedure to explore a ternary mixture diagram to find the appropriate gradient profile in liquid chromatography with fluorescence detector. Application to determine four primary aromatic amines in napkins

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Contentslistsavailableat ScienceDirect

Journal of Chromatography A

journalhomepage: www.elsevier.com/locate/chroma

Procedure to explore a ternary mixture diagram to ﬁnd the appropriate gradient proﬁle in liquid chromatography with

ﬂuorescence detector. Application to determine four primary aromatic amines in napkins

M.M. Arce

^a

, D. Castro

^a

, L.A. Sarabia

^b

, M.C. Ortiz

^a^,^∗

, S. Sanllorente

^a

a Departamento de Química, Facultad de Ciencias, Universidad de Burgos, Plaza Misael Bañuelos s/n, Burgos 09001, Spain

b Departamento de Matemáticas y Computación, Facultad de Ciencias, Universidad de Burgos, Plaza Misael Bañuelos s/n, Burgos 09001, Spain

a rt i c l e i nf o

Article history:

Received 4 April 2022 Revised 11 June 2022 Accepted 13 June 2022 Available online 15 June 2022 Keywords:

Primary aromatic amines Ternary mobile phase Gradient elution Optimization Food contact materials

a b s t r a c t

The purposeofthiswork is todevelop atoolto searchfor agradientprofile with ternary orbinary mixturesinliquidchromatography,thatcanprovidewell-resolvedchromatogramsintheshortesttime formultianalyteanalysis.Thisapproachisbasedexclusivelyonexperimentaldataanddoesnotrequire aretentiontimemodel ofthecompoundstobeseparated.Themethodologyhasbeenappliedforthe quantificationoffourprimaryaromaticamines(PAAs)usingHPLCwithfluorescencedetector(FLD).Ani- line(ANL), 2,4-diaminotoluene(TDA),4,4 -methylenedianiline(MDA) and 2-aminobiphenyl (ABP)have beenselectedsincetheirimportanceinfoodcontactmaterials(FCM).

Inordertoachievethat,partialleast squares(PLS) modelshavebeenfittedtorelateCMP(control methodparameters)andCQA(criticalqualityattributes).Specifically,PLSmodelshavebeenfittedusing 30experimentsforeachoneofthefourCQA(resolutionbetweenpeaksandtotalelutiontime),consider- ing33predictorvariables(thecompositionofthemethanolandacetonitrileinthemobilephaseandthe timeofeachoneofthe11isocraticsegmentsofthegradient).Thesemodelshavebeenusedtopredict newcandidategradients,andthen,someofthosepredictions(theoneswithresolutionsabove1.5,inab- solutevalue,andfinaltimelowerthan20min)havebeenexperimentallyvalidated.Detectioncapability ofthemethodhasbeenevaluatedobtaining1.8,189.4,28.8and3.0μgL⁻¹forANL,TDA,MDAandABP, respectively.

Finally,the application ofchemometrictools likePARAFAC2allowed the accuratequantiﬁcationof ANL,TDA,MDA and ABPinpapernapkinsinthe presenceofotherinterferingsubstances coextracted inthesamplepreparationprocess.ANLhasbeen detectedinthe threenapkinsanalysed inquantities between33.5and619.3μgL⁻¹,whileTDA ispresent inonlytwonapkinsinquantitiesbetween725.9 and1908μgL⁻¹.Ineverycase,theamountofPAAsfound,exceededthemigrationlimitsestablishedin Europeanregulations.

ThisisanopenaccessarticleundertheCCBY-NC-NDlicense (http://creativecommons.org/licenses/by-nc-nd/4.0/)

1. Introduction

Primaryaromaticamines(PAAs)arechemicalcompoundsused indifferentindustrial productionprocessesinthemanufacture of pesticides, dyes, polymers, drugs, cosmetics, and textiles among manyothers.Moreover,theycanbeusedintheproductionoffood contactmaterials(FCM)orcanbeoriginatedasaby-productfrom othercompoundsusedintheirmanufacture,thatisthecaseofiso-

∗Corresponding author.

E-mail address: [email protected] (M.C. Ortiz) .

cyanates,usedasadhesivesinmultilayermaterials.PAAsarecon- sideredfoodcontaminants [1],this increasesthe needfora new analyticalmethodologyfortheirdeterminationandquantiﬁcation.

According to the International Agency for Research on Can- cer(IARC),thisgroupofcompounds issuspiciousofcausingcan- ceramong other adverse effects.For instance,PAAs such as4,4- methylenedianiline(MDA)or2,4-diaminotoluene(TDA) areclassi- ﬁedaspossiblecarcinogensforhumansaccordingtotheIARClist (group2B), whileaniline(ANL)isin group2A(probably carcino- genic)andthe2-aminobiphenyl(ABP)isnotincludedinanyofthe groupsestablishedbythisagency[2].

https://doi.org/10.1016/j.chroma.2022.463252

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For FCM of paper and cardboard, the migration of any compound belongingtothisfamily,shouldnot bedetected abovethe detectionlimitof0.01mgkg⁻¹[3,4].Moreover,PAAsalsoarereg- ulatedforpaperandboardobtainedfromrecycledﬁbres,beingthe appliedlimit0.1mgkg^-1[5].

Different authorshavedetermined severalcompounds ofPAAs familyusingtechniquessuchasexcitation-emissionmolecularflu- orimetry (EEM) [6], gas chromatography/mass spectrometry (GC- MS)[7],liquidchromatography-massspectrometry(LC-HRMS and LC-MS/MS) [8], high performance liquid chromatography with diode array detection (HPLC-DAD) [9], and lately, with an ultra- high-performance liquid chromatography-tandemmass spectrometry (UHPLC-MS/MS) method [10]. Nevertheless, it has not been foundrecentpublicationsthatuseliquidchromatographywithflu- orescence detector(HPLC-FLD).However,forthedeterminationof ANL, TDA, MDA and ABP, detectionby FLD is a good alternative due to: i) thelow cost compared toMS/MS (something that not everylaboratorycanafford),ii)thenativefluorescenceofthecom- pounds,iii)thegreatersensitivityoftheFLDdetectorcomparedto themoreusualDAD.

In the reviewed literature, it has been observed that the re- searches that employ liquid chromatography for the analysis of PAAs, usegradientelution, generally,withbinarywater:methanol mixtures as mobile phase [8,9,11,12]. But the use of the binary mixture water:acetonitrile [10] and even the ternary water:methanol:acetonitrile [13] have also been published. For this reason, in this work gradient elution with ternary mobile phase isexploredasacasestudy.

The optimisation of chromatographic methods with isocratic elutionisfrequent[14,15].Lesscommonistheoptimisationofgra- dientmethods, andthereare examplesinthe literatureinwhich theratiobetweentwosolventsintheorganicphaseisintroduced asafactortobeoptimized(whichimpliesaternarymixture)when thegradientproﬁleconsistsofsteeplinearone-segmentedproﬁle [16–18].Onthecontrary,theuseofmulti-segmentedgradientshas twoadvantages:ontheonehand,itallowstheseparationofcom- plex samples,and on the other hand, atthe same time, it com- presses parts ofthe chromatogram, wherejusta few andwidely separatedpeaksarerecordedtoreduceanalysistime.

