Study of n-Butyl Acrylate Self-Initiation Reaction Experimentally and via Macroscopic Mechanistic

16 Pages·2016·1.56 MB·English

processes
Article
Study of n-Butyl Acrylate Self-Initiation Reaction
Experimentally and via Macroscopic
Mechanistic Modeling
AhmadArabiShamsabadi1,NazaninMoghadam1,SrirajSrinivasan2,PatrickCorcoran1,
MichaelC.Grady3,AndrewM.Rappe4andMasoudSoroush1,*
1 DepartmentofChemicalandBiologicalEngineering,DrexelUniversity,Philadelphia,PA19104,USA;
[email protected](A.A.S.);[email protected](N.M.);[email protected](P.C.)
2 ArkemaInc.,9001stAvenue,KingofPrussia,PA19406,USA;[email protected]
3 DuPontExperimentalStation,Wilmington,DE19803,USA;[email protected]
4 TheMakineniTheoreticalLaboratories,DepartmentofChemistry,UniversityofPennsylvania,Philadelphia,
PA19104-6323,USA;[email protected]
* Correspondence:[email protected];Tel.:[phone]
AcademicEditor:MichaelHenson
Received:14February2016;Accepted:15April2016;Published:23April2016
Abstract: Thispaperpresentsanexperimentalstudyoftheself-initiationreactionofn-butylacrylate
(n-BA)infree-radicalpolymerization. Forthefirsttime,thefrequencyfactorandactivationenergy
of the monomer self-initiation reaction are estimated from measurements of n-BA conversion in
free-radicalhomo-polymerizationinitiatedonlybythemonomer. Theestimationwascarriedout
usingamacroscopicmechanisticmathematicalmodelofthereactor. Inadditiontoalready-known
reactionsthatcontributetothepolymerization,themodelconsidersan-BAself-initiationreaction
mechanism that is based on our previous electronic-level first-principles theoretical study of
the self-initiation reaction. Reaction rate equations are derived using the method of moments.
The reaction-rate parameter estimates obtained from conversion measurements agree well with
estimatesobtainedviaourpurely-theoreticalquantumchemicalcalculations.
Keywords: free-radical polymerization; spontaneous thermal polymerization; monomer
self-initiation;methodofmoments;n-butylacrylate
1. Introduction
Acrylicpolymersareusedwidelyincoatings,asadhesivesandfunctionaladditives. Increasingly
tight limits on volatile organic contents of paints and coatings [1,2] have required the paints and
coatingsindustriestodecreasethelevelofsolventsintheirproducts. Toensureadequatebrushability
and sprayability of the low (20–40 wt%) solvent-content paint and coatings, polymers with low
average molecular weights (M <10,000) have been produced via high-temperature (120–190 ˝C)
w
polymerizationprocesses[3–5]. Atthesehightemperatures,secondaryreactionssuchasmonomer
self-initiation,β-scission,inter/intra-molecularchaintransferandbackbitingreactionsareinfluential
andthusrequirestudy[6].
Thermalpolymerizationofalkylacrylatesintheabsenceofexternalinitiatorshasbeenreported[7].
Theoccurrenceofmonomerself-initiationreactionallowsonetouselessthermalinitiators,typically
organicperoxidesorazonitriles,whicharerelativelyexpensiveandasresiduescancausedefectsinthe
finalproduct,especiallyonweathering[8]. Studiesusingelectronsprayionization-Fouriertransform
massspectrometry(ESI-FTMS),nuclearmagneticresonance(NMR)spectroscopy,andmacroscopic
mechanistic modeling did not identify the initiating species or the mechanism of initiation in the
spontaneousthermalpolymerization[7,9]. However,quantumchemicalcalculations[10–13]together
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Processes2016,4, 15 2of16
withmatrix-assistedlaserdesorptionionization(MALDI)[14]showedthatmonomerself-initiationis
oneofthelikelymechanismsofinitiationinspontaneousthermalpolymerizationofalkylacrylates.
