force field Molecular investigation mechanics of some acrylic polymers usingSPASIBA Vibrational Spectroscopy

VibrationalSpectroscopy74(2014)20–32

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Vibrational

Spectroscopy

j o ur na l h o me pa g e : w w w. e l s e v i e r . c o m / l o c a t e / v i b s p e c

Molecular

mechanics

investigation

of

some

acrylic

polymers

using

SPASIBA

force

field

M.O.

Bensaid

_,

_L.

_Ghalouci

_,

_S.

_Hiadsi

_,

_F.

_Lakhdari

_,

_N.

_Benharrats

_,

_G.

_Vergoten

M’Naouar,31000Oran,Algeria

b_{LaboratoiredesMatériauxMixtes,UniversitédesSciencesetdelaTechnologied’OranMohamedBoudiaf,Algeria}

c_{UMRCNRS8576“GlycobiologieStructuraleetFonctionnelle”,UniversitédesSciencesetTechnologiesdeLille,59655Villeneuved’AscqCedex,France}

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received17April2014

Receivedinrevisedform2July2014 Accepted3July2014

Availableonline11July2014 Keywords:

Forcefield SPASIBA Acrylicpolymers

Potentialenergydistribution Vibrationalanalysis

a

b

s

t

r

a

c

t

TheFirstgenerationSPASIBAforcefieldisusedtostudynormalvibrationalmodesofPMMA,andthen extendedtootherthermoplasticpolymers,namelyPMA,PMAAandPAA,inordertodetermineits param-eterstransferability.Tothisend,FTIRandFTRspectraofpurePMMAsamples,preparedbytheemulsion polymerizationofMMAandinitiatedbysodium,arerecordedin400–3500cm−1and200–3500cm−1, respectively.Adetailedvibrationalanalysiswasperformedontheobtainedspectraandtheobserved fre-quenciesareassignedtotheirrespectivevibrationalmodes,supportedbypotentialenergydistribution (PED)analysis.OurnumericalresultsrevealanRMSvalueof7.8cm−1correspondingtoIRwavenumbers and8.7cm−1relativelytoRamanwavenumbers.OurvibrationalcalculationsonPMA,PMAAandPAA polymersrevealthattheparameterstransferabilitycriterion,establishedbyShimanouchi,isverifiedfor theSPASIBAforcefield.

©2014ElsevierB.V.Allrightsreserved.

1. Introduction

The molecular modeling of acrylic polymers has recently attractedmuchinterestduetotheiroutstandingpropertiessuchas highelectricalresistivity,lowwaterabsorption,fairtensilestrength andexcellentopticalcharacteristicsaswellascommercial impor-tance[1].ThePolyMethylmethacrylate(PMMA)polymeroffers aparticularregardsinceiteasilyallowsstudyingdifferent phys-icalproperties related topolymers[2]. PMMA is alsothemost usedmember, among a setofthermoplastic polymers,in wide varietyofapplicationsinvirtueofitsexcellenttransparencyand goodmechanicalandchemicalproperties[3–6].X-raydiffraction techniquesarethemostcommonlyappliedcomplementary disci-plinetomicroscopyforstructuralstudies.Forexample,theatomic position(atleastfortheheavieratoms)andgeometrical parame-terscanbeobtainedfromX-raydiffractionexperiment.However, whenaddressingvibrationalmodesstudy,X-raydiffractionisnot abletoprobevibrationalsensitivemodesofchemicalstructures. Bothpolymerconfigurationandconformationalsensitivemodes canbeprobedbymeansofvibrationalspectroscopytool[7,8].This laterhelpsalottounderstandthedynamicalbehaviorofapolymer

∗ Correspondingauthor.Tel.:+213776439402. E-mailaddress:bwassini@yahoo.fr(M.O.Bensaid).

chain.Therefore,InfraredandRamanspectroscopiesremainthe mostimportantandcommontechniquesavailableinresearchand industriallaboratories.Comparedtoexperimentalvibrationaldata, ab-initio/dftmethodsgiveverygoodreproductionofwavenumbers assignmentsofthefundamentalsbandsforsmallmolecules. How-ever,forlargemolecules(i.e.,withmorethan100atoms)oneneeds averypowerfulcomputer.Withlargermolecules,thetimerequired forcomputationbecomesprohibitivelylarge,andonemustresort tomoreapproximatemethodssuchasmolecularmechanicsforce fieldapproach. Nowadays,thereis avarietyofforcefields ded-icatedtothermoplasticpolymers.Thebestknownforatomistic simulationofpolymericsystems,areCOMPASS[9],CVFF[10],PCFF [11]andDREIDING[12]forpolyethyleneoxide,TRIPOS5.2[13]for polyrotaxanes,CHARMM[14]andAMBER[15]forpolystyreneand GROMOS[16]forpolypyrrole.Forbiomolecularsystems,CHARMM, AMBERandSPASIBA(SpectroscopicPotentialAlgorithmfor Sim-ulatingBiomolecularConformationalAdaptability)seemtobethe mostappropriateforcefields.SPASIBAconsistsofapairingbetween amolecularmechanicsforcefieldderivedfromtheAMBERpackage [17]andtheUrey–Bradley–Shimanouchi(UBS)spectroscopicforce field[18].

Comparedtotheothersforcefieldsofsecondgeneration(e.g. PCFF,COMPASS,...)whichcombinebondedterms,non-bonded termsandcrosstermstomakemoreaccuratetheirsvibrational analysisresults,SPASIBAlikefirstgenerationforcefieldreplaces http://dx.doi.org/10.1016/j.vibspec.2014.07.001

M.O.Bensaidetal./VibrationalSpectroscopy74(2014)20–32 21 thecrossterms(difficulttoparameterized)byUBSconstantsterms

forbondlengthsandbondangles.Thismakesitanaccurateforce fieldandsimpletohandleforvibrationalanalysisstudies.Literature surveyrevealsthatSPASIBAwasalreadyparameterizedforlipids [19], proteins, oligosaccharides and glycoprotein [20], aliphatic aminoacids[21],alkanes[22], alkenes[23],chondroitin sulfate [24],aliphaticethers[25],alcohols[26]andesters[27].However, tothebestofourknowledge,theaccuracyofthisforcefieldhasnot beentestedyetonthermoplasticpolymers(exceptforpolyaniline (PANI)[28])incontrasttoCHARMMandAMBER.Hence,theaimof thisworkistofillthisbreachinliteraturebyconductingaSPASIBA forcefieldstudyonsomethermoplasticpolymers,namelyPMMA, PMA,PMAAandPAA.Thispaperisorganizedasfollows:in Sec-tion2,experimentalproceduretodetermineInfraredandRaman vibrationalfrequenciesofPMMAisdescribed.Section3exposesthe adoptedcomputationalmethod.InSection4,wepresentand dis-cussourexperimentalandnumericalresultsonthelightofprevious worksfollowedbyaconclusion.

2. Experimentalprocedure

Purifiedanddistilledmethylmethacrylate(Aldrich,USA)was usedforthepolymer’spreparation.ThepowderofthePMMAwas synthetizedwitha radicalreactionprocess basedonthe emul-sion polymerization of the methyl methacrylate using sodium persulphateasinitiatorandsodiumdodecylsulfateas emulsify-ing agentat 80◦C. Each PMMA pelletwas preparedby mixing 1mg of thepowdered sample with100mg of dried potassium bromidepowder.Themixturewascarriedoutusingapestleand agatemortar,andthenpressedinaspecialdieuptoapressure of700kg/cm2 _{toyieldatransparentdisk.TheFourierTransform} Infrared (FTIR) spectrum of the PMMA polymer was recorded intherange 400–3500cm−1 usinga NicoletAvatar360Fourier TransformInfraredSpectrometer.Thescanningspeedwasheldat 30cm−1min−1 withaspectral widthof20cm−1.Frequenciesof allsharpbandsarewithina resolutionof±2cm−1.TheFourier TransformRaman(FTR)spectrumofourPMMAsample(pumped by532nmlaserlight)wasrecordedintherange200–3500cm−1 witharesolutionof2cm−1usingaLabRamXploraconfocalRaman microscope(HoribaJobinYvon)equippedwithaconfocal micro-scope(OlympusBX51).TheFTIRandFTRspectraobtainedareused asanexperimentalbasistoestablishthePMMAmoleculeforcefield throughnormalcoordinateanalysis.

3. Computationalmethod

WefirstconductedavibrationalanalysisonaPMMApolymer chainwith100monomersof15atomseach.Thefollowed computa-tionalmethodiswelldescribedinRefs.[20,29].Inourcalculations, thedielectricconstantisusedequalto1.The1–4VanderWaals interactionsandthefull1–4electrostaticpotentialhavebeen cho-sentodescribethenon-bondedinteractionsinourpolymer.The SPASIBAforcefieldconstantsfororganicmolecules[22,23,25–27] are usedas starting point to determineour newPMMA struc-tureparameters.These constantsarerefinedtoobtainthebest fit betweenthe calculated frequencies and theircorresponding peaks observed in the FTIR/FTR spectra, and then transferred toacrylic acid derivatives in order to analyzetheir vibrational normal modes and their assignments using PED analysis. To investigatetheforcefieldparametersaccuracyoftheconsidered polymer,therootmeansquare(RMS)valuesbetweencalculated and observed wavenumbers are estimated using the following expression: RMS=











v

Wecansummarizetheforceconstantsoptimizationandnormal modesanalysisprocedureaccordingtothefollowingsteps: 1.The monomerof each polymerchain usedin oursimulation

was generated initially by the GAUSSIAN 98 program [30]. Thestartingmonomerstructurewasoptimizedusingquantum mechanicsattheHartree–Focklevelwith6–31G**basissetin ordertocalculatethepartialcharges.Eachmonomerwasthen exportedtotheSPASIBAforcefieldprogramwheretheywere propagated100timestoobtainourinitialstructures(PMMA, PMAA,PMAandPAA)destinedtobeoptimizedbytheSPASIBA forcefieldprogram.