There arefew worksinwhich multi-segmentedternary gradi- entelutionisoptimized[19,20]eventhoughithasbeendeveloped forbinarygradients 35yearsago inRef.[21]ormore recentlyin Ref. [22]. This approximation requires a retention time model of thecompoundstobeseparated.Theparametersofthismodelhave tobeadjustedfromexperimentalchromatograms,andafteritsval- idationwithnewchromatograms, itisusedtosearch foran opti- malgradient.

ThisresearchisintendedtogenerateacompleteHPLCmethod- ologywithmulti-segmentedgradientelutionusingternarysolvent mixtures that simpliﬁes buildingof thedesign space, that is,the multivariatesetofparametersoftheanalyticalprocedurethatpro- vide the same analytical quality.For this, it is critical to have a function that relatesCMP (controlmethodparameters) withCQA (critical quality attributes). The proposal is to use a partial least squares(PLS)modelthatrelatestheparametersofagradientelu- tion with the CQA of a chromatogram (e.g. resolution between peaksandtotaltime).

The selection oftheoptimalconditions inHPLCwithout are- tentionmodelbasedonfirstprinciplesisbeingusedwithincreas- ing frequency, in particular to define the design space and the MODR(methodoperabledesignregion)seereviews[23,24].Multi- linearleastsquaresregressionsaregenerallyused,butalso,partial leastsquares[23,25]andinparticular,forHPLCinisocraticcondi- tions[14,15]orwithsupercriticalfluidchromatographyingradient mode [25]. Neuralnetworks havealso been used, butwithlittle success,asdiscussed insection 2.4.1 ofthereview byCela et. al.

[20].However,theuseofretentionmodelsbasedonﬁrstprinciples hasimportantdiﬃcultiesinitsresolution,especiallywithgradient elution[26]andinthegradientdesigntobeusedinaseparation [27].

The multilinear gradient elution theory for binary mobile phasesinreversed-phaseliquidchromatographydevelopedinRef.

[28]isgeneralised toternarygradients inRef.[29]by usingare- tention time model which depends on sixparameters calculated fromternaryisocraticdata.

As it hasbeen demonstrated in Ref. [19], any arbitrarygradi- entcanbeapproximatedby asegmentedgradientandthemodel fortheretentiontimecanberaisedfromchromatogramsobtained inisocratic mode. Inthislast reference, a ternary/binary mixture design consisting of 18 points and another three for validation havebeenused.Bothapproachesareusefultocalculatethereten- tiontimeswith[29] orwithouta retentionmodel[19]. However, theyare nothelpfulforthepurposeofthisinvestigation,because theydonotrelatetheternarygradientproﬁlewiththeresolutions, since the estimation of the retention times are made with data fromternarymixturesobtainedinisocraticmode.

Inthe caseofisocraticseparations withternary mixtures, PLS hasbeenusedasan alternativemodelto thefunctionalone,and that, allows to build the design space of the chromatographic method [15]. Within the theoretical framework of the multi- segmentedgradient, defining the relationship betweenevery pa- rameter that intervene in the problem (the composition of the ternarymixtureandthetimeofeachsegment)andtheresolution betweencontiguous peaksand thefinal time, requiresto have a very flexible model capable of handling the structure underlying all thosepredictorvariables. Furthermore,andmostimportant,it iseasy todetermine thenullspacebecauseit islinked tokernel ofthePLSmodel,apropertythathasbeenusedinRef.[30].

ThemaindrawbackassociatedisthatPLSisaglobalmodelde- fined for the entire triangle of mixtures and all possible multi- segmented gradient, which also has to be estimated with a re- ducednumber of runs. As a consequence, the estimates ofindi- vidualvaluesoftheresolutionsandthefinaltime,willbeaffected by large confidence intervals, therefore inthe strategy to follow, alreadydiscussedinRefs.[14,15],decisionswillbemadebasedon theextremesoftheconfidenceintervalandnotatthefittedcentre value.Undoubtedly,onceoneormorechromatographicconditions thatleadtocompliancewiththeCQAhavebeenproposed,exper- imentalverificationoftheresolutionsandtotaltimeisneeded.

ConsideringthePLSmodeltobeestimated,inamultilineargra- dientinpstages,itisnecessaryto indicatetheptimesinwhich theslopeofeachofthetwoconstituentsoftheorganicphasewill change andthe pvaluesof the percentageof each modifier that definethe slopeofeachramp.Thus, thesamenumberofparam- etersareneededinordertodefine themulti-segmented gradient withternarymobilephase(seeRef.[29]),sothereisnoadvantage inthecontextofPLSmodelling.However,thetheoreticalmodelof retention is mathematically easier [31] for multi-segmented elution than for multilinear elution, so it is expected that PLS will be able to model datafrom the formerelution type more easily thanthelatter. Moreover,multi-segmented elutionprovideswell- shapedpeaks[31].

In this context, the novelty of this work is the optimisation ofthegradient elutionwhen workingwithbinaryand/orternary water:methanol:acetonitrilemixtures,beingthetarget agoodres- olution betweencontiguous peaks and a total time of the chro- matogramasshortaspossible. Allthis, withoutusing theoretical modelsofthe retentiontime ofthecompounds. Onthecontrary, theproposalisanexperimentalsearchingprocedureforthemulti- segmentedgradientbymeansofaPLSmodel.

Inpractice, thedesign formulti-segmented gradients mayre- quireagreatnumberofexperiments.Toavoidthis,thepreliminary

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experiments have beenplanned in such waythat they includea highnumberofpossiblegradientprofileswithlittleexperimental effort. Withthese experiments, a partial leastsquares (PLS) pre- dictionmodelisfittedandvalidated,whichisthenappliedtonew proposals of gradient profiles. Among them, themost suitable is selected to obtain a fullyresolved chromatogram in the shortest final time.Oncetheconditionsofthemobilephase gradienthave been selected,the validation ofthe predictionischecked experi- mentally.

The method developed is applied to determine the fourPAAs (ANL,TDA,MDAandABP)inextractsofthreepapernapkins(Nap1, Nap2andNap3),oneofthemmadeofrecycledﬁbres(Nap2).The extracts areobtainedaccordingtotheUNE-EN647 standard[32]. Thisstandardestablishesthemethodofpreparinganextractinhot water, to investigate the extractedcontent of certain compounds presentinpaperorcardboardintendedtocomeintocontactwith food. The presence ofinterferents inthe extracts hasbeen over- comeusinga calibrationbasedonthePARAFAC decompositionof theﬂuorescencespectrarecordedateachelutiontime.

2. Materialandmethods 2.1. Chemicalsandreagents

Aniline (ANL ≥ 99.5%, CAS no. 62-53-3), 2,4-diaminotoluene (TDA98%, CASno.95-80-7),4,4-methylenedianiline(MDA≥ 97%, CAS no. 101-77-9), and 2-aminobiphenyl (ABP 97%, CAS no. 90- 41-5) were acquiredinSigma-Aldrich (Steinheim, Germany).Ace- tonitrile(CAS no.75-05-8)andmethanol(CASno.67-56-1),both LiChrosolv® isocratic grade forliquid chromatography,were sup- plied by Merck (Darmstadt, Germany). Deionized water was ob- tainedbyusingtheMilli-QgradientA10waterpuriﬁcationsystem fromMillipore(Bedford,MA,USA).