Polymercharacterizationstudiesusingspectroscopicmethodshavebeencarriedouttoexplore
thedominantpolymerizationreactions[7,9]. Pulsed-laserpolymerization(PLP)andsizeexclusion
chromatographyhavebeenusedtostudyintra-molecularchaintransfertopolymer(CTP)reactions
in polymerization of alkyl acrylates [15,16]. The rate coefficients of the propagation reactions of
styrene[17],andmethylmethacrylate(MMA)[18],andchaintransferreactionsofbutylmethacrylate
(BMA)[19]attemperaturesabove30˝ChavebeenestimatedusingPLP.Althoughthepropagationrate
coefficientofn-butylacrylate(n-BA)at70˝ChasbeencalculatedusingPLPat500Hz[20],thepresence
ofbackbitingandβ-scissionreactionshashinderedthepredictionofalkylacrylates’propagationrate
coefficientatelevatedtemperatures[21–23]. Attemperaturesabove30˝C,intra-andinter-molecular
CTP reactions in free-radical polymerization of n-BA [24,25] and intra-molecular CTP reactions in
2-ethylhexylacrylatepolymerization[26]havealsobeenstudiedusingNMRspectroscopy. Although
theseanalyticaltechniqueshavebeenveryusefulincharacterizingacrylatepolymers,theyalonecannot
conclusivelydeterminereactionmechanismsorestimatekineticparametersofreactions. Macroscopic
mechanisticmodelingcombinedwithadequatepolymersamplemeasurementshasproventobea
powerfultooltoestimatetheratecoefficientsofindividualreactions. Macroscopicmechanisticmodels
havealsobeenusedextensivelytoestimatetheratecoefficientsofinitiationbyconventionalthermal
initiators, propagation, chain transfer and termination reactions in free-radical polymerization of
acrylates[9,16,27–32]. Kineticparametersofseveralreactionsinspontaneousthermalpolymerization
ofn-BAunderseeminglyoxygen-freeconditions(solventwasbubbledwithnitrogenbutnotn-BA,
andanitrogenblanketwasusedinsidethereactor)wereestimatedthroughdetailedmacroscopic
mechanisticmodeling,andtheentireinitiationwasattributedtomonomerself-initiation,leadingto
anunrealistically-largeself-initiationratecoefficient[9]. StyreneandMMAself-initiationapparent
rate coefficients estimated through macroscopic mechanistic modeling have been reported [27,28].
Amacroscopicmechanisticmodelofn-BAspontaneouspolymerization,whichaccountedforinitiation
onlybythemonomer,wasusedtoestimatethen-BAself-initiationratecoefficientfrommeasurements
ofconversionunderseeminglyoxygen-freeconditions[9],againleadingtoaverylargereactionrate
coefficient for monomer self-initiation, because the entire monomer conversion was attributed to
initiationonlybythemonomer[29].
Macroscopicmechanisticpolymerizationmodelsaremoreusefulthansemi-empiricalmodels.
The accuracy of mechanistic polymerization models strongly depends on our quantitative
understandingofindividualreactionsoccurringduringthecourseofpolymerization. Thesemodels
have been used to study low and high-temperature polymerization reactions of n-BA [33,34].
The method of moments [35–37] or the “tendency modeling” approach [38–41] can be used to
derive rate equationsneeded in macroscopic mechanistic models. Models obtained using the
tendency-modeling rate equations do not account for the number of monomer units in polymer
chains,andthereforetheyarelesscomplexthanmodelsthatarebasedonthemethod-of-moments
rateequations. Modelsthatarebasedonthemethodofmomentscanbeusedtoestimatekineticrate
coefficientsmoreaccurately. Applicationsofbothtypesofmodelscanbefoundintheliterature[42–46].
In our previous work, we studied self-initiation of alkyl acrylates such as methyl, ethyl and
n-butylacrylateaswellasmethylmethacrylatetheoreticallyusingdensityfunctionaltheory[10–13].
Wefoundthatself-initiationofalkylacrylateshasthreeelementaryreactionstepsinseries:
(i) Twomonomersreactandformasingletdiradical
M`M Ñ ˚MM˚ (1)
s
(ii) Thesingletdiradicalthenundergoesintersystemcrossingtoformatripletdiradical:
˚MM˚ Ñ ˚MM˚ (2)
s t
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(iii)The triplet diradical finally reacts with a third monomer, leading to the formation of
twomono-radicals:
˚MM˚`M Ñ MM˚`M˚ (3)
t
We also calculated the kinetic parameters of the three preceding reactions [10–12]. The first
reaction is the fastest reaction, whereas the second reaction is the slowest (rate limiting) reaction.