2.Determinationoftheforcefieldparameterswhich reproduce theavailableexperimentalvibrational spectra.Theoptimized SPASIBAparametersemployedinthepresentworkareshown inTable1(a)–(d).

3.Computationofthepolymergeometrywiththelowerenergy usingswitchedsteepestdescenttoconjugategradientmethod. Theconvergenceisreachedwhenthetotalforcebecomesless than10−5kcalmol−1 ˚A−1_.

4.Determinationofthefundamentalvibrationssupportedby nor-malcoordinatesanalysisandPEDcalculations.

5.TransferabilityevaluationoftheSPASIBAforcefieldconstantsto theotheracrylicpolymers,namelyPMA,PMAAandPAA.

TherepeatingunitsofacrylicpolymerswiththeirSPASIBAatom typesarepresentedinFig.1(a)–(d).Thefourstructureshavethe samebackboneconfigurationanddifferentsidechain.

DerreumauxandVergoten[20]reportedthattheequilibrium bond lengths are explicitly expressed in the UBS bond angle energy toimprovethetransferabilityof thebendingforce con-stant from one molecule to another. The SPASIBA Force field parameters are determined fromnormal modes analysis. A set of 39 independent force constants wereconsidered as starting parameters (see Table 1(a)–(d)) and were refined by adjust-mentprocedures toobtainthebestaveragedifferencebetween the calculated and observed values. We notice that the spe-cificUrey–Bradley–ShimanouchiforceconstantsKappa,LCH2and trans-gauche used in this work and originated directly from Ref. [20]are notgiven here.The finalempirical setof SPASIBA parametersdeducedfromthevibrationalanalysisisdisplayedin Table1(a)–(d) and might beconsideredasdatabasefor further polymericstudies.

4. Resultsanddiscussion

4.1. AssignmentsfortheinfraredandRamanspectra

OurobservedFTIRandFTRspectraaregiveninFigs.2and3, respectively. The FTIR spectrum in Fig. 2 is characterized by two intense peaks relative to stretching carbonyl group vibration (C O)at 1730cm−1 and stretchingester group vibra-tion (C O) at 1149cm−1. In the [3000–2854]cm−1 range the (C H) groups exhibit stretching modes, whereas in the [1485–1387]cm−1 range the (C H)groups exhibit deformation mode. Theweakpeak at1060cm−1 isdue tothe(OCH3) rock-ing mode. The broad peak ranging from 1260 to 1000cm−1 is attributed to the stretching vibration of the (C O) ester bond. The peaks at 989and 966cm−1 correspond respectively to (O CH3) symmetric stretching and CH3 rocking. The FTR spectrum in Fig. 3 shows several narrow peaks, specific to

22 M.O.Bensaidetal./VibrationalSpectroscopy74(2014)20–32 Table1

EmpiricalSPASIBAforceconstantsrelatedtoacrylicpolymers.

(a)ParametersofbondingenergetictermforSPASIBAforcefield

Bonds Startingparameters Refinedparameters

K(kcalmol−1) R0(Å) K(kcalmol−1) R0(Å)

CT HC 320.0b _1.110b _{325.0 1.110} C OE 310.0f _1.360f _{335.0 1.364} C O 615.0b _1.236b _{760.0 1.236} CT OE 245.0f _1.470f _{345.0 1.430} CT C 160.7b _1.506b _{190.0 1.506} CT CT 165.0b _1.530b _{165.0 1.530} CT C9 165.0c _1.530c _{165.0 1.530} C9 HM 291.3c _1.110c _{308.5 1.110} HE OEg _536.0b _0.950b _{565.5 0.960}

(b)ParametersforvalenceenergetictermforSPASIBAforcefield

Valenceangle Startingparameters Refinedparameters

H(kcalmol−1rad−2) 0(◦) F(kcalmol−1˚A2) H(kcalmol−1rad−2) 0(◦) F(kcalmol−1˚A2)

HM C9 HM 29.60c _107.70c _10.50c _{30.00 108.50 10.07} OE CT HC 17.50e _109.00e _120.00e _{20.55 109.50 57.70} HC CT HC 29.60d _108.50d _10.07d _{29.00 108.70 10.07} C OE CT 30.00f _114.00f _30.00f _{20.30 117.00 100.50} O C CT 14.00c _123.60c _35.00c _{21.58 126.50 58.14} C CT C9 18.70b _111.80b _47.47b _{18.70 111.80 47.47} O C OE 65.00f _125.00f _100.00f _{59.70 126.00 120.50} CT C OE 40.00f _112.20f _100.00f _{20.30 113.00 80.50} CT CT CT 18.70b _111.80b _47.47b _{18.70 111.80 47.47} CT CT C9 18.70b _111.80b _47.47b _{18.70 111.80 47.47} CT C9 CT 18.70b _111.80b _47.47b _{18.70 111.80 47.47} CT C9 HM 15.10c _109.50c _69.40c _{14.10 109.40 70.00} CT CT HC 15.89b _109.50b _69.43b _{15.89 109.50 69.43} C9 CT HC 15.90a _109.50a _69.40a _{14.90 109.40 69.90} CT CT C 20.14b _106.50b _47.47b _{20.14 106.50 47.47} HC CT C 15.65b _109.50b _78.37b _{15.65 109.50 78.37} C9 CT C9 18.70c _111.80c _47.50c _{18.70 111.80 47.47} C CT HCh _16.00b _109.50b _77.00b _{15.65 109.50 78.37} C OE HEi _28.45b _107.00b _41.00b _{28.50 110.00 41.00}

(c)DihedralangleenergetictermforSPASIBAforcefield

Torsions Startingparameters Refinedparameters

Vn/2(kcalmol−1_{) Phase(}◦_{) n(order) Vn/2(kcalmol}−1_{) Phase(}◦_{) n(order)}

X CT C9 X 0.160b ₁b ₀b _{0.160 0 1} X CT C O 0.130f ₀f ₃f _{0.550 0 3} X C OE X 3.330f ₁₈₀f ₂f _{1.500 180 2} X CT OE X 0.010f ₀f ₃f _{0.300 0 3} X CT CT X 0.150d ₀d ₃d _{1.300 0 3} X C CT X 0.250d ₁₈₀d ₂d _{0.550 0 3} CT OE C CT -1.175f ₁₈₀f ₂f _{1.500 180 2} X OE C X 3.330f ₁₈₀f ₂f _{1.500 180 2} CT CT C O 0.130f ₀f ₃f _{0.067 180 3} C OE CT HC 0.270f ₀f ₃f _{0.900 0 3}

(d)OutofplanebendingtermforSPASIBAforcefield

Torsions Startedparameters Refinedparameters

Vn/2(kcalmol−1_{) Phase(}◦_{) n(order) Vn/2(kcalmol}−1_{) Phase(}◦_{) n(order)}

X X C O 12f ₁₈₀f ₂f _{11 180 3} a_Ref.[19]. b _Ref.[20]. c _Ref.[21]. d _Ref.[24]. e_Ref.[25]. f _Ref.[27]. g_{ForPAAandPMAA.} h _ForPMAA.

i _ForPAA.

the PMMA chain. In the [3000–2800]cm−1 range the Raman transitionsare themostprominentand areidentified as(C H) stretchingvibrationsofCH2andCH3.Thepeakat1729cm−1 cor-responds to (C O) stretching vibration. The [1481–1453]cm−1

range is dominated by (C H) bending vibration, whereas [1288–813]cm−1rangecorrespondsto(C O)stretchingvibration. The(CH2)waggingandtwistingvibrationsat1406and1324cm−1, the (C C␣) stretching vibrations at 1124cm−1, the (CH3)

M.O.Bensaidetal./VibrationalSpectroscopy74(2014)20–32 23

ααCT

C9

C

O

OE

CT

CT

HM

HM

HC

HC

HC

HC

HC

HC

CT

C9

C

O

OE

CT

HC

HM

HM

HC

HC

HC

CT

C9

C

O

OE

HE

CT

HM

HM

HC

HC

HC

CT

C9

C

O

OE

HE

HC

HM

HM

Fig.1.MonomerunitsandSPASIBAatomtypesof(a)poly(methylmethacrylate) [PMMA],(b)poly(methylacrylate)[PMA],(c)poly(methacrylicacid)[PMAA],and (d)poly(acrylicacid)[PAA].

twistingmodeat1044cm−1,the(C C O)in–planebending vibra-tionsat600and559cm−1andthe(O C O)deformationvibrations at454cm−1areonlyobservedinFTRspectrum.OurFTIRandFTR spectraconfirmthepresenceofallfunctionalgroupsspecifictothe PMMApolymer.WenotethatmostbandsidentifiedinourFTIRand FTRspectraarealreadyreportedinreferences[31–36].