2.2. Instrumental

For the preparation of the extracts of PAAs, a water bath equipped with a Digiterm 200 immersion thermostat (JP Selecta S.A., Barcelona,Spain)wasused.Arotary evaporator (ILMVAC,Il- menau,Germany)wasalsoemployedforthepre-concentrationof the extracts, witha pressure of 72mbar anda temperature between 50 and 60 °C for the elimination of water. A centrifuge (SigmaLaborzentrifugen,Osterode,Germany)wasusedtoseparate thepossibleremainingpaperﬁbresinthesample.

The determination of the fourprimary aromaticamines, ANL, TDA, MDA, and ABP, was carried out by using an Agilent 1260 Infinity HPLC chromatograph (Santa Clara, CA, USA) equipped with a quaternary pump (G1311C), a sampler (G1329B), a ther- mostatic column compartment (G1316A), and a fluorescence detector (G1321B). An InfinityLab Poroshell 120 SB-C18 column (150 × 4.6 mm, 4

μ

^m), ^purchased ^by ^Agilent Technologies, was used for theseparation. Deionizedwater, methanol,andacetoni- trilewereusedasmobilephases.

Theconditionsforchromatographicanalyseswereprogrammed in gradient elution mode.Mobile phaseconsists ofdifferent per- centagesofawater:methanol:acetonitrile(A:B:C,v/v)mixture,de- pendingontheconditionsinthedifferentexperimentsconducted, whichareexplainedinthefollowingSections3.1and3.3,keeping themobilephaseﬂowrateﬁxedat0.5mLmin⁻¹ andthecolumn temperatureat40°C.

In every analysis, the injection volume was 10

μ

^L. ^The ^ﬂuo-

rescence detector was programmed to measure the fluorescence intensity ata fixed excitation wavelength of225 nm. Fouremis- sionwavelengthswereselectedtobetteridentificationofthefour PAAs inchromatograms, being310and342nm theonesforANL, 350nmforTDAandMDA,and385nmforABP.However,onlythe

350nm wavelengthwaschosen fortheevaluation ofthe quality ofchromatogramsthrough fourresponses.The other threewave- lengthswereusedtounequivocallyidentifyeachchromatographic peak,becauseinsome ofthegradients used,theinversionofthe retentiontime oftwo ofthe aminesanalysed occurs.The resolution Rs_i,i₊₁ between the consecutive i-th and(i+1)-th chromato- graphicpeaksiscalculatedwithEq.(1)wheret_R,iistheretention time and w_0.5,i is the width athalf height of the i-thchromato- graphicpeak.

Rsi,i+1= 2.35

(

^tR,i+1− tR,i

)

2

(

^w⁰.5,i+1+w0.5,i

)

⁽¹⁾

Theresultsobtainedfromthreegradient proﬁlesareshownin Fig.1.Thewell-resolvedchromatogram inFig.1atakes26.5min, onthe contrary,although thechromatogram inFig. 1btakesless time,itshowslargeoverlappingbetweencontiguouspeaks.Fig.1c showsthe chosen experiment asan adequate gradient proﬁle to separateandquantifythefourprimaryaromaticamines.

ResponsesY₁, Y₂ andY₃ refers tothe resolution(Rs)between contiguous peaks at the emission wavelength of 350 nm, com- putedasinEq.(1)withthepeakidentiﬁcationinFig.1,Y₁=Rs₁₂, Y₂=Rs₂₃,Y₃=Rs₃₄.Y₄isthetimewhichthechromatogramtakes (t_f),computedbytheﬁnaltimeofthelastelutedpeak.

Asthepurposeofthisworkistomodelthrough PLStherela- tionshipbetweentheelutionconditionsandtheCQAofthechro- matogram(which arethethree resolutionsandtheﬁnal time),it isnecessarytomaintaintheirvalues,eveniftheybecomenegative duetothecrossingofsome ofthepeaksundercertainchromato- graphicconditions.Iftheseresolutionsaresummarizedinasingle indexsuch as theusual "criticalresolution", theperspective that experimental dataprovides aboutthe truerelation betweenCMP andCQA isaltered. Thatis the reasonwhy thepeak assignation ismaintained:(1)ANL,(2)TDA,(3)MDAand(4)ABPevenwhen peakcrossingbetweenANLandTDAoccurs.

Fortheanalysisoftheextracts ofnapkins, toobtain datama- trices for each analysed sample, software has been programmed to record the whole emission spectra between 290 and 430 nm (each1nm)foreachelutiontimeoftheentireanalysis.Therefore, ifthere is anyinterferent in the samples,a multi-way technique willbeused,inthiscasePARAFAC,fortheunequivocalidentiﬁca- tionofthePAAs.

2.3. Standardsolutions

Individual standard stock solutions of 500 mg L⁻¹ were prepared by dissolving each standard in methanol and they were stored and protected from light at 4 °C. A mixture with different concentration levels of each PAA (4, 10, 6 and1 mg L⁻¹ for ANL,TDA,MDAandABP,respectively)waspreparedfromthestan- dard stocksolutions by dilutionwithmethanol. Thismixture solution wasused forthe exploratory experimentscarried out and explainedinSection3.1.

Once the more adequate conditions for the gradient proﬁle (Section3.3)wereselected,aunivariatecalibrationmodelforeach primaryaromaticaminewasﬁttedusingtheintegratedpeakarea at350nmemissionwavelengthasresponse.Forthistask,tencal- ibrationstandards, four ofthem analysed induplicate, were prepared. Firstly, individual stock solutions of 25 mgL⁻¹ were prepared from the ones of 500 mg L⁻¹ by dilution withmethanol.

Thetencalibrationstandards,whichcontainedcrossingconcentra- tion levels ofeach PAA, were preparedfrom theindividual stock solutionsof25mgL⁻¹ by dilutionwithmethanol.Theseconcen- trationlevelswere0,0.05,0.1,0.25,0.5,0.75,1,2,3and4mgL⁻¹ forANL;0,0.5,0.75,1,1.5,2,4,6,8and10mgL⁻¹forTDA;0,0.1, 0.25,0.5,0.75,1,1.5,2,4and6mgL⁻¹forMDA;and0,0.1,0.25,

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Fig. 1. Chromatograms obtained with different gradient profiles: (a) the one codified as 13 in column 1 in Table 1 ; (b) the one codified as 03 in column 1 in Table 1 ; (c) the one codified as 36 in Table 3 . Peak identification: (1) ANL, (2) TDA, (3) MDA and (4) ABP.

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0.5, 0.75, 1,1.25, 1.5, 1.75and2mgL⁻¹ forABP.Thesesolutions werestoredandprotectedfromlightat4°C.

2.4. Proceduretoobtaintheextractfromnapkins

ForthequantiﬁcationofPAAsinnapkins(Section3.4),moredi- lutedcalibrationstandardswereneeded.Forthistask,newcalibra- tionstandards, twoofthemanalysedinduplicate,were prepared.