Therefore,theoverall(apparent)self-initiationreaction:
3M Ñki MM˚`M˚ (4)
issecondorder.
Inthispaper,weexperimentallyestimatethekineticparameters(activationenergyandfrequency
factor)oftheoverall(apparent)n-BAself-initiationreactioninEquation(4)frommonomerconversion
measurements using a macroscopic mechanistic polymerization reactor model guided by our
first-principles investigations of the mechanism. These estimates are compared with our existing
estimatesofthesameparametersobtainedviaquantumchemicalcalculations.
Theorganizationoftherestofthispaperisasfollows. Section2presentsthemathematicalmodel.
Section3discussestheexperimentalandanalyticalprocedures. Section4describestheparameter
estimationstudy. Finally,concludingremarksaregiveninSection5.
2. MathematicalModeling
2.1. ReactionMechanisms
The most likely polymerization reactions occurring in spontaneous thermal solution
polymerization of n-BA in the absence of oxygen are given in Table 1. The reactions include
monomer self-initiation [10–12], secondary and tertiary chain propagation, intra-molecular chain
transfer to polymer (backbiting), inter-molecular chain transfer to polymer, β-scission, chain
transfer to monomer [47], chain transfer to solvent, termination by combination, and termination
by disproportionation reactions [48,49]. While not all of these reactions strongly affect monomer
conversion,thelistofthereactionsisgivenhereforcompleteness. Forexample,nosolventhasbeen
usedinthestudypresentedherein. Here, MandSdenotethemonomerandsolvent, respectively.
U represents a dead polymer chain with n monomer units and a terminal double bond. D is a
n n
dead polymer chain with n monomer units but without a terminal double bond. R * represents a
n
secondaryradicalwithnmonomerunits. R ** isatertiaryradicalwithnmonomerunitsgenerated
n
throughintermolecularCTPreactions. R ***denotesatertiaryradicalwithnmonomerunitsformed
n
bybackbitingreactions. SCBandLCBrepresentashortandalongchainbranchingpoint,respectively.
Table1.Polymerizationreactions[34].
a. Apparentmonomerself-initiationreaction
3M Ñki R˚` R˚
1 2
b. Propagationreactions
R˚` M Ñkp R˚
n n`1
kt
R˚˚` M Ñp R˚ p`LCBq
n n`1
kt
R˚˚˚` M Ñp R˚ p`SCBq
n n`1
R˚n ` Um kÑmac R˚n`˚m
c. Backbitingreactions(n>2)
R˚ Ñkbb R˚˚˚
n n
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Table1.Cont.
d. β-scissionreactions(n>3)
R˚˚˚ Ñkβ U ` R˚
n 3 n´3
R˚˚˚ Ñkβ R˚ ` U
n n´3 3
R˚˚˚ Ñkβ U ` R˚
n n´2 2
R˚˚˚ Ñkβ R˚`U
n 2 n´2
R˚n˚ Ñkβ Un´m` R˚m
R˚n˚ Ñkβ R˚m` Un´m
e. Intermolecularchaintransfertopolymerreactions
R˚n ` Dm mÑktrP Dn` R˚m˚
R˚n ` Um mÑktrP Dn` R˚m˚
f. Chaintransfertomonomerreactions
R˚n ` M kÑtrM Dn` R˚1
R˚n˚` M kÑttrM Dn` R˚1
R˚n˚˚` M kÑttrM Dn` R˚1
g. Chaintransfertosolventreactions
R˚n ` S kÑtrS Dn` R˚0
kt
R˚n˚` S ÑtrS Dn` R˚0
kt
R˚n˚˚` S ÑtrS Dn` R˚0
h. Terminationbycouplingreactions
R˚n ` R˚m Ñktc Dn`m
R˚n ` R˚m˚ 2Ñkttc Dn`m
R˚n ` R˚m˚˚ 2Ñkttc Dn`m
R˚n˚` R˚m˚ Ñktttc Dn`m
R˚n˚` R˚m˚˚ 2Ñktttc Dn`m
R˚n˚˚` R˚m˚˚ Ñktttc Dn`m
i. Terminationbydisproportionationreactions
R˚n ` R˚m Ñktd Dn` Um
kt
R˚n ` R˚m˚ Ñtd Dn` Um
kt
R˚n ` R˚m˚ Ñtd Dm` Un
kt
R˚n ` R˚m˚˚ Ñtd Dn` Um
kt
R˚n ` R˚m˚˚ Ñtd Dm` Un
ktt
R˚n˚` R˚m˚ Ñtd Dn` Um
ktt
R˚n˚` R˚m˚˚ Ñtd Dn` Um
ktt
R˚n˚` R˚m˚˚ Ñtd Dm` Un
ktt
R˚n˚˚` R˚m˚˚ Ñtd Dn` Um
Inter- and intra-molecular CTP reactions lead to the formation of tertiary radicals, which are
capableofundergoingpropagation[50]andβ-scissionreactions. Theβ-scissionreactionsproduce
secondaryradicalsanddeadpolymerchainswithaterminaldoublebond. Thisledtothegeneration
ofshorterdeadpolymerchains,thusloweringtheaveragemolecularweightofthepolymerproduct.