4.2. Optimizedgeometricalparameters

Smallmodelscanbeminimizedtoaglobalminimum. How-ever,multipleminimizationsfromdifferentstartingconformations shouldberuntoconfirmthataglobalminimumhasindeedbeen found.Largermodelslikeoursystemscanoftenbeminimizedto severaldifferentconformationsthatamoleculemightassumeat

3500 3000 2500 2000 1500 1000 500 20 30 40 50 60 70 80 90 100 86 0 TRANSMITTANCE (%)

Wavenu

mber (Cm

)

PMMA FTIR Spectrum

2 85 0 29 50 30 00 59 0 75 0 84 1 98 9 10 60 1 19 4 12 42 13 64 1 45 0

Fig.2.TheobservedFTIRspectrumofPMMA.

0K.But,aglobalminimum maynever befoundfortheselarge models,becauseofthecomplexityofthepotentialenergysurface. Inourcase,unfortunately,thereisnoguaranteethattheminimum wehavefoundisnecessarilyaglobalminimum,butbycomparing ourresultswithotherexperimentalandtheoreticalones (espe-ciallythoseofVacatelloandFlory[43])wecansaythatwehave reachedagoodminimum.

Theoptimizedgeometricalparameters(bondlengths,valence anddihedralangles)ofourstudiedPMMApolymeraresummarized inTable2,usingSPASIBAatomtypesnotationsgiveninFig.1.Our PMMAbondlengths,valenceanglesanddihedralangles respec-tivelypresentaveragedeviationsof0.006 ˚A,0.3◦and1.4◦compared toliteraturevaluesgiveninTable2.

Theconformationalisomersgeneratedbyrotationaroundthe X–C9–CT–Xbonddeterminestheconformationalstructureofthe chain backbone (trans(t) and gauche(g)), whereas, the rotation aroundtheX–CT–C–Xbonddeterminestheorientationoftheester groupsrelativelytothechain.

500 1000 1500 2000 2500 3000 35000 1000 2000 3000 4000 5000 96 6 98 9 RAMAN SHIFT (cm-1₎ IN TE NSITY (A.U) PMMA FT-RAMAN spectrum 47 6 60 0 81 3 1 45 3 172 9 284 6 2 95 3 300 0

24 M.O.Bensaidetal./VibrationalSpectroscopy74(2014)20–32 Table2

MeanvaluegeometricalparametersofPMMAoptimizedbySPASIBAforcefieldalong withotherexperimentalandtheoreticalresults.BondsaregiveninÅandvalence anddihedralanglesindegrees.

Parameters Ourresults Otherworks CT HC 1.110 1.10a,g_,1.08c C OE 1.354 1.31c_,1.36b,e,f,g_,1.37d C O 1.203 1.19c_,1.21a_,1.22b,e,f,g_,1.27d CT OE 1.429 1.39d_,1.46a_,1.45b,e,f,g_,1.42c CT C 1.540 1.32a_,1.49d_,1.52e,f,g CT CT 1.530 1.52c_,1.53b,d,e,f,g CT C9 1.530 1.53b,d,e,f,g C9 HM 1.115 1.08c_,1.10g HM C9 HM 106.25 107.5g_,120c OE CT HC 110.21 – HC CT HC 108.93 108c_,109c_,107.5g C OE CT 118.32 110f_,112.4a_,114.0b_,116c_,117d O C CT 123.35 121.0b,e_,122f,g_,124.0c_,125d C CT C9 108.79 109.5b,d,e_,111f O C OE 123.88 124.0a,f,g_,122c CT C OE 112.36 114.0b,e,f,g_,113c CT CT CT 110.79 110b,c_,109c_,111g CT CT C9 114.75 122.0b_,115.25d CT C9 CT 124.03 113.0e_,124.0a,f_,122.0b,d CT C9 HM 105.74 – CT CT HC 111.24 109.5g CT CT C 109.89 109c_,110c C9 CT C9 111.69 106f_,109c_,109.5d_,114.0a_,110.0b,c,d,e X CT C9 X −25.12,13.12 −23,11g_,−22,12g X CT C X −11.15,174.13 −8g_,171g a_Ref.[37]. b _Ref.[38]. c _Ref.[39]. d _Ref.[40]. e_Ref.[41]. f _Ref.[42]. g_Ref.[43].

OurPMMA dihedralanglesvaluescorroborate wellwiththe resultsofVaccateloandFlory[43].Thus,wecanconcludethatour polymerisofttsequencewith(10/1)helixconformation.

From Table2, we can state that our optimized geometrical parametersofPMMApolymerareingoodagreementwith liter-atureresults, and canbetakeninto accountfor thevibrational analysisandassignments.

4.3. Normalmodeanalysis

Wehavecarriedoutthenormalmodevibrationsanalysisusing theSPASIBAforcefieldrefinedconstants.Table3summarizesthe PMMAinfraredandRamanfrequencies,theirrelativeintensities andthecalculatedvibrationalfrequenciesusingPEDanalysis.We notethatredundantmodesandPEDcontributionsbelow10%are omitted.TheR.M.Sdeviationsbetweenthepredictedandobserved wavenumbersfrominfraredandRamanfrequenciesare7.8 and 8.7cm−1,respectively.

Inthe3000–2800cm−1range

Thevibrationsinthisregionrefertothe(C H)stretchingmodes inPMMAstructure.The(C H)stretchingvibrationsofPMMAare attributableto three distinct constituent groups: the␣-methyl groupdirectlyattachedtomainchaincarbon,thesidechainester methylgroupandthebackbonemethylenegroup.Theliterature assignmentsofthesebroadenedandhighlyoverlappedbandslead tolackofdistinctnessbetween␣CH3,OCH3 andCH2groups.The sevenbands, generallyreported in infraredand Ramanspectra [46,47],aretypicallyaround3025,3000,2950,2930,2910,2890 and 2850cm−1. In our FTIR and FTR spectra we observed just threebands characteristic ofPMMA sample around3000,2950 and2846cm−1.Thisdifferencemaybeduetothestrong overlap-pingbandscharacter.ThePEDinthis regionrevealsthat(C H)

stretchingmodesaredominatedbyacombinedstretching char-acterbetweensymmetricandasymmetricin␣CH3,OCH3andCH2 groups.However,calculatedfrequenciesat3011and3000cm−1are puremodeswithaveryhighcontribution.Ourcalculationsresults inthisregioncorroboratewellwithRefs.[46–48].

At1730cm−1

Thestretchingcarbonylgroupshows averyintensemodein ourIRspectrumandamediummodeat1729cm−1inourRaman spectrumfrequency.ThePEDassignmentsshowthatthestretching (C O)isapuremodewithahighcontribution(100%).Thisresult isinagreementwithprevioustheoreticalandexperimentalworks [31–36,45,47,49,54].

Inthe1500–1300cm−1region

Theregionbelow1500cm−1isthefingerprintofbothinfrared and Ramanspectra.Thespectra inthis region arehighly over-lappedandmainlydominatedbythesymmetricandasymmetric vibrations(deformationsin-planebending,twisting,wagging, scis-soring)of theestermethyl,␣-methyland methylenegroups. A lowskeletal (C C)stretchingvibrationisalsopresent. OurPED calculationsshowamixedvibrationalmodescharacterbetween asymmetricalbending vibrationsof␣-methyl and estermethyl groups.

In1300–950cm−1region

DespitethespectraofPMMAinthisregionhavebeenanalyzed byseveralearlierstudies[31,52,56,59],thebandassignmentsare notwelladdressedasreportedinref[60].Inaddition,thisregion isverysensitivetothetemperature,pressure,configurationand conformationalchanges[50,61].However,theabsorptionbandsin thisregionareknowntobeassignedtotheasymmetric stretch-ingof(C C O)modecoupledtothe(C O)stretchingmodeinthe estergroup[31,50,59].Thisregionexhibitstwodoubletsbands cor-respondingtoasymmetricstretchingof(C O);onecalculatedat (1150,1189cm−1),observedat(1149,1194cm−1)FTIRandat(1145, 1182cm−1)FTR and the secondcalculated at (1244, 1262cm−1), observedat(1242,1273cm−1)FTIRandat(1240,1288cm−1)FTR.The splittingofthesevibrationfrequenciesisattributedtothe rota-tionalisomerismoftheestergroup[52].Manyauthors[31,34,52] presentthesedoubletsassensitiveconformationaldoublets. How-ever,(C C)stretchingvibrationsmodescalculatedat(1064cm−1), observed at (1060cm−1)FTIR and at (1064cm−1)FTR seem tobe insensitive to the conformation changes. This doublet is only presentinsyndiotacticPMMA[31,34].ThePEDcalculationsofthis regionrevealthatthemajorityofvibrationalnormalmodesare stronglymixedbetweenthemwithlowcontributionscomparedto othervibrationalregions.Thismaybethemaincauseofthenot wellassignmentsdefinitioninthisregion.

Inthe950–250cm−1region

Accordingtoourtheoreticalresults,the900–250cm−1 range cover mainly frequencies of complicated coupled vibrational modes, involvingthe deformation (rocking and in-plane bend-ing)ofCH3group,deformation(in-planebendingandout-of-plane bending)of(C O)and(C O)groupsandstretchingof(C C)and (C O)groups.

The860cm−1vibrationalmode,presentinourcalculated fre-quencies,seemstobealmostdominatedbythe841cm−1 band inourFTIRspectrum(seeFig.2).Thisindicatesthelackof crys-tallinityinoursyndiotacticPMMApolymersample[58].Vacatello andFlory[43]andSundararajan[62]reportedthatisotacticPMMA doesnotabsorbat860cm−1.ThePEDindicatesastrongmixingof theinternaldisplacementcoordinateswithverylowcontribution totheenergypotentialdistribution.