Firstly, individual stocksolutions of 1mg L⁻¹ for ANL, MDA and ABP werepreparedfromthe onesof25mgL⁻¹ by dilutionwith methanol.Thecalibrationstandardswerepreparedfromtheindi- vidual stocksolutionsof1mgL⁻¹ forANL, MDAandABPandof 25mgL⁻¹forTDAbydilutionwithmethanol.Theseconcentration levels were 2.5,5,10,15,20,35and50μg L⁻¹ forANL; 50,100, 200,300,400,500and600μgL⁻¹forTDA;10,20,30,45,60,80, 100and250μgL⁻¹forMDA;10,20,30,45,60,80and100μgL⁻¹ forABP.Moreover, forsome extractsof napkins,it wasnecessary to preparemore concentrated calibrations standards:0.1, 0.5 and 1mgL⁻¹forANL;0.75,1.5and4mgL⁻¹forTDA.Thesesolutions werealsostoredandprotectedfromlightat4°C.

The preparationof the extracts of the three types of napkins wascarriedout followingtheUNE-EN647standard inforce[32], which indicates how to extract PAAs from paper and cardboard materials intended to come intocontact withfood. 10 g of each napkin, previously cut into pieces between 1 and 2 cm², were weighedandplacedinanErlenmeyerﬂask, where200mLofwa- ter wereadded.Theextractionprocesswascarriedoutinawater bathat80± 2°C.

After 2h, thesolutionwasdecanted, andthe sampleresidues retainedintheflaskwerewashedseveraltimes.Subsequently,the solutionwasfilteredwithafilterplateofporosity 4(ranged5to 15μm).Thisfiltratewastransferredtoa250mLvolumetricflask, filling up to the markwith water.Water wasremoved fromthe sampleswitharotaryevaporatortoobtainthecorresponding PAA extracts. Theseextracts werereconstitutedinmethanol,fillingup to 10mL inavolumetricflaskandthen centrifugedfor3 minat 6000rpm andat10 °Cto separate thepossible remaining paper fibresinthesample.

2.5. Gradientmodelling

Thefeasibilityofusingagradientelutionprofiletoapproximate any possible gradient elution program, linearor not, has already been showninRef. [19].Todo that,once therangebetween the lowestandhighestproportionofmodifierinthemobilephasehas been decided,thechromatogram isdescribedby gproportions of themodifierobtainedbydividingthetotalrangeintogequalseg- ments.Byvaryingthedurationofeachofthesegsegmentsofthe chromatogram,asuitablemodelisobtainedtodescribethegradi- entelutionusingternarysolventmixtures.

ByusingthecodiﬁcationdescribedinRef.[19],aprocedurehas been developed to set up a gradient proﬁle that makes possible to plantheexplorationoftheternary water:methanol:acetonitrile mobilephase.Eachchromatogramwillbeencodedbytwoparam- eters,Land

α

^.

L deﬁnesthebinarymixture whosecomposition isthe begin- ningofthemobilephase gradientproﬁle.Ltakesvaluesbetween 0and200,whereL=0is100%methanol,L=100is100%water andL=200is100%acetonitrile.

α

îs^theângle^formed^by ^the^line^defining^the^gradient^profile

andthe horizontaldepictedfromL.

α

^can ^take ^values^between⁰

and120 °,coinciding 0° withthe horizontaland120° withthe side of the triangle. Note that when L ∈(0, 100),

α

^is ^oriented

clockwise,while whenL∈(100,200) itis orientedcounterclock- wise.InFig.1,inadditiontothechromatograms,theLand

α

^val-

uesofthechromatographicgradientproﬁlesappliedineachofthe threecasesareshown.

ForthegradientdeﬁnedbyLand

α

^,^different^gradient^elution

proﬁlesintimecanbeprogrammed.Toobtainoneofthem,amax- imumtime ts foreach segmentandatotal maximumtimett are deﬁned,andthegsegmentsofthegradient(t₁,t₂,…,tg),aregen- erated,beingt_i(i=1,…,g)anintegerbetweenzeroandt_s,chosen randomlywithuniformdistributionandtherestrictiontt=g

i=1t_i, t_iisthetimethatthecompositionofthemobilephaseremainsin eachsegmentofthegradient.

Forinstance,inordertoobtainthechromatogramsofFig.1,it hasbeen usedg = 11,ts = 8andtt = 35min.The mixturedia- gramsshowthevaluesofLand

α

^that ^deﬁne^the^trajectory^from

theinitialtotheﬁnalcomposition,andthesequenceofthe11cor- respondingternarymixtures,indicatedusingcircles,foreachcase.

In Fig.1a the second and thesixth mixtures are missing, be- causet₂=t₆=0,asshowninrow13inTable1.Theproﬁleofthe percentage of methanoland acetonitrile in each segment is also drawn,notethatthefouranalyteshaveelutedin26.5min,sothe experimentalproﬁleonlyreachesthet₉.

This situation is more pronounced in the chromatogram of Fig. 1b,whose experimental profile only needs until t₃ (see row 3 in Table 1), because at7 min all the analyteshave eluted. Fi- nally,Fig.1cshowstheprofileofabinarywater:methanolgradient (experimentcodedas36inTable3),that startswith30%organic phaseandendsat100%.Onceagain,theexperimentalprofileonly uses8ofthe11gradientprofiletimesasallfouranalyteselutein 15.6min.

2.6. Software

Theset-up ofaternary gradientprofilehasbeenprogrammed asa GUI inMATLAB [33].The source code is freely available via GitHub[34]andisdescribedintheSupplementaryMaterial.Open- Lab CDS ChemStation software was used for acquiring data. The PLSToolbox[35] forusewithMATLAB[33] wasemployedforfit- tingPLS models andto carry out PARAFAC2 decompositions. The regressionmodelswerefittedandvalidatedapplyingSTATGRAPH- ICSCenturion18[36].Decisionlimit(CC

α

⁾^and^detection^capability

(CC

β

⁾^were^calculated^using^the^DETARCHI^program^[37]^.

3. Resultsanddiscussion

3.1. Explorationofexperimentaldomain

When designing the experimentation, its practical viability in terms of analysis time must be contemplated. It wasconsidered acceptable to use three sessions of 8 h. This, resulted in limit- ing the chromatogramsfor theconstruction ofthe PLS model to 30and thevalidation ofthe proposed solutions to7. Inpractice, including some failed experiments and stabilisation time, all 37 chromatogramsweredone inlessthan26 h.Toevaluatethisex- perimental effort, it isnecessary to take intoaccount thesearch spacehas33dimensions(compositionofmethanolanacetonitrile andtime ofeachofthe11segments considered),so,itcannot be consideredexcessivetoexploreitwith30experiments.Thesearch spacecould be reducedwithprevious knowledge,forexample,if thepercentage ofwatercannot be greaterthan 60%, thenumber ofinitialtrialswillbereducedto20.

Theinitialexplorationhasbeencarriedoutwiththe20gradi- entsshownin Fig.2a,wheretheblack pointsindicate thevalues of L(10, 30,60, 90,110, 140, 170 and 190) andthe colours, the differentvalues of

α

⁽⁰ ^{° in} ^red, ³⁰^{° in} ^pink,⁶⁰ ^{° in}^blue, ⁸⁰^°

inyellow,90° inorangeand120° in green).Thedesignthathas been used, is a modiﬁcation of the theoretical D-optimal design for20 experiments with8 and 6levels of L and

α

^, respectively.