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2.2. RateEquations
Reactionrateequationsarederivedusingthemethodofmoments. Weassumethatallreactions
given in Table 1 except for the self-initiation reaction are elementary. As expected, accounting
for β-scission and inter-molecular CTP reactions leads to closure problems; that is, a moment of
achainlengthdistributiondependsonahighermomentofthesameordifferentdistributions[36].
For example, as the inter-molecular CTP reaction rate coefficient depends on the number of
polymerized monomer units in the dead polymer chains, the zeroth moments of the chain length
distributionsofthedeadpolymerchainsdependontheirfirstmoments. Toaddressthisproblem,for
eachchainlengthdistribution,aspecificdistributionmodelisassumedtoderiveanapproximationthat
relatesthethirdmomentofthedistributiontolowermomentsofthesamedistribution. Inparticular,
chainlengthdistributionsofthedeadpolymerchainswithorwithoutaterminaldoublebondare
assumedtobere-scaledGammadistributions[51],andthechainlengthdistributionofthetertiary
radicalsR˚˚isassumedtohaveanormaldistribution.
n
Theresultingrateequations;thatis,theproductionrateequationsforM,S,R *,R *,R *,R *,and
0 1 2 3
thezeroth,first,andsecondmomentsofdeadpolymer,secondaryradical,andtertiaryradicalchain
lengthdistributions, aregivenintheAppendix. [X]representsthemolarconcentrationofspecies
X. δ *, δ *, and δ * arethezeroth, first, andsecondmomentsofthesecondaryradicalchainlength
0 1 2
distributions. δ **,δ **,δ **,andδ **arethezeroth,first,second,andthirdmomentsofthechainlength
0 1 2 3
distributionofthetertiaryradicalsgeneratedbytheintermolecularCTPreactions. δ ***, δ ***, and
0 1
δ ***arethezeroth,first,andsecondmomentsofthechainlengthdistributionofthetertiaryradicals
2
formedbythebackbitingreactions. Thejthmomentsofthechainlengthdistributionsoftheliveand
deadpolymerchainsare:
ÿ8 ÿ8 ÿ8
δ˚ “ njrR˚s, δ˚˚ “ njrR˚˚s, δ˚˚˚ “ njrR˚˚˚s
j n j n j n
n“0 n“1 n“1
ÿ8 ÿ8
λ “ njrD s, Γ “ njrU s
j n j n
n“1 n“1
andδ “δ˚`δ˚˚`δ***.
0 0 0 0
2.3. BatchReactorModel
Molebalancesonallspeciesandbalancesonthemomentsleadtoabatchreactormodelthat
consistsof21first-orderordinarydifferentialequations:
drJs
“r , rJsp0q“rJs
dt J 0
where J “ M,S,R˚,R˚,R˚,R˚,δ˚,δ˚,δ˚,δ˚˚,δ˚˚,δ˚˚,δ***,δ***,δ***,λ ,λ ,λ ,Γ ,Γ ,Γ . All initial
0 1 2 3 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
concentrationsareassignedtobezeroexceptforthatofmonomer,whichisnonzeroandisdenotedby
[M] . Themonomerconversioniscalculatedusing:
0
rMs ´rMs
X “ 0
rMs
0
In this model, volume effects and diffusional limitations are ignored as most of conversion
measurements reported herein are below 50%. Also, depropagation is not considered, as it is
insignificantforalkylacrylatemonomers. However,itissignificantformethacrylatemonomers[5].