M.O. Bensaid et al. / Vibrational Spectroscopy 74 (2014) 20–32 25 Table3

PMMAObservedandcalculatedIRandRamanwavenumbers(incm−1),theirassignments(symmetric,asymmetric,rocking,twisting,wagging,scissoringandbending)andtheirpotentialenergydistribution,comparedtoother experimentalandtheoreticalworks.

Observedwavenumbers Calculated Wave-numbers

Assignments AssignmentsPED(%) OTHERWORKS

FTIR FTR FTIRSyn(Iso) FTRSyn(Iso) Theo. Assignments(Exp/Theo)

– – 3011 – (100%)␯asCTHC(OCH3) 3026f(3029)f(3030)i,j

(3025)i3025h,i

3026f₍₃₀₂₇₎f

3013d(3027)o 3031i

3011d₃₀₃₁f _{AsymstretchOCH}

3d,f,h,i,j,o,sym stretchOCH3i 3000m 3000m 3000 C Hasym stretchingin OCH3 (99%)␯asCTHC(OCH3) 2995a,c,e,i(2995)c,i,r3000d 2998j,k₍₃₀₀₀₎i,j₂₉₉₈h,i (3002)i₂₉₉₆g,i₍₃₀₀₄₎i 3001e₍₃₀₀₂₎e,i (3006)o₂₉₉₈b 3002b₃₀₀₁p 3004i₃₀₃₁i 3002d,i _Asymstretch OCH3a,b,c,d,e,g,h,i,j,o,p,r,asym stretch␣CH3a,h,i,j,p,symstretch ␣CH3i,symstretchCH2c,asym stretchCH2i,outofplaneOCH3i 2950vs 2953vs 2958 C Hasym stretchingin CH2 (85%)␯asC9HM+(13%) ␯asCTHC(OCH3) 2948a,c,e,i,r₍₂₉₄₈₎c,i 2952f,g,i,j₍₂₉₅₄₎f₂₉₅₃d (2953)i,j₍₂₉₅₃₎i₂₉₅₈i,k (2958)i₂₉₅₆i₍₂₉₅₆₎i₂₉₅₇h 2962s₂₉₆₀s 2953d,e (2953)e,f 2950f,i₂₉₅₇a,i (2953)o₂₉₅₄b,i 2957p₂₉₆₀i 3002i2955i 2951d₂₉₅₂f₂₉₅₇i₂₉₅₀i _Symstretch OCH3a,b,c,e,f,g,h,i,j,p,r,asym stretch␣CH3c,f,h,i,j,o,s,sym stretch␣CH3a,c,e,h,i,p,sym stretchCH2c,i,asymstretch CH2a,b,d,e,h,i,j,p,inplaneOCH3i – – 2925 C Hsym stretchingin ␣CH3 (80%)␯sCTHC (␣CH3)+(18%)␯sC9HM 2920a,c,g,i₍₂₉₂₀₎c,e,i₂₉₂₉f (2914)f₂₉₁₅i₂₉₃₀i,j₍₂₉₂₅₎ i,j₍₂₉₃₀₎i₂₉₃₄i₍₂₉₂₈₎i 2928i₂₉₁₅i₂₉₂₅k₂₉₃₃h 2932e₍₂₉₃₂₎e 2938f₍₂₉₁₉₎f 2920a₂₉₂₀b 2939i₂₉₂₈i 2931f₂₉₃₈i₂₉₂₀i _{AsymstretchCH} 2f,symstretch CH2a,b,e,h,i,j,symstretch ␣CH3e,h,i,j,symstretch OCH3a,b,i,asymstretchOCH3g,i – – 2910 C Hsym

stretchingof OCH3

(73%)␯sCTHC (OCH3)+(26%)␯asC9HM

2915a,k₍₂₉₁₀₎i₂₉₁₀i₂₉₀₇h ₍₂₉₁₉₎o₂₉₁₅i _{SymstretchOCH}

3a,h,i,sym stretchCH2a,asymstretchCH2o – – 2889 C Hsym stretchingof ␣CH3 (57%)␯sCTHC (␣CH3)+(39%)␯sC9HM 2885h,i,j(2890)i,j2890i 2895k₂₈₉₂h₂₈₈₃s₂₈₈₂s 2893 f,i₂₈₉₀i 2880i 2892 f _{Symstretch␣CH} 3f,h,i,j,s,stretch OCH3h,i,j,asymstretchCH2s 2850w 2846m 2858 C Hsym stretchingin CH2 (86%)␯sC9HM+(12%) ␯sCTHC(OCH3) 2835c,e₍₂₈₃₅₎c₂₈₅₀a,f,i (2840)f₂₈₄₀d₂₈₄₄g 2845i,j,k₍₂₈₄₂₎i,j₍₂₈₆₀₎i 2860i₂₈₅₅h,i₍₂₈₄₅₎i₂₈₄₂i 2847h₂₈₅₇h₂₈₄₈s 2845e,f,i (2845)e₍₂₈₄₂₎f 2849a₂₈₄₀d (2842)o₂₈₆₄b 2848p₂₈₅₇i 2847i 2851f₂₈₃₅d _SymstretchCH 2f,o,s,stretching CH2h,i,defCH2i,symstretch OCH3a,b,c,d,e,g,h,i,j,p,asym stretchOCH3i,symstretch␣CH3

h,i_,inplaneOCH 3i 1730vs 1729m 1730 C Ostretching (100%)␯CO 1730a,c,e,i₁₇₄₀f₁₇₃₁f (1736)f₍₁₇₃₀₎c,i₁₇₂₇d (1750)r1732g1733k1758s 1735e₍₁₇₃₅₎e 1731f_(1738, 1725)f1736a,i 1730d(1738, 1725)o₁₇₂₄b 1736p 1732f₁₇₂₄d _{StretchC O}a,b,c,d,e,f,g,i,o,p,r,s_,

OCH3rockingf,defCCOo

1485m 1481m 1488 Inplaneasym defof␣CH3 (53%)␦asHCCTHC (␣CH3)+(42%) ␴HMC9HM 1483a,c,d,e,g,h₍₁₄₈₃₎c 1487f₍₁₄₈₆₎f₁₄₈₃j₍₁₄₈₃₎j 1485r₁₄₉₂k 1488e₍₁₄₈₈₎e 1487d,f₍₁₄₈₆₎f 1490a₍₁₄₈₆₎o 1483i₁₄₈₀i 1478f₁₄₈₀d _CH 2scia,f,␣CH3asym defc,d,e,h,i,j,o,r_,CH 2bendo 1450ms 1453ms 1450 Inplaneasym defofOCH3 (75%)␦asHCCTHC (␣CH3)+(22%)␦asHCCTHC (OCH3) 1464f,s₁₄₆₅a,c,g,j (1465)c,j,l₍₁₄₅₀₎l₁₄₇₀k 1465e₁₄₅₀f,g,h,r₍₁₄₅₃₎f 1452a,c₁₄₅₂j₍₁₄₅₂₎j (1465)r₁₄₅₅k₁₄₆₀h (1445)c1447d 1461i₁₄₆₀i 1451f,i₁₄₅₆a 1452b₁₄₆₀i,p 1452i₁₄₅₃d,e (1455)e₍₁₄₄₇₎o 1464f₁₄₅₀f₁₄₄₆d _␣CH 3asymdefa,b,d,f,h,i,j,p,s, OCH3asym defa,c,e,f,g,h,i,j,l,p,r,s_,CH 2 bendc,j,h,l,r_,OCH 3rockingf,sym defOCH3c,o,rockingCH2e 1434ms – 1437 Inplanesymdef

ofOCH3 (65%)␦sHCCTHC(OCH3) 1445e1436f(1442)f 1438a,c,j,l,g,h,r₁₄₃₇d (1438)j₁₄₄₂k,s (1447)f₍₁₄₃₂₎o 1435i₁₄₃₈i 1438f₁₄₃₀d _OCH

3symdefa,c,d,e,f,l,r,OCH3 bendg,i,j,h_,OCH

3asymbendo, OCH3rockingo,bendCH2s – 1406w 1402 CH2twisting (61%)

␶␻HMC9HM+(16%) ␻HMC9CT+(16%) ␻HCCTHC

1398d₁₃₉₀j₍₁₃₉₀₎j₁₃₉₁k ₁₄₀₀a₁₃₈₈o ₁₃₈₈d _CH

2twistorwaga,h,CH3defd, ␣CH3symbendj,o

26 M.O. Bensaid et al. / Vibrational Spectroscopy 74 (2014) 20–32 Table3(Continued)

Observedwavenumbers Calculated Wave-numbers

Assignments AssignmentsPED(%) OTHERWORKS

FTIR FTR FTIRSyn(Iso) FTRSyn(Iso) Theo. Assignments(Exp/Theo)

1387m 1383w 1382 Inplanesymdef

of␣CH3 (61%)␦sHCCTHC(␣CH3) 1388a,c,e,g,h,l,r(1388)c 1382f₍₁₃₈₆₎f₁₃₈₀s 1390e,i (1387)d,e₁₃₈₉f (1388)f 1392f₁₃₈₁d _␣CH 3sym,defa,c,e,f,h,i,l,r,s,CH2 defd_,OCH 3bendg 1364vw 1366w 1363 CH2wagging (50%)␻HMC9CT+(20%) ␯CTC9 1370c,e,h,k₁₃₇₆a₍₁₃₇₀₎c 1367d₁₃₇₀j₍₁₃₇₀₎j₁₃₆₈g 1374s₁₃₇₁s 1370e₍₁₃₇₀₎e ₁₃₆₄d _␣CH