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Table 1

L, α^{and t}i parameters that deﬁne the gradient proﬁle used for each one of the 30 exploration experiments carried out in the laboratory, and the four responses calculated from the chromatogram obtained in each case.

Code Fig. 2 (a) Code Table S1 L α ^t1 t 2 t 3 t 4 t 5 t 6 t 7 t 8 t 9 t 10 t 11 Y 1 Y 2 Y 3 Y 4

01 20 ^∗# 10 0 2 3 5 3 3 3 1 3 5 5 2 0.00 0.00 2.05 3.996

02 13 30 0 4 2 4 4 1 4 5 3 4 3 1 0.93 0.96 8.18 6.822

03 16 ^∗ 30 0 5 0 4 3 5 2 4 4 1 2 5 0.00 1.55 7.65 6.840

04 14 ^∗ 30 30 1 3 6 6 5 2 4 0 1 1 6 0.00 1.83 8.55 6.642

05 15 ^∗ 30 60 1 3 1 0 5 3 5 4 3 5 5 0.00 1.63 8.18 6.674

06 05 60 0 4 2 2 2 5 5 1 3 3 3 7 -1.15 14.16 26.67 36.421

07 09 60 0 4 3 1 5 2 0 6 2 3 6 5 -1.43 13.65 25.16 35.665

08 06 60 30 1 1 6 4 3 4 3 4 3 4 2 -1.07 9.92 20.43 19.303

09 07 60 60 1 0 0 0 3 4 3 6 5 6 7 -0.86 5.61 12.72 10.436

10 23 60 60 1 0 0 0 3 4 3 6 5 6 7 -1.30 5.88 14.20 10.198

11 08 60 120 1 1 5 0 3 3 6 3 3 5 5 -1.24 9.19 18.90 15.635

12 01 90 80 5 0 4 3 7 0 3 3 3 5 2 -4.17 22.11 18.75 26.338

13 12 90 80 5 0 4 3 7 0 3 3 3 5 2 -3.81 20.33 16.94 26.505

14 22 90 80 5 0 4 3 7 0 3 3 3 5 2 -4.33 23.09 19.45 26.529

15 27 90 80 0 8 8 4 8 1 4 0 0 1 3 -2.88 23.69 26.25 35.341

16 02 90 120 6 2 0 1 6 4 1 3 5 1 6 -3.88 18.78 22.61 26.021

17 28 90 120 0 0 1 0 1 4 6 4 6 8 5 -1.77 9.85 16.52 15.127

18 03 110 80 7 2 5 1 2 0 4 4 3 3 4 -1.82 17.26 16.51 26.032

19 29 110 80 0 4 0 7 2 4 0 6 2 4 6 -1.27 19.40 19.99 22.828

20 04 110 120 4 4 6 1 4 1 1 4 3 3 4 -1.54 15.36 16.40 25.895

21 30 110 120 0 4 4 4 4 3 5 5 0 5 1 -1.04 15.07 19.51 23.429

22 24 ^∗ 140 0 4 3 1 5 2 0 6 2 3 6 3 0.00 7.65 17.02 26.253

23 10 140 60 5 3 5 5 3 0 2 3 2 1 6 0.92 4.83 13.78 16.567

24 11 140 90 2 5 2 2 2 5 4 2 1 5 5 0.93 4.21 15.75 14.724

25 25 # 170 0 4 2 4 4 1 4 5 3 4 3 1 1.26 0.00 5.05 5.454

26 17 # 170 30 4 4 3 1 3 0 3 3 4 5 5 1.06 0.00 5.01 5.486

27 18 # 170 60 4 4 6 4 0 1 5 2 5 1 3 1.43 0.00 4.80 5.494

28 19 # 170 120 5 5 1 5 3 0 1 3 5 5 2 1.62 0.00 4.76 5.512

29 21 ^∗# 190 0 5 2 4 1 2 5 4 5 3 0 4 0.00 0.00 1.37 3.881

30 26 ^∗# 190 0 5 2 4 1 2 5 4 5 3 0 4 0.00 0.00 1.32 3.863

( ^∗) Experiments excluded for modelling Y 1 . (#) Experiments excluded for modelling Y 2 .

Fig. 2. Directions deﬁned by L and αparameters for different gradient proﬁles. (a) The 20 ones used for the 30 exploratory experiments carried out in the laboratory and (b) the 14 ones used for the 21 out of 45 proposed conditions for prediction.

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As shown inFig. 2a, the number ofgradients has been reduced to two whenL= 90orL= 110, becausea longﬁnal time isex- pectedundertheseconditions.Also, onlyasinglegradient(

α

= 0

°) isconsidered whenmethanol andacetonitrileare,respectively, at90%(L=10andL= 190)becausethevariationintherangeof ternary mixtures is very small.Thedesign used isa compromise betweenthestatisticalpropertiesoftheD-optimaldesignandthe analyticalmeaningofLand

α

^.

As itcanbe seen,forthesame valueofL,thechromatograms for different values of

α

^have ^been ^recorded. ^Four ^replicates ^of

somepairsofvaluesofLand

α

^have^been^performed(experiments codedas10,13,14and30).Also,theanalysishasbeencompleted by generating differentseriesof t_i insix pairsof Land

α

^values

(experiments coded as03,07,15, 17, 19and21 inFig.2a andin Table 1, column1). Therefore,a total of30 chromatogramswere recordedinthelaboratory.

3.2. FittingandanalysisofaPLSpredictionmodel

Ineachofthe30chromatograms,definedbythepreviousgra- dient profiles, fourresponses havebeen obtainedthat define the quality ofthe chromatogram: thethree resolutions betweencontiguous peaks (Y₁, Y₂, Y₃) and the final time (Y₄) (see details in Section 2.2). The experimental values obtained are shown in Table 1.As itcan be seen,there isa tendencydependingon the value thatLtakes.ForY₄ (t_f)thelowestvaluesareobtainedwith theextremevaluesofL(closeto0and200),andasLapproaches to100,thesetimesincrease.Buttheeffectof

α

^is^alsoappreciated, forexample,forL=60Y₄variesfrom36to10min.

Thetimeproﬁleeffectonthegradientisalsoobserved,forex- ampleforL=90and

α

=120° (binarywater:methanolphase)the resolution Rs₁₂ (Y₁ inTable 1) is halvedwhenchanging thetime profilefromchromatogram16to17.TheothertworesolutionsY₂, Y₃ and thefinal time Y₄ are alsoreduced.In addition, thechromatograms with thelowest final time (L = 10,30, 170 and190) havepoorRs₁₂and/orRs₂₃ resolutions.ForvaluesclosetoL=100, resolutionsare better,ensuringtheseparationoftheanalytes,but thetimet_fisincreased.

Based on the experimental results, it is clear that the optimal ternarygradient elutionprofileisdifferentdependingonthe characteristicofthechromatogramconsidered:resolutionsorfinal time.Tofindasolutionofcompromise,itisproposedtofitapre- diction modelusingthe33predictorvariablesthat correspondto the11t_ivaluesandthedifferentpercentagesofmethanolandace- tonitrilethatdefinetheconditionsofeachoneofthe30recorded chromatograms. Since these33predictors arecorrelated,it isap- propriatetoconsiderapartialleastsquares(PLS)model.Therefore, amodelisfittedforeachoftheresolutionsandforthefinaltime.