3. ExperimentalandAnalyticalProcedures
Themonomer,98%n-butylacrylatestabilizedwith50ppmof4-methoxyphenolasinhibitor,is
fromAlfaAesar. Batchreactorsare4-inchstainlesssteelSwageloktubes(SwagelokInc.,Huntingdon
Processes2016,4, 15 6of16
Valley,PA,USA),cappedatbothendswithSwagelokstainlesssteelcaps. The4-inchlengthgivesa
reactionvolumeof4.8mL.Thesetubescanwithstandpressuresupto3300psig.
Foreachsetofbatchexperiments,30–50mLofn-BAisdrippedthroughaninhibitorremoval
column DHR-4, from Scientific Polymer Products of Ontario, New York, in order to remove the
inhibitor. Theinhibitor-freemonomeriscollectedina50-mLround-bottomflaskequippedwitha
standardtaper24/40groundglassjoint. AfteronehourofUHPnitrogenbubbling,weremovethe
needles and wrap the rubber septum tightly with aluminum foil secured with tight rubber bands.
Theround-bottomflaskwiththeinhibitor-free,nitrogen-bubbledn-BA,theopenreactiontubes,and
thetubecapsarethenmovedtothevacuum-nitrogen-purgechamberofanitrogen-atmosphereglove
box(LCTechnologySolutions,Salisbury,USA).Afterseveralvacuum-nitrogenpurgecycles,theflask,
tubesandcapsarethenmovedtothemainchamberoftheglovebox,inwhichoxygenisremoved
reactivelyandwaterphysicallyfromthenitrogengasinside. Theoxygenconcentrationintheglove
boxiskeptbelow0.1ppm.Insidetheglovebox,thesealedflaskisthenopenedand2.5mLofmonomer
arepipettedintoeachreactiontube,afterwhichtheotherendcapisattachedandtightened. Upon
removalfromtheglovebox,eachreactiontubeisweighed,andtheweightisrecorded. Thefluidized
sandbathisthenheatedtoadesiredconstantreactiontemperature. Aftermaintainingthesandbathat
thedesiredtemperatureforseveralhours,tworeactortubesatatimeareplacedinthesandbathand
arethenpulledoutofthefluidizedsandbathafteraspecificperiodoftime. Thetubesarethencooled
quicklyinacoldwaterbathtostopfurtherpolymerization. Afterdryingeachtube,thereactiontube
isweighed,andtheweightisrecorded. Ifanytubeshowsaweightloss,thetubeisdiscardedfromthe
experiment. Thecontentofeachtubeisthenemptiedintovials. Thetimethatareactortubespendsin
thesandbathminusoneminuteisconsideredasthereactiontimeofthereactortube. Ourprevious
studieshadshownthatittakesapproximatelyoneminuteforthemonomerinsideareactortubeto
reachthesandbathtemperature.
Theconversionineachreactiontubeismeasuredwithagravimetricmethod. A57mmaluminum
dishisweighted(wgt1).Then,1.5mLofthereactionmassispipettedfromeachvialintothealuminum
dish,andthedishisthenweighed(wgt2).Threemillilitersoftolueneisthenaddedtothereactionmass,
whichcompletelydissolvesintheaddedtoluene. Next,thedishisplacedinavacuumovenovernight
at50˝Ctoallowthesolventandtheunreactedmonomertoevaporate.Thedishisthenweighedathird
time(wgt3). The%conversioniscalculatedusingtheequation((wgt1´wgt3)ˆ100)/(wgt1´wgt2).
4. ResultsandDiscussion
ParameterEstimation
Ratecoefficientsofallreactionsexceptforthemonomerself-initiationreactionaregiveninTable2.
Table2.Reactionratecoefficientvalues.
ActivationEnergy
Parameter FrequencyFactor Ref.