3sym,defa,c,s,twistorwag CH2e,j,CH2wagd,s – 1324w 1323 CH2wagging (43%)␻HMC9CT+(31%) ␯C9CT+(13%) ␯CTCT+(10%)␦Sctcthc 1340f₍₁₃₃₈₎f ₁₃₂₅e₁₃₂₆f (1335)f₁₃₂₇d (1335)o 1335f₁₃₂₀d _CH 2wagf,o,CH2twistd,CC stretchingo_,␣CH 3symbendo – – 1310 CH2wagging (33%)␻HMC9CT+(24%) ␯CTC+(17%)␯C9CT 1316f₁₃₀₃s ₁₃₁₀f _CCstretchf_,CH 2wagf,CH2twists 1273vw 1288w 1262 Asymstretching of(C O) (50%)␯asCOE+(29%) ␯asOECT+(12%)␯CTC 1295e₍₁₂₉₅₎c₁₂₇₈f₍₁₂₆₈₎i 1270a,c,g,l,r₍₁₂₆₀₎c,r 1267d₁₂₆₈n₍₁₂₆₀₎l₁₂₇₆k 1273m₍₁₂₆₅₎m 1272e₍₁₂₈₁₎e (1270)f₁₂₇₆a (1270)o₁₃₃₆b 1264p

1271f₁₂₆₁d _CCstretchf,o_,asymstretch

CCOa,b,c,l,n,p,r_,stretch COa,b,c,d,n,p,r_,asymstretch COCe,l_,CH 2twisto,CCbendo, CCCdefo_,␣CH 3symdefl,r 1242m 1240w 1244 Asymstretching of(C O) (58%)␯asCOE+(22%) ␯asOECT 1252e₁₂₄₂f,g,m₁₂₄₀a,c,l (1252)c,l,r₁₂₃₉d,m₁₂₃₈n 1240r₍₁₂₃₉₎l₁₂₄₈k₁₂₅₁s 1238e₁₂₄₁f (1231)f₁₂₃₄a 1240d₍₁₂₃₁₎o 1238b 1241f₁₂₃₈d _COstretchb,c,d,f,l,n,o,r,s_,CC

stretchf,r_,asymstretch

CCOa,b,c,l,n,r_{,asymstretchCOC}e_,

CH2twisto,COinplanebendo, bandassociatedwithvibrations ofestergroupsofPMMAg

1194m 1182w 1189 Asymstretching of(C O C) (55%)␯asOECT+(17%) ␯asCOE+(15%)␦OECTHC 1190a,c,e,r₁₁₉₃f,m₁₁₉₇d,s (1198)f₍₁₁₉₀₎c,r₁₁₉₂n (1191)l₁₁₉₁l₁₁₉₄g₁₂₀₀k (1195)m 1188a,e₍₁₁₉₀₎e 1183f₁₁₈₇d (1190)o 1191f₁₁₉₀d _OCH

3rockf,s,o,OCH3,asym bendf,_CH

2twistf,o,skeletal stretchingcoupledwithinternal CHdefvibrationc,n,r_,asym

stretchCOCa,e,l_,CH

3wagd,CH2 wago_{,bandassociatedwith}

vibrationsofestergroupsof PMMAg 1149ms 1145w 1150 Asymstretching of(C O C) (44%)␯asOECT+(22%) ␯asCOE+(15%)␦OECTHC 1150a,c,e,g,r₁₁₄₉f,l,m (1150)c,r₁₁₄₇d₁₁₄₈n (1147)l,m₁₁₅₅k 1160d,e₍₁₁₅₂₎e 1158f₁₁₆₁a (1157)o₍₁₁₅₀₎o

1156f₁₁₅₅d₁₁₃₈d _CCstretchf,l,o_{,skeletalstretching}

coupledwithinternalC Hdef vibrationc,n,r_,asymstretch

COCa,e,l,o_,CH 3wag(CH3 twist)d_,CH 2wago,␣-CH3rocko, CH2twisto – 1124w 1110 Stretchingof (C C) (29%)␯CTCT+(16%) ␯CTC9+(14%) ␦OECTHC+(10%) ␦CTCTHC 1122e,f,s₍₁₁₁₅₎f₁₁₂₅n (1104)l₁₁₆₁l₁₀₉₉s 1123e₍₁₁₂₀)e 1126f₍₁₁₂₃₎f 1125a₁₁₂₇d (1123)o₍₁₁₁₃₎o 1118f₁₁₂₁d _OCH

3rockf,o,OCH3asym bendf,o_{,backbonestretch}

CCa,e,l,n,s_,CH 3wagd 1060w 1064w 1064 C CStretching (46%)␯CTCT+(25%) ␯CTC9+(15%)␦OECTHC 1065f₁₀₆₃a,c,g₁₀₆₀n₁₀₆₈k 1057s 1063e₍₁₀₅₀₎e 1064f₍₉₉₆₎f 1067d₁₀₆₂b 1081p 1068f₁₀₆₄d _OCstretchf_,OCH 3rockf,s,band arisesfromintramolecular interactionc,n_{,backbonestretch}

CCa,b,e,g,p_,CH 3twistd – 1044vw 1046 CH3twisting andC C stretching (33%)␶␻HCCTC9+(31%) ␯CTC9+(13%)␶␻CTCTHC 1050d ₁₀₄₆d ₁₀₄₂d _CH 3twistd

– – 1023 OCH3rocking (45%)␳OECTHC+(31%) ␯COE+(15%)␦HCCTHC

1026f(998)f1038s 1027d 1022d OCstretchf,OCH3rockf,CC stretchd,CH2rocks 989m 989m 980 C Ostretching andInplane bendingof OCH3 (25%)␯aCOE+(21%) ␯CTCT+(20%) ␦OECTHC+(11%) ␯CTC9+(10%) ␯aOECT+(10%)␯CTC 989t₉₉₆e₉₉₂f₍₉₉₆₎c₉₉₀d,g 988a,c,r₉₉₆k₍₉₉₆₎r₍₉₉₅₎t (995)e₉₉₀d (996)o₉₈₈e 987f₍₉₉₆₎f₉₉₁a 988b₉₉₉p 991f₉₈₁d₉₈₅f _␣CH

3rockf,OC,stretchf,o,asym stretchCOCc,g_,rockOCH

3a,b,

M.O. Bensaid et al. / Vibrational Spectroscopy 74 (2014) 20–32 27 966w 965m 957 OCH3rocking (32%)␳CTCTHC (␣CH3)+(22%) ␳HMC9CT+(17%) ␯CTC+(15%) ␯CTCT+(10%)␯COE 951e,f₍₉₅₁₎c,f 967a,c,d,f,g,r,t₍₉₅₀₎r₉₇₂k 968s₉₄₆s₍₉₅₃₎t 967e,f₍₉₅₃₎e,f (960)f₉₇₀a,d (960)o₍₉₅₃₎o 935f₉₈₀f₉₆₈d _␣CH 3rocka,c,e,f,g,o,r,s,CH2 rockf,o_,CCstretchd,f,o 912vw – 913 CH3rockingand CH2rocking (33%)␳CTCTHC (␣CH3)+(27%) ␳HMC9CT 913d,f910a,c,t915g916k 912e915f920d 914b₉₂₅p 915 f₉₀₅d _CH 2rockb,f,p,CH3rockd 860vw – 860 CH3rockingand CH2rocking (36%)␳CTCTHC+(30%) ␳HMC9CT+(14%) ␯C9CT+(12%)␯CTCT 863f₈₆₀t ₈₇₇e₈₇₆f₈₇₈b 880d 881f₈₆₈d _CCstretchf_,CH 2Rockb,f,t,CO stretchf_CH 3rockd 841w 837w 839 CH2rocking (30%)␳HMC9CT+(26%) ␳CTCTHC+(16%) ␯COE+(13%) ␯C9CT+(11%)␯CTCT 842a,c,e,g₍₈₄₂₎c₈₄₀d₈₃₀k (843)f₈₄₅k₈₄₄s₈₄₁t 842e₍₈₄₁₎e 833a₈₄₀d (844)f,o 828d _CCstretchf,o,s_,CH 2 rocka,b,d,e,g,f,o,t_,COstretchf,o 808vw 813s 796 C Osym stretching (24%)␯sOECT+(21%) ␯sCOE+(19%) ␯CTCT+(10%)␳HMC9CT 810e,f,g₍₈₀₈₎f₈₀₇a,c,d,q (810)c₇₈₆q₈₂₇g₈₁₂k 815e₍₈₀₉₎e,f 812f₇₉₆a₈₁₀d (809)o₈₁₈a 812b₇₈₆q

800f₈₀₅d₈₀₃q₇₉₆q _COstretchf,_CCstretchf,o,q_,sym

stretchCOCa,b,e,g,o_{,C Oin} planebendf 750m – 767 C Ooutof planebending (64%)␥CO+(16%) ␯COE+(15%)␦OCOE 759e₇₄₇f₍₇₆₄₎f₇₄₉a,r,t (759)c,r,t₇₅₂g 767e₍₇₇₄₎e 736a₇₃₃d (782)o₍₇₆₄₎o 732b₈₅₃p