Some considerationshavebeentakenintoaccount,Y₁ hasavalue ofzeroinseven chromatograms,which indicatesthat,withthose experimental conditions,the Rs₁₂ resolution cannot be modelled.

That alsohappens withother seven chromatograms forRs₂₃. For Y₁ andY₂themodelhasbeenﬁttedwiththe23non-nullvalues, excluding thechromatograms marked in Table1 with (^∗) or (#), respectively.ForanswersY₃andY₄ithasbeenpossibletousethe 30chromatograms.

The characteristics of theﬁtted models are shownin Table 2. Thenumberoflatentvariableswaschosenbyleaveoneoutcross- validation procedure, beingnecessary 4 latent variables for each model. The global percentage of variance explained in training variesbetween92and96%andincross-validation,variesfrom79 to 85%. As a reference, in the PLS models of [25] the R² values obtainedarerangedfrom0.942to0.994,quitesimilarto theval- uesobtainedinthepresentworkbetween0.921and0.964. These models onlyneed between72and77% ofthevariance ofthe 33 predictors. The absence ofoverﬁtting has been evaluated by do-

Table 2

PLS models fitted for each experimental response with data from Table 1 . L.V., number of latent variables, R ² , variance explained of Y block in fitting, R ² c.v., variance explained of Y block in cross-validation. P -value is the significance for the cross- validated permutation tests.

Response L.V. R ² R ² c.v. Var. explained X block (%)

P -value

W ^∗ S ^∗∗ R ^∗∗∗

Y 1 ( Rs ¹² ) 4 0.9418 0.8138 77.40 0.001 0.013 0.006 Y 2 ( Rs 23 ) 4 0.9640 0.8499 73.58 0.002 0.014 0.005 Y 3 ( Rs 34 ) 4 0.9207 0.7928 73.40 0.001 0.005 0.006 Y 4 ( t f ) 4 0.9341 0.8034 72.60 < 0.0005 0.002 0.005 ( ^∗) Pairwise Wilcoxon signed rank test.

( ^∗∗) Pairwise signed rank test.

( ^∗∗∗) Randomisation t-test.

ing three permutation tests(50 iterations)using the residuals in cross-validation,becausetheyaremoresensitivetodetectoverfit- ting. The p-valuesreported in Table 2 vary between 0.0005and 0.014.That is,themodel fittedforeach Y_i, i =1, …,4is distin- guishablefrom one createdrandomly shuffling theresponse at a confidencelevelbetween0.9995and0.986whichisalevelmuch higherthanusual0.95.

OncethePLSmodelshavebeenbuilt,themulti-segmentedgra- dientproﬁle is analysed foreach L and

α

ⁱⁿ^relation ^to ^the ^res-

olutions and final time obtained, their confidence intervals and thedesiredCQAvalues.Basedon this,24newgradients arepro- posed which come from previous directions of the training set (Fig.2a)butwithatimeprofileofthegradient(t₁,t₂,…,t_g)cho- senbasedontheexperimentalresultsalreadyobtained.Someoth- ers are added in order to explore promising regions of L and

α

values.In this casethere are 21 corresponding to 14 new directions shownindifferentcoloursinFig. 2b, wherethevaluesofL studied(20,30,40,70, 100,150,160and180)havebeenmarked againwithblackpointsandthe

α

^values^with^different^colours⁽⁰

° in red, 15 ° in pink, 60° in blue, 90 ° in orangeand 120 ° in green).ForﬁvepairsofLand

α

^values,^other^different^series^for^ti

havebeengenerated.Rememberthatthespacetobeexploredhas 33dimensions,sotestingdifferentproﬁlesforthegradientimplies handling33parameters.Thesegradientproﬁlesandthecalculated valuesYˆ_i,i=1,...,4obtainedwiththePLSmodelscanbeconsulted inTableS1inSupplementaryMaterial.

It is known that PLS regression, like all least squares methods,makespredictionsofaveragevalues,notindividualones.This, alongwiththelargedimensionalityofthesearchspaceandthere- ducednumberofchromatograms,causeslargeconfidenceintervals forthe estimated values ofthe resolutions andfinal time which has already been confirmedin the case of isocratic elution [15]. Thisfactcan beseen inFig.3whichshowstheconfidenceinter- vals calculated at95% confidence level.In thisspecific case, it is imposed,tothepredictionsobtainedfromthe75chromatograms, that the resolutions must be greater or equal to 1.5 in absolute value and that the final time less than 20 min. Taking this into account,sevenproposalshavebeenfoundthat fulfilbothrequire- ments (marked withthecorresponding codein Table3). Thene- cessityto considernot themeanvalue butthe intervalisshown, for example, in chromatograms 75, 44, 46 whose estimates to- gether withtheir confidenceintervalsdo not guaranteethat Rs₂₃ isgreaterthan1.5,asoccursexperimentally(Table3).

3.3. Experimentalveriﬁcationofthepredictions

Oncethese seven conditionswere selected, thecorresponding chromatogramswere recordedinlaboratory. The resultsobtained for each of the four responses are shown in Table 3. As it can be seen, three conditions of the proposals do not fulﬁl the prediction ofRs₂₃ (Y₂),chromatograms withcode75,44 and46.Of

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Fig. 3. For the 30 exploratory experiments (in black) and the 45 proposed conditions (in red), predicted values and its conﬁdence interval at 95% conﬁdence level calculated from the PLS models for (a) Rs 12 , (b) Rs 23 , (c) Rs 34 and (d) t f .

Table 3

L, αand t i parameters that deﬁne the gradient proﬁle used for each of the seven validation experiments carried out in the laboratory, and the four responses calculated from the chromatogram obtained in each case.

Code Table S1 Fig. 3 L α t 1 t 2 t 3 t 4 t 5 t 6 t 7 t 8 t 9 t 10 t 11 Y 1 Y 2 Y 3 Y 4

75 20 0 4 2 4 1 2 8 4 5 1 0 4 0.69 0.00 5.09 4.867

38 60 60 1 0 2 4 3 0 0 6 6 6 7 -1.47 9.17 19.60 13.792

55 70 120 0 1 0 1 4 3 0 4 6 8 8 -1.59 9.12 21.58 13.921

36 70 120 1 0 1 4 3 0 4 5 5 6 6 -2.10 13.46 19.73 15.624

28 90 120 0 0 1 0 1 4 6 4 6 8 5 -1.92 11.41 18.43 15.041

44 170 0 6 3 4 4 1 4 5 3 1 3 1 1.48 0.00 5.26 5.504

46 170 120 8 7 1 5 3 0 1 3 5 0 2 1.26 0.00 5.53 5.494

the remainingfourproposals,asthereisnotmuch differencebe- tween thefinal time obtained, thechromatographicconditions of case36,thathavebetterresolutionRs₁₂(Y₁),arechosen.Todecide if the PLS model provides resolutions andfinal time valuessim- ilar to the experimental ones, the four regressions Y_i (estimated value withPLS)versusY_i (experimentalvalue),i =1,2,3,4have been built.The nullhypothesis that statestheestimated andex- perimental values are the same, cannot be rejected (at the 0.05 levelofsignificance)asshowninTable4.Despitehavingexplored

ternary mixtures, the optimisation leads to a gradient proﬁle of water:methanolbinarymixtures.