(kJ.mol´1)
kp 2.21ˆ107 L¨mol´1¨s´1 17.9 [30]
ktp 1.20ˆ106 L¨mol´1¨s´1 28.6 [49]
k 7.41ˆ107 s´1 32.7 [33]
bb
ktrM 2.90ˆ105 L¨mol´1¨s´1 32.6 [47]
kt 3.89ˆ109 L¨mol´1¨s´1 8.4 [31]
ktt 5.30ˆ109 L¨mol´1¨s´1 19.6 [34]
t
kβ 1.49ˆ109 s´1 63.9 [34]
ktrP 4.01ˆ103 L¨mol´1¨s´1 29.0 [15]
CtrS 1.07ˆ102 35.4 [34]
Processes2016,4, 15 7of16
Table3.Reactionratecoefficientdefinitionsandcorrelations[34,48].
kt “ktc` ktd
kt “ kt ` kt
t tc td
ktt “ ktt` ktt
t tc td
ktd “δskt
ktttd “ bδtkttt
kttd “δst ktkttt
ktc “p1´δsqkt
ktttc “p1´δtbqkttt
kttc “p1´δstq ktkttt
ktrS “CtrSkp
kt “ ktpk
trM kp trM
kmac “γkp
Theunknownratecoefficient,k,isestimatedfrommonomer-conversionmeasurements. Reaction
i
ratecoefficientdefinitions,correlationsanddimensionlesskineticparametervaluesareprovidedin
Tables3and4.
Processes 2016, 4, 15 7 of 16
Table4.Dimensionlesskineticparametervalues[34,48].
Table 4. Dimensionless kinetic parameter values [34,48].
Parameter DimensionlessValue
Parameter Dimensionless Value
δ s 00.1.1
δst 0.7
0.7
𝛿𝛿𝑠𝑠δt 0.9
γ 00.5.9
𝛿𝛿𝑠𝑠𝑡𝑡
0.5
𝛿𝛿𝑡𝑡
Thesystemofordinarydifferentialequations(ODEs)isintegratednumericallyusingtheMATLAB
The system of ordinary diffe𝛾𝛾rential equations (ODEs) is integrated numerically using the
routinebvp5c. Forparameterestimation,theMATLABfunctionfminsearch,whichisbasedonthe
MATLAB routine bvp5c. For parameter estimation, the MATLAB function fminsearch, which is
Nebldaesre-dM oena tdhsei mNeplldeexr-aMlgeoardit shimm,pilsexu saelgdotroitfihnmd, itsh uesveadl utoe foinfdki tthhea vtamluine iomf ikzi ethsatth mesinuimmiozfetsh tehesq suuamre d
erroofr sthbee stwqueaernedm eerarsoursre bmetewnetesna nmdeamsuodreeml-penretsd aicntde dmvoadleul-epsroefdcicotnedv evrasliuoens. of conversion.

FigFuirgeur1e. 1M. Meaesausruermemenetnstsa nanddm mooddeell pprreeddiiccttiioonn ooff mmoonnoommeerr ccoonnvveersrisoino nata t14104 0°C˝.C S.SSRSsR =s =susmu mof of
squared residuals.
squaredresiduals.

Figure 2. Measurements and model prediction of monomer conversion at 160 °C.
Processes 2016, 4, 15 7 of 16
Table 4. Dimensionless kinetic parameter values [34,48].
Parameter Dimensionless Value
0.1
0.7
𝛿𝛿𝑠𝑠
0.9
𝛿𝛿𝑠𝑠𝑡𝑡
0.5
𝛿𝛿𝑡𝑡
The system of ordinary diffe𝛾𝛾rential equations (ODEs) is integrated numerically using the
MATLAB routine bvp5c. For parameter estimation, the MATLAB function fminsearch, which is
based on the Nelder-Mead simplex algorithm, is used to find the value of ki that minimizes the sum
of the squared errors between measurements and model-predicted values of conversion.

Figure 1. Measurements and model prediction of monomer conversion at 140 °C. SSRs = sum of
Processes2016,4, 15 8of16
squared residuals.

Processes 2016, 4, 15 8 of 16
Processes 2016F, i4g, F1u5irg eu2r.e M2. eMaseuarseumremenetnstas nadndm mooddeellp prreeddiiccttiioonn ooff mmoonnoommeerr ccoonnvveresriosino nat a1t6106 °0C˝. C. 8 of 16

FigFFuiirggeuu3rre.e M33.. eMMaseeuaasrsueumrreememneetnnsttass n aadnnddm mmodooddeelellp pprrereedddiicicctttiiiooonnn ooofff mmmooonnnooommmeeerrr cccooonnnvvveeerrsrsisiooinon n aatta 11t881008 0°°CC˝..C .