755f₇₂₅d₇₆₁q _{C Ooutofplanebend}d,f,o_,rock

CH2c,stretchCCskeletal modea,b,c,g,p,r_,COinplane bendd_,Cbendo,r – – 742 C Ooutof planebending (42%)␥CO+(13%) ␯COE+(13%) ␦OCOE+(10%) ␯CTCT+(10%) ␯C9CT+(10%)␯CTC 749c₇₅₀d,s₇₄₉q₇₅₃k ₍₇₄₂₎e₇₃₂q ₇₃₉d₇₆₁q _RockCH 2c,s,stretchCCc,e,q,C O outofplanebendd

– 600m 607 In-plane bending (C C O) (44%)␦CTCO+(30%) ␯CTCT 643f₅₉₈a,f₍₆₀₉₎f ₆₀₁e₆₀₂f_(597, 562)f₆₀₄a₆₀₀d 600b₍₅₉₇₎o 602p

660f₅₉₅d _CCOOstretcha,b,f,o,p_,COinplane

bendd,f,o_,symbendCCOa,e,b,p

590w 559w 570 Inplanebending of(C C O) (32%)␦CTCO+(26%) ␦C9CTCT+(24%) ␯CTCT+(15%)␯CTC 560e₍₅₅₉₎f,i₅₅₂a₍₅₆₀₎c 554c₅₅₂q₍₅₆₈₎i 555e₍₅₆₁₎e 537a₅₆₀d (562)o₅₅₈b 552q

550d₅₉₁q _DefCCCa,b,e,i_{,CCinplanebend}d_,

CCstretchi,o,q_,COinplane bendo_,wagof␣CH 3i – 526vw 501 Inplanebending of(C C O) (35%)␦COECT+(30%) ␯CTCT

508f₅₀₅a₅₁₀c,k ₅₀₉n₅₀₄a₅₁₃d ₅₀₂d _CCOdefn_,CCbendd,n_,inplane

asymdefCCOorC Oinplane defa 482vw 485vw 482 Inplanebending ofC C O) (27%)␦COECT+(25%) ␦CTC9CT+(17%) ␦CTCOE+(13%)␦CTCTCT 486f₍₄₈₀₎f,i₄₈₄a,c,e,g₄₈₅k ₄₈₄e,f₍₄₈₀₎e (481)f₄₈₇a,d (481)o

484f₄₇₈d _CCOdefc,f,o_,CCbendd,f,i,o_,Out

ofplanedefCCOa,e,g_,CCCdefo,i

– 454vw 459 Inplanebending of(O C O) (25%)␦CTCO+(23%) ␥COE+(20%) ␦CTCOE+(10%) ␦C9CTCT+(10%)␦CTCTC

28 M.O. Bensaid et al. / Vibrational Spectroscopy 74 (2014) 20–32 Table3(Continued)

Observedwavenumbers Calculated Wave-numbers

Assignments AssignmentsPED(%) OTHERWORKS

FTIR FTR FTIRSyn(Iso) FTRSyn(Iso) Theo. Assignments(Exp/Theo)

– 391vw 390 Inplanebending of(C O C) (40%)␦COECT+(16%) ␦CTCTCT+(14%) ␦CCTCT+(13%)␦CTC9CT 400a(391)i420k 391f400a (390)o 392

f _DefCOCa_Cbendo_,CCCdefo_,wag

of␣CH3i – 365w 365 Inplanebending of(C O C) (35%)␦COECT+(32%) ␦CTC9CT+(17%) ␦CTCTCT+(14%)␦CTCTC 364f₍₃₆₅₎f₃₆₀a ₃₆₆e₍₃₇₃₎e 363f₍₃₇₂₎f₃₇₀a 367d₍₃₇₂₎o (341)o

360f₃₆₁d _CCCdeff,o_,COCdeff,o_,inplane

symbendCCOa,e,o_,COoutof

planebendd – – 327 Inplanebending of(C C C) (33%)␦C9CTCT+(32%) ␦COECT 320a₃₂₀q ₃₀₄a₍₃₁₄₎o 296q 370q _DefCCCa,o,q_,Cbendo – 299w 283 Inplanebending of(C C C) (25%)␦C9CTC+(20%) ␦COECT+(15%)␦CTCTC9

301f,e₃₀₀d ₂₉₅f₂₉₁d _{COoutofplanebend}d

– 252vw 260 Inplanebending of(C C C)

(25%)␦C9CTC+(20%) ␦COECT+(16%) ␶OECT+(15%)␦CTCTC9

319f₂₇₆f₍₃₁₄₎f₂₉₅a ₂₇₅f₍₃₁₄₎f₂₆₇d ₂₈₄f₂₅₀d _{COinplanebend}f_,CCCdeff_,CC

bendd,f

– – 203 Torsionof (C O)

(55%)␶OECT 216q₂₂₅q₍₁₈₈₎i ₂₀₀d₍₂₂₁₎o

216q

192d₂₀₁q₁₈₂q _{CCoutofplanebend}d,q_,CO

torsiono_,CCCbendo,q_,defOCH

3i – – 189 Torsionof

(C O)

(40%)␶COE+(28%) ␶OECT+(15%)␦C9CTC

163d ₁₆₉d _{CCoutofplanebend}d

– – 146 Torsionof(C C) (60%)␶CTC9 153f₁₄₀d ₁₇₀f₁₄₄d _CCtorsiond – – 116 Torsionof (C O) (72%)␶COE+(22%)␶CTC (113)i₍₁₀₉₎i _COtorsioni – – 87 Torsionof (C O)

(78%)␶COE+(20%)␶CTC 95q ₍₈₅₎o ₇₃q _CCstretcho_,Cbendo_,CCCdefo

OutofplanebendofCCCq_,CO

torsioni

– – 62 Torsionof (C O)

(81%)␶COE 58q _{Hinderedrotationortranslation}q

Note1:␣CH3isthemethylgroupandOCH3istheestermethylgroup.

Note2:vs:verystrong;s:strong;ms:mediumstrong;m:medium;w:weak;vw:veryweak;

␯:stretching;␦:inplanebending;␥:outofplanebending;␶:torsion;␳,rocking;␯s:,symmetricstretching;

␯as:asymmetricstretching;␦s:symmetricdeformation;␦as:asymmetricdeformation;␶␻:twisting;␻:wagging␴:scissoring.

a_Ref.[31]. b _Ref.[33]. c _Ref.[34]. d _Ref.[35]. e_Ref.[36]. f _Ref.[44]. g_Ref.[45]. h _Ref.[46]. i _Ref.[47]. j _Ref.[48]. k_Ref.[49]. l _Ref.[50]. m _Ref.[51]. n _Ref.[52]. o_Ref.[53]. p _Ref.[54]. q _Ref.[55]. r_Ref.[56]. s _Ref.[57]. t_Ref.[58].

M.O.Bensaidetal./VibrationalSpectroscopy74(2014)20–32 29 Below250cm−1

Fewbandsareobservedandcalculatedbelow250cm−1.The C OandC Ctorsionalvibrationswereexpected.ThePEDindicates largecoupledcontributionsbetweenthesetorsionalvibrations.

4.4. TheaccuracyandtransferabilityoftheSPASIBAparameters Theaccuracyofamolecularmechanicsforcefieldisrelatedto itsforceparameterstransferabilityfromonemoleculetoanother. Good parameters should generally be able to reproduce vari-ousphysicalpropertiesofdifferentmolecularsystemswithsame chemicalstructures.

Theaimofthissubsectionistocheckthetransferabilityof SPA-SIBAforceconstants(developedfor PMMA)toPMA,PMAAand PAApolymers.Tothisend,wehaveanalyzedthenormalmodesof thesepolymersbymeansofthesamePMMAcalculationsmethod andsamenumberofmonomerunits.MostofthePMMAforcefield refinedparametersareusedtoestablishthevibrational wavenum-bersoftheothersstudiedpolymers,withadditionalforceconstant namely(HE OE)bondingenergetictermspresentonthePMAA andPAAstructures,(C CT HC)forPMAAand(C OE HE)forPAA valenceangleenergeticterms(seeTable1(a)and(b)).

OptimizedgeometricalparametersofourPMA,PMAAandPAA polymersaresummarizedinTable4(a)–(c).Thebondlengthsand valence anglesaveragedeviations relativelytoliterature values giveninTable4(a)–(c)are(0.037 ˚A,2.2◦)PMA,(0.020 ˚A,5.4◦)PMAA and(0.037 ˚A,3.1◦)PAA.

Thediscrepanciesobservedinanglesvaluesbetweenourresults andliteraturevaluesaremainlyduetothedifferencebetweenthe modelsusedforcomparison(copolymersagainstour homopoly-mersof100monomers).Wenotehere,thatourPMA,PMAAand PAApolymersexhibiteachthesame10/1helixconformationwith ttsequencededucedaboveforourPMMApolymer.

InTable5wesummarizethecalculatedvibrational wavenum-bersandtheirPEDattributionsofPMA,PMAAandPAAalongwith ourPMMAandpreviousexperimentalresults.

AsitcanbenoticedfromTable5,allstudiedacrylicpolymers present almost same symmetrical and asymmetrical stretching vibrational normal modes of CH3 and CH2 groups in the mid-infraredregionwithhighPEDcontribution.Theseresultsagreewell withexperimentalvibrationalbandsintheFTIRorFTRspectrum oftheacrylicpolymersreportedintheliteratureforPMA[57,66], PMAA[57,67,68]andPAA[68–70].