Undertheseconditions, aunivariate calibrationmodel isbuilt (using the peak area as response) with ten concentration levels (explained in Section 2.3). Table 5 shows the parameters of the calibrationandaccuracy linesforeach PAAs. Allofthem are sig- nificantmodels,withoutlackoffitat95%confidenceandtheyare alsounbiasedbecauseinterceptsareequaltozeroandslopesequal toone.

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Table 4

Parameters of the regression models (predicted data versus experimental results) ﬁtted for the four responses considered.

Y 1 (Rs 12 ) Y 2 (Rs 23 ) Y 3 (Rs 34 ) Y 4 (t f )

Number of data 30 30 37 37

Intercept -0.0010 -1.0057 1.4378 1.8218

Slope 0.9924 1.0635 0.8723 0.9048

Correlation coeﬃcient 0.9661 0.9648 0.9374 0.9581

P -value (H 0 : Intercept equal to zero and slope equal to one) 0.9861 0.3627 0.0612 0.1007

Table 5

Performance criteria of the analytical method. Parameters of calibration (ﬁtted with peak areas as response) and accuracy lines (s yx is the standard deviation of regression).

ANL n = 14 TDA n = 14 MDA n = 14 ABP n = 14 Calibration

line

Linear range (mg L ⁻¹ ) 0–4 0–10 0–6 0–2

Intercept 2.4091 -4.8377 0.8839 -0.0389

Slope 104.05 7.9798 18.674 19.660

Correlation coeﬃcient 0.9999 0.9928 0.9995 0.9999

s yx 2.1806 3.3250 1.0711 0.2253

P -value (H 0 : Regression is not signiﬁcant) < 10 ⁻⁴ < 10 ⁻⁴ < 10 ⁻⁴ < 10 ⁻⁴

P -value (H 0 : There is not lack of ﬁt) 0.2489 0.5086 0.1122 0.4457

Accuracy line P -value (H 0 : Intercept equal to zero and slope equal to one) 1.0000 1.0000 1.0000 1.0000

3.4. Applicationtosamples

Once thevalidation ofthe methodhasbeen veriﬁed,it isap- pliedtothedeterminationofthefourprimaryaromaticaminesin extractsobtainedfrompapernapkins.

Thesamplesobtainedfromtheextractsofpapernapkinshavea complexmatrix.Forthisreason,itisnecessarytoapply achemo- metric techniquewiththe second order advantage, whichmeans it provides theunequivocalidentiﬁcationof theanalytes, even in the presence ofnon-modelled interferents. There are several pa- persthat showtheadvantageofapplyingthePARAFAC/PARAFAC2 decomposition technique to data obtained from samples with a complex matrix [38–41]. This technique is applied to three-way datatensors(I× J× K)thatcancomefromdifferentinstrumental methods(HPLC-DAD,HPLC-FLD,GC-MS,EEM,etc)[42].

3.4.1. PARAFAC/PARAFAC2models

Ingeneral,athree-waydataarray X ofdimensionI× J× Kis madeupofrealnumbers,x_ijk,i=1,…,I;j =1,…,J;k=1,…,K.A PARAFAC modelofrankFforthedataarray X= (x_ijk)iswritten [43,44]asEq.(2):

xi jk=

F f=1

ai fbj fck f+ei jk,i=1,2,...,I; j=1,2,...,J; k=1,2,...,K

(2) wheree_{i jk} areresiduals oftheﬁttedmodel.PARAFACisatrilinear model, ascanbe seen inEq.(2),since itis linearin eachof the three proﬁles (orways). HPLC-FLD datacan bearranged foreach chromatographicpeak inathree-way array Xandanalysed with thePARAFACdecompositiontechnique.Inthiscase,thedimension of thedatatensor X isI× J × K,whereforeach oftheK sam- plesanalysed,theintensitymeasuredatJwavelengthsisrecorded at Ielution timesaround the retentiontime of every compound.

According to Eq.(2) PARAFAC decomposes a HPLC-FLD data ten- sor XintoFfactorsandeachfactorconsistsofthreeloadingvec- torsa_f,b_fandc_f,(f=1,2,…F)withdimensionsI(elutiontimes),J (wavelengths)andK(numberofsamples)respectively.Inpractice, each profile(wayormode)ofthearrayisidentifiedbyits mean- ing, forexample,chromatographic,spectral orsampleprofiles for HPLC-FLDdata.Theorderoftheprofilesisnotpredetermined,and theresearcherdecidesit.

Chromatographicdataaretrilineariftheexperimental dataar- ray is compatible with the structure in Eq.(2). The core consis- tency diagnostic (CORCONDIA) [45] measures the trilinearity de- greeoftheexperimentalthree-wayarraywhenF≥ 2.Ifthethree- way array is trilinear, then the maximum CORCONDIA value of 100% is achieved. Additionally, the trilinearity is veriﬁed by us- ingpartitionsinthedataset(split-halfanalysis),thevarianceex- plainedandthechemicalcoherenceofthethreeproﬁles[42,45].

The PARAFAC solution isunique when the three-way array is trilinear and the appropriate number of factors has been cho- sentofit thePARAFAC model[42].The uniquenessproperty, also known as "second order property" makes it possible to identify compounds unequivocally by their chromatographic and spectral profiles as laid down in some official regulations and guidelines [38,46,47], even in the presence ofa coeluentthat appears with theanalyteofinterest.

However,PARAFAC2isusedtocorrectdeviationsfromtrilinear- itywhen small shifts in the retention time of the analytesfrom sampletosampleappearinthechromatogram[48,49].Inthiscase, PARAFAC2appliesthesameproﬁles(b_f,f=1,…,F)alongthespec- tralmodeandenablesthechromatographicmodetovaryfromone matrixtoanother.

Then, Eq. (2) should be modiﬁed as in Eq. (3) to describe a PARAFAC2model:

X=

xijk

=

F f=1

a^k_ifbjfckf+eijk

, i=1,2,...,I; j=1,2,...,J;

k=1,2,...,K (3)

wherethesuperscriptkisaddedtoaccountforthedependenceof thechromatographicproﬁleonthek-thsample.

In the construction of the PARAFAC/PARAFAC2 model, con- straints on the proﬁles can be imposed, for example, non- negativity.

3.4.2. PARAFAC2modelsforPAAs

Asalreadymentionedbefore,inthisworkthethreeproﬁlesof thearrangedtensorsofdimension(I× J× K)correspondtochro- matographic (I), spectral (J) and sample (K) proﬁles, respectively.

It has been observed that for all of them the application of the PARAFAC2decompositionhasbeennecessarybecauseofthereten- tiontimeshifts.

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Table 6

Characteristics of the PARAFAC2 decomposition models obtained for the determination of the four PAAs in napkins.