Thecalculated(C O)stretchingfrequenciesat1730cm−1(for PMMA,PMAandPAA)andat1732cm−1 forPMAAwerealready reported in previous experimental results in 1700–1750cm−1 region[66–71].Wenotealsothatthesymmetricaland asymmetri-calofCH3andCH2deformationvibrationsinthe[1500–1430]cm−1 regionwereobservedbymanyauthorsforsomeAcrylicpolymers [57,66–70].

Below1430cm−1,andatthesamewavenumber,thePED cal-culationsgivedifferentassignmentsforthestudiedpolymers.As it can beobserved from Table 5, PAA and PMAA exhibit same (C O) stretchingcoupledwith(O H)in-plane bending attribu-tions,whereas,PMMAandPMApresentasymmetricaldeformation ofestermethylgroup.Thesedissimilaritiesinmodeattributions areduetothesensitivityoftheSPASIBAforcefieldtotheatomic positionsinthechemicalstructureandwerealreadyreportedin manypreviousexperimentalresults[48,66,67,70].ThePED calcu-lationsshowthepresenceofthehydroxylstretchingvibrationof (O H)grouparound3447cm−1and3441cm−1forPMAAandPAA, respectively.These (O H)stretching vibrationsarepuremodes withhighcontributionstothepotentialenergydistribution.From vibrational wavenumbers and their assignments of thestudied

Table4

MeanvaluegeometricalparametersofPMA,PMAAandPAAoptimizedbySPASIBA forcefieldalongwithotherexperimentalandtheoreticalresults.Bondsaregivenin Åandvalenceanddihedralanglesindegrees.

(a)OptimizedgeometricalparametersofPMA

Parameters Ourresults Otherworks[63]

CT HC 1.110 1.069,1.070,1.076,1.080 C OE 1.352 1.352,1.350 C O 1.203 1.206,1.207 CT OE 1.430 1.452 CT C 1.530 1.473,1.474 CT C9 1.560 1.316 C9 HM 1.107 1.072,1.073 HC CT HC 108.81 109.0,110 OE CT HC 109.49 105,110 CT C OE 113.13 111,113 O C CT 123.61 125,126 C9 CT HC 110.93 124 C CT C9 112.78 120,123 CT C9 HM 108.69 121,122 HM C9 HM 105.51 117 O C OE 124.02 122,123 HC CT C 111.66 114,116 C9 CT C9 111.80 – CT C9 CT 119.01 – X CT C9 X −26.44,17.13 – X CT C X −7.01,179.03 –

(b)OptimizedgeometricalparametersofPMAA

Parameters Ourresults Otherworks

CT HC 1.102 – CT CT 1.542 – C O 1.200 1.234a_,1.230b C OE 1.352 1.368b CT C 1.542 – CT C9 1.573 – C9 HM 1.101 – HE OE 0.960 0.971a_,0.967b CT C9 HM 102.35 – C CT C9 111.14 – O C CT 128.26 – C OE HE 105.06 109.97a HM C9 HM 106.05 – HC CT HC 107.65 – O C OE 119.10 113.22b CT CT C9 110.77 – CT C9 CT 127.45 – CT CT HC 111.12 – CT CT C 111.44 – C9 CT C9 102.41 – X CT C9 X −20.84,22.71 – X CT C X −11.78,178.32 –

(c)OptimizedgeometricalparametersofPAA

Parameters Ourresults Otherworks[63]

CT HC 1.110 1.069,1.070,1.072 C OE 1.360 1.356,1.357,1.358,1.359 C O 1.199 1.199,1.204,1.205 CT C 1.540 1.470,1.471,1.485,1.487 CT C9 1.567 1.306,1.315,1.316 C9 HM 1.109 1.072 HE OE 0.965 0.961,0.963,0.968 CT C9 HM 109.91 120,121,122,124 HM C9 HM 104.78 117,118 C9 CT HC 105.62 121,122,123,124 C CT C9 114.02 120,123,126 O C CT 127.30 122,124,125,127 C OE CT 113.87 111,113,116,118 C OE HE 108.68 112,115,117 O C OE 118.95 120,122 CT C9 CT 119.77 – HC CT C 101.10 114,116,118 C9 CT C9 113.36 – X CT C9 X −26.18,16.82 – X CT C X 6.56,174.39 – a_Ref.[64]. b_Ref.[65].

30 M.O. Bensaid et al. / Vibrational Spectroscopy 74 (2014) 20–32 Table5

CalculatedwavenumbersandPEDofPMA,PMAAandPAAobtainedusingtheoptimizedforceconstantsfromtheempiricalSPASIBAforcefield(PMMAwavenumbersvaluesandattributionsarereproducedhereformoreclarity).

Calculatedwavenumbers(cm−1 ) PED%assignments Otherworks

PMMA PMA PMAA PAA PMMA PMA PMAA PAA PMA PMAA PAA

FTIR/FTR Assignments FTIR/FTR Assignments FTIR/FTR Assignments

– – 3447 3441 – – (98%)␯OEHE (98%)␯OEHE (3572–3540)a,g O Hstretcha,g 3100–3200i OHstretchi

3000 3075 3006 3076 (99%)␯asCTHC(OCH3) (97%)␯asCTHC (83%)␯asCTHC (100%)␯asCTHC 2998b _{CH3 asym}stretchb 3001g _{CH2 stretch}g 2958 2964 2962 2967 (85%)␯asC9HM+(13%)

␯asCTHC_(OCH3)

(63%)␯asC9HM (63%)␯asC9HM (63%)␯asC9HM 2970b StretchCHb (2960–2971)a,g _{CH3 asym}

stretcha,g – 2943 2941 2942 – (41%)␯sCTHC+ (27%)␯asC9HM (40%) ␯sCTHC+(27%) ␯asC9HM (43%) ␯asC9HM+(24%) ␯Scthc

2959b Symstretch_CH3b 2939g _{CH3 sym}stretchg

2925 2930 2930 2929 (80%)

␯sCTHC(␣CH3)+(18%) ␯sC9HM

(68%)␯asC9HM (61%)␯asC9HM (67%)␯asC9HM 2924b _{CH2 asym}stretchb 2928a _{CH2 asym}stretcha (2877–2930)i,f _{CH2 or}CHstretchf CH2 asymstretchi 2889 2885 2883 2882 (57%)␯sCTHC (_␣CH3)+(39%)␯sC9HM (52%) ␯sC9HM+(43%) ␯sCTHC (53%) ␯sCTHC+(45%) ␯sC9HM (55%) ␯sC9HM+(41%) ␯sCTHC

2883a _{CH2 asym}stretcha 2882a _{CH3 sym}stretcha

2858 2845 2842 2845 (86%)␯sC9HM+(12%) ␯sCTHC(OCH3)

(85%)␯sC9HM (83%)␯sC9HM (85%)␯sC9HM 2847b2848a _{CH2 sym}stretcha,b 2839a _{CH2 sym}stretcha 2860i _{CH2 stretch}symi

1730 1731 1734 1731 (100%)␯CO (99%)␯CO (99%)␯CO (95%)␯CO 1733b1758a vC Oa,b (1673–1767)a,c,d,g,h C Ostretcha,g,d,h COOc (1686–1742)d,e,f,i C Ostretchd,e,f,i 1488 1485 1483 1485 (53%)␦asHCCTHC (_␣CH3)+(42%) ␴HMC9HM (38%) ␦asHCCTHC+(24%) ␦asOECTHC+(18%) ␯OECT (60%) ␦asHCCTHC+(26%) ␯OEHE (54%) ␦asHCCTHC+(25%) ␯OEHE 1487c1483d OHc,_{CH3 def}d 1450 1450 1450 1453 (75%)␦asHCCTHC (_␣CH3)+(22%) ␦asHCCTHC(OCH3) (71%) ␦asHCCTHC+(10%) ␦HMC9HM (49%) ␦HMC9HM+(16%) ␦asHCCTHC (62%) ␦HMC9HM+(13%) ␦CTCTHC 1452b1442a _{CH3 asym}defb CH2 benda (1448–1455)c,d,g 1455a _{CH3 asym,}defg, CH2c,_{CH2 def}a,d (1451–1460)d,e,f,i _CH2,defe,i_CH2 defd,f 1437 1434 1432 1434 (65%)␦sHCCTHC(OCH3) (64%) ␦asHCCTHC+(19%) ␦HMC9HM (64%) ␦asHCCTHC+(35%) COEHE (72%) ␦asHCCTHC+(31%) COEHE 1434b _{CH3 sym}defb,_CH2 defb 1432h O–H/acidcarboxyl stretchh – 1416 1424 1419 – (55%)␦asHCCTHC (52%)␯COE+(23%) ␦COEHE+(10%) ␯C9CT (44%)␯COE+(33%) ␦COEHE+(10%) ␯CTC 1415c1413c COOc (1413–1415)d,f,i COstretchd,f,OH defd,f,_{CH2 bend}i 1402 1403 1401 1397 (61%) ␶␻HMC9HM+(16%) ␻HMC9CT+(16%) ␻HCCTHC (31%) ␶␻HMC9HM+(23%) ␦sHCCTHC+(14%) ␻CTC9HM+(13%) ␻HCCTCT (45%)␯COE+(39%) ␦COEHE (43%)␯COE+(38%) ␦COEHE 1389c1390d COOc,COstretchd, OHdefd

1402d1400i COOsymstretchd,

i_{,OHinplanebend}i 1363 1369 1371 1379 (50%)␻HMC9CT+(20%) ␯CTC9 (43%) ␻HMC9CT+(21%) ␦HCCTC9 (30%)␦sHCCTCT+ (12%)␯COE+(12%) ␯C9CT (29%) ␦sHCCTCT+(23%) ␦HCCTC9 (1374–1180)a,b _{CH3 wag}b,_CH2 waga (1371–1381)a,d,g _{CH3 sym}defa,g 1323 1346 1331 1333 (43%)␻HMC9CT+(31%) ␯C9CT+(13%) ␯CTCT+(10%)␦sCTCTHC (34%) ␦sHCCTHC+(23%) ␦HCCTC9+(15%) ␦HMC9HM (30%) ␻HMC9CT+(12%) ␦CTCTC (41%) ␻CTC9HM+(16%) ␦HCCTC+(14%) ␦C9CTHC

1330b CHdefb 1354g1324c C–O–Hbendg_CH2c 1320–1345d,e,f _CH2wagd,CHdefd, CH2 twiste,f 1310 1302 1280 1295 (33%)␻HMC9CT+(24%) ␯CCT+(17%)␯C9CT (38%) ␻CTC9HM+(17%) ␯CTC+(14%) ␯COE+(10%) ␦HCCTC (29%) ␻CTC9HM+(24%) ␯CTC9+(15%) ␯CTCT+(14%)␯CTC (49%) ␻HMC9CT+(12%) ␯CTC 1302a1175–1302a _{CH2 twist}a (1280–1304)a _{CH2 wag}a 1262 1267 1258 1276 (50%)␯asCOE+(29%) ␯asOECT+(12%)␯CTC (55%) ␯asCOE+(21%) ␯asOECT+(12%) ␯CTC+(10%) ␦CTC9HM (48%) ␦COEHE+(24%) ␯COE (56%) ␦COEHE+(30%) ␯COE 1260b CCOOstretchb, skeletalstretchb 1262a,d COstretcha,OH defd 1244 1256 1243 1255 (58%)␯asCOE+(22%) ␯asOECT (45%) ␯asCOE+(16%) ␯CTC+(14%)␯OECT (53%) ␦COEHE+(18%) ␯COE (53%) ␦COEHE+(26%) ␯COE

1251a C Ostretcha 1197–1245a _{CH2 twist}a 1247d1248f COstretchd,OH defd,C Ostretch coupledwithO H in-planebendf 1189 1167 1179 1174 (55%)␯asOECT+(17%) ␯asCOE+(15%)␦OECTHC (34%)␯OECT+(16%) ␯C9CT+(13%) ␯COE+(10%) ␦COEHC (69%) ␦COEHE+(25%) ␯COE (28%) ␦COEHE+(22%) ␯CTC9+(20%)␯COE (1161–1175)a,b CCOOstretchb, skeletalstretcha,b, CH2 twista (1171–1176)a,c,d COOHc,dC C stretcha 1170d COOHd

M.O. Bensaid et al. / Vibrational Spectroscopy 74 (2014) 20–32 31 1150 1131 1122 1131 (44%)␯asOECT+(22%) ␯asCOE+(15%)␦OECTHC (47%)␯OECT+(19%) ␯CTC9+(13%) ␦CTCTHC (58%)␯COE+(27%) ␦COEHE (32%)␯COE+(29%) ␦COEHE+(14%) ␦HCCTC9

1120b C Cstretchb (1066–1122)a,g C–Ostretchg_␣CH3

stretcha 1130i CHbendi 1046 1051 1052 – (33%)␶␻HCCTC9+(31%) ␯CTC9+(13%)␶␻CTCTHC (41%) ␳HMC9HM+(27%) ␯CTC+(15%)␯CTC9 (43%) ␳HMC9HM+(14%) ␯CTC9+(12%)␦CCT – 1050b(721–1038)a,b C Cstretchb_CH2 rocka 1010–1057a _{CH3 rock}a 1026f _{CH2 rock}f 957 956 949 940 (32%)␳CTCTHC (_␣CH3)+(22%) ␳HMC9CT+(17%) ␯CTC+(15%) ␯CTCT+(10%)␯COE (37%) ␳HCCTHC+(20%) ␳HMC9CT+(10%) ␯CTC (43%)␥OE HE++(22%) ␦HCCTC9 (39%)␥OE HE+(22%)␦HCCTC9 956b _{CH3 rock}b (933–950)a,c,g _{CH2 wag}g,_␣CH3c, OHoutofplane benda 945i OHbendi 839 848 855 842 (30%)␳HMC9CT+(26%) ␳CTCTHC+(16%) ␯COE+(13%) ␯C9CT+(11%)␯CTCT (46%)␯CTC+(18%) ␳CTC9HM (49%)␯CTCT+(29%) ␦CTC9HM+(18%) ␦HCCTC9 (22%)␯CTC+(14%) ␦CTC9HM

844a C COOstretcha 857c _CCH3c (830–846)e,f,i C COOH stretche,f,CH bendi 796 824 799 812 (24%)␯sOECT+(21%) ␯sCOE+(19%) ␯CTCT+(10%)␳HMC9CT (32%) ␳CTCTHC+(24%) ␳CTC9HM+(15%) ␯C9CT (47%)␯CTC+(15%) ␶␻HMC9CT (35%)␯CTC+(28%) ␶␻CTC9HM 825b _{CH3 rock}b 800a,c C COOHa,c,CC stretchc (800–804)e,f,i C COOstretche,i, CH2 twistandCH bendi 742 744 730 745 (42%)␥CO+(13%) ␯COE+(13%) ␦OCOE+(10%) ␯CTCT+(10%) ␯C9CT+(10%)␯CTC (44%) ␳CTC9HM+(32%) ␥CO+(11%) ␯COE+(11%) ␦OCOE (50%) ␦CTC9CT+(12%) ␦OCOE (55%) ␦CTC9CT+(23%) ␦OCOE

721a755b _{CH2 rock}a,b 721c CCCskeletaldefc (COH) 745i CHbendi – 631 636 630 – (44%)␥CO+(30%) ␦CTCO+(10%) ␯CTCT (28%) ␦CTC9CT+(22%) ␦OCOE (36%) ␦OCOE+(26%) ␦CTC9CT+(20%) ␦CTCO 625b _CH3OCO out-of-planebendb (631–642)c,g C–HvinylwaggCCC skeletaldefc(COH)

607 608 593 584 (44%)␦COECT+(30%) ␯CTCT (51%)␥CO+(25%) ␦CTCO+(10%) ␯CTCT (55%)␥CO+(33%) ␦CTCO+(10%) ␯CTCT (53%)␥CO+(29%) ␦CTCO+(11%) ␯CTCT 584a C Ooutofplane benda 595c584a CCCskeletaldefc C Ooutofplane benda 501 511 511 512 (35%)␦COECT+(30%) ␯CTCT (23%) ␦COECT+(15%) ␦OCOE+(13%) ␦C9CTCT+(12%) ␯CTCT (37%)␦CTCO+(15%) ␻CTCOE+(13%) ␦CTCTC (17%) ␦CTCOE+(13%) ␦CCTCT+(12%) ␯CTCT

565b CCOin-planebendb 512–533c CCCskeletaldefc

365 367 362 365 (35%)␦COECT+(32%) ␦CTC9CT+(17%) ␦CTCTCT+(14%)␦CTCTC (47%) ␦COECT+(29%) ␦CCTCT+(10%) ␯CTC (46%) ␦COECT+(23%) ␦CTCTC9 (49%) ␦CTCOE+(12%) ␦C9CTC9+(12%) ␯C9CT

470–480b COCin-planebendb 358h C–C–Cbend/twisth

– – 341 348 – – (55%)␶COE+(32%) ␦C9CTCT+(11%) ␦CTCOE (54%)␶COE+(14%) ␦C9CTC+(11%) ␦CTCO+(10%) ␦C9CTCT 345b COCout-of-plane torsionb 343c CCCskeletaldefc

Note1:␣CH3isthemethylgroupandOCH3istheestermethylgroup.

Note2:␯:stretching;␦:inplanebending;␥:outofplanebending;␶:torsion;␳,rocking;␯s:,symmetricstretching.

␯as:asymmetricstretching;␦s:symmetricdeformation;␦as:asymmetricdeformation;␶␻:twisting;␻:wagging␴:scissoring.

a_Ref.[57]. b _Ref.[66]. c _Ref.[67]. d _Ref.[68]. e_Ref.[69]. f _Ref.[70]. g_Ref.[71]. h _Ref.[72]. i _Ref.[73].

32 M.O.Bensaidetal./VibrationalSpectroscopy74(2014)20–32 polymerswecanstatethattheprincipleoftransferabilityproposed

byShimanouchi[18,74]isconfirmed.

5. Conclusion

In thepresent study, we carried out a complete vibrational assignmentsandanalysisofacrylicpolymersusingSPASIBAforce field.Theresultsofnormalcoordinateanalysishavebeendiscussed andcomparedtoprevioustheoreticalandexperimentalworks.We wereabletoreproduceallfundamentalvibrationalmodesandtheir assignmentsobserved inFTIRand FTRspectra.Theprinciple of transferabilityestablishedbyShimanouchihasbeenalsovalidated. Consequently,theparametersoftheSPASIBAforcefieldobtained fromourstudymightbeusefulforfurthervibrationalnormalmode calculationsofmoleculescontainingthesamechemicalsubgroups asouracrylicpolymers.

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