Analyte

Time window

(min) I × J × K

Number of

factors CORCONDIA (%)

Variance of X (%)

Split-half analysis (%)

Correlation coeﬃcient ( n = 141)

Concentration range (μg L ⁻¹ ) Napkin

ANL 7.00–7.31 59 × 141 × 13 2 100 99.82 99.8 0.9988 0–50 Nap1

7.00–7.31 59 × 141 × 10 2 100 99.64 95.5 0.9962 0–1000 Nap2, Nap3

TDA 6.55–6.85 57 × 141 × 13 2 100 99.59 93.6 0.9864 0–600 Nap1

6.55–6.85 57 × 141 × 11 2 100 99.89 98.2 0.9826 0–4000 Nap2

6.55–6.85 57 × 141 × 14 3 98 99.90 97.5 0.9637 0–750 Nap3

MDA 10.75–11.00 47 × 141 × 18 3 99 99.90 95.7 0.9978 0–250 Nap1, Nap2, Nap3

ABP 15.25–15.55 56 × 141 × 17 3 98 99.90 96.8 0.9993 0–100 Nap1, Nap2, Nap3

Columns 1and 2 in Table6 detail the time window selected foreachanalyteandeacharrangedtensor,whilecolumn3shows its dimensions. The size of the spectral proﬁle (J) is always 141, whichcorresponds totheemission wavelengthsbetween290and 430nm.However,thesizeofthechromatographicandsamplepro- ﬁles,differfromonetensortoanotherdependingonthetimewin- dowofthechromatogram(I)andthenumberofsamplesincluded ineachconsideredtensor(K),whichdependsonthenapkinsam- plesconsidered(column10inTable6)andthecalibrationrangeof thestandardsamples(column9inTable6).

Oncethetensorsarearranged,thePARAFAC2decompositionis carried out. For all models, a non-negativity constraint was applied in the three profiles, with the exception of the model for ABP(lastrowinTable6),whereitwasimposedthenon-negativity constraintjustinthesampleprofile.Eachone oftheseven models werefittedwiththenumberoffactors shownincolumn4 in Table 6. This number of factors was chosen using the CORCON- DIAindex,thepercentageofvarianceexplained,andthesimilarity found when performing the split-halfanalysis (columns 5,6 and 7respectively).The valuesobtainedfortheCORCONDIA indexare closeto100%inthesevencases,explaining,atleast,the99.59%of varianceandwithasimilaritythatvariesbetween93.6and99.8%, whichindicatesthatthePARAFAC2decompositionisadequate.

Fig. 4 shows, as an example, the PARAFAC2 model for ABP.

Fig.4ashowsthechromatographicproﬁle,Fig.4bthespectralone andFig.4cthesampleone,beingthebluefactortheanalyteand theorangeandyellowonestheinterferents.

As indicated in the model of Eq. (3), PARAFAC2 estimates a chromatographic profile a_f^k for each k sample and each f fac- tor. In this casethere are three factors (F = 3) identified by the colour code, and for each of them, 17 chromatographic profiles (shown in Fig.4a). It is evident that only the blueprofile shows the typical appearance of a chromatogram, while the estimated chromatogramsfortheinterferentsarepoorlydistinguishablefrom noise.Inotherwords,inthechromatographicpeakoftheABP,no deformationcausedbytheinterferentswouldbeperceptible.Con- tinuingwithEq.(3),thespectral profileestimates thethreefluo- rescencespectra,b_f,commontoallsamplesshownwiththesame colourcodeinFig.4b.Thesearewell-shapedspectrathatarerec- ognizable,particularlytheABPone.Finally,Fig.4cshowsthecor- responding valuesof thethree sampleloadings,c_f, f= 1,2,3.It is observed that inthe calibrationsamples,the loading increases withtheconcentration,infactthisallowsthecalibrationbyrepre- sentingtheassociatedABPloadings (inblue) versusthe trueABP concentrationofthecalibrationstandards.

The unequivocalidentiﬁcationofeachamine, isdoneby com- paring the chromatographic and spectral proﬁles, obtained with the PARAFAC2 decomposition, with those of a reference sample analysedinthelaboratory.

On the one hand, in the case of the chromatographic pro- ﬁle,theusual criteriaofmanyEuropeanregulationsonveterinary residuesand/orpesticides[46,47]hasbeenfollowed,therefore,the retentiontime obtainedwithPARAFAC2 decomposition,mustcor-

respondto theretention time ofa referencesample, admitting a tolerance of ± 0.1 min. PARAFAC2 technique has been used, so, achromatographicprofileisobtainedforeachsampleoftheten- sor.Consideringtheretentiontimeofthereferencesamples(ANL 7.254min,TDA6.762min,MDA10.964minandABP15.351min), allthechromatographicprofilesfulfiltheaforementionedpremise.

Additionally,inthecaseofthespectralprofile,theunequivocal identification has been carried out through the correlation coef- ficient.The valuesobtained foreach ofthe tensors arranged are shownincolumn8 inTable6,beingall ofthemcloseto1,what guaranteestheidentityoftheamine.

3.4.3. Performancecriteria

Oncethefactorthatcorrespondstoeachanalytehasbeeniden- tiﬁed, its sample loadings are used for calibration asthe instru- mentalsignal,inordertocarryouttheregressionofloadingsver- sustrueconcentration.Althoughthecorrespondingcalibrationand accuracylines(concentrationobtainedwithPARAFAC2versustrue concentration)havebeenﬁttedandvalidatedforeachtensorused, Table7onlyshowsthoseusedtocalculatethedecisionlimit(CC

α

⁾

andthedetection capability(CC

β

⁾ ^for^each ^analyte,^which^corre-

sponds to rows 1,3, 6 and 7 in Table 6. The calibration models aresignificantanddonotshowlackoffitataconfidencelevelof 95%,exceptfortheMDA (seerows6and7inTable7). However, the corresponding accuracy line indicates that the MDA concentration valuespredictedversus the trueconcentration, are signif- icantlythe same(row11in Table7).The methodis validatedby means of the accuracy lines, being the p-values of the joint hy- pothesistest (H₀:Interceptequalto zeroandslope equaltoone) greaterthan0.05,andtheprecisionistheresidualstandarddevia- tion(s_yx)(rows11and5ofthesametable).Therefore,themethod isunbiased.Thelasttwo rowsofTable7showthevaluesofCC

α

andCC

β

^for^each ^PAA,^being^theprobability offalse positiveand false negativeequal to 0.05. It canbe seenthat TDA is theleast sensitiveamine andthat thismethod,althoughitonlyallows the quantiﬁcationofamountsgreaterthan189.4μg L⁻¹ofTDA,isca- pableofquantifyingconcentrationscloseto2μgL⁻¹ofANL.

3.4.4. Primaryaromaticaminesinnapkins

Foreach tensorused (see Table 6),the corresponding calibra- tionandaccuracylineshavebeenﬁttedandvalidatedinorderto predicttheamountofeachPAAinthenapkinsamples.Therange ofcalibration standardsis differentforeach of theseregressions, depending on the concentration of each amine present in each napkin.

ANL has been found in the three napkins, in quite different amounts,33.5,619.3and77.7 μgL⁻¹.InthecaseofTDA,itisnot detectedinNap1,whilequantitiesof1907.9and725.9μgL⁻¹have beenfound intheothers. However,MDA andABPhavenot been detectedinanynapkin.Inallthecases,thehigherconcentrations correspondtotherecycledﬁbrenapkin.

The concentrations found exceed the migration limit estab- lishedintheEuropeanregulationsforFCMofpaperandcardboard