FigFuirgeu4r.e M4. eMaseuarseumreemnetnstasn adndm mododelelp prereddicicttiioonn ooff mmoonnoommeerr ccoonnvveerrssioionn ata 2t0200 0°C˝.C .
Figure 4. Measurements and model prediction of monomer conversion at 200 °C.
Figures 1–5 show measurements and model predictions of n-BA conversion at different constant
Figures 1–5 show measurements and model predictions of n-BA conversion at different constant
reactor temperatures (140, 160, 180, 200 and 220 °C). At each temperature, ki, is estimated by fitting
reactor temperatures (140, 160, 180, 200 and 220 °C). At each temperature, ki, is estimated by fitting
the model predictions to the measurements. As can be seen, the model fits the measurements very
the model predictions to the measurements. As can be seen, the model fits the measurements very
well at all four temperatures.
well at all four temperatures.
Processes2016,4, 15 9of16
Figures1–5showmeasurementsandmodelpredictionsofn-BAconversionatdifferentconstant
reactortemperatures(140,160,180,200and220˝C).Ateachtemperature,k,isestimatedbyfittingthe
i
modelpredictionstothemeasurements. Ascanbeseen,themodelfitsthemeasurementsverywellat
allPfProoroucecsressestese s2m 2001p166e, ,4 r4,a ,1 1t5u5 res. 9 9o fo 1f 61 6

FiFgFiuiggruuerr5ee . 55M.. MMeaeesaaussuruerrmeemmeneenntsttssa aannndddm mmooodddeeelll ppprrreeedddiiiccctttiiiooonnn ooofff mmmooonnnooommmeeerr rc cocoonnnvveverersrsiosioinon an at ta2 t2222002 ° 0C°C˝. C. .
OnOOcnencctehe tethheree rareecaatcicottinioonnr a rrtaaetteec occooeeeffiffffciiciceiieennnttt i iisss eeessstttiiimmmaaattteeeddd aaattt 111444000,,, 111666000,, , 11818080,0 , 2,2020000 0a anandnd d2 2222002 ° 0°CC˝, ,Ct ht,hete rh ereaeacrtceitaoicontn io n
frequency factor and activation energy are estimated using the Arrhenius plot (see Figure 6).
frefqrueqenuceyncfya cftaocrtoarn adnadc aticvtiavtaiotinone neenregrygya areree esstitmimaateteddu ussiinngg tthhee AArrrrhheenniiuuss pplloott ((sseeee FFigiguurer e6)6. ).

Figure 6. Arrhenius plot of to estimate and .
Figure 6. Arrhenius plot of to estimate and .
Figure6.Arrheniusplotofk toestimateE andA .
𝑘𝑘𝑖𝑖i 𝐸𝐸𝑖𝑖i 𝐴𝐴𝑖𝑖i
The estimated frequency factor and activation𝑘𝑘 e𝑖𝑖nergy as wel𝐸𝐸l 𝑖𝑖as the𝐴𝐴ir𝑖𝑖 95% confidence intervals
The estimated frequency factor and activation energy as well as their 95% confidence intervals
arTeh geiveesnti imn aTtaebdlefr 5e.q Ause ncacyn fbaec tsoerena nind tahcisti vtaabtlieo,n theen eexrgpyeraimsewnetallllays etshteimira9t5e%d sceolfn-ifinditeiantcieonin rtaetrev als
are given in Table 5. As can be seen in this table, the experimentally estimated self-initiation rate
arecgoievfefinciienntTsa abrlee i5n. exAcsellceannt abgerseeemenenint wthitihs tthaobslee ,ctahlceuelaxtpeedr uimsienngt qaullaynetustmim cahteemdicsaell fc-ainlciutilaattiioonnsr ate
coefficients are in excellent agreement with those calculated using quantum chemical calculations
coef(fiwcitiehnint sa afarectionr oefx 2ce–l3l eonf tthaogsree reempoernttedw iint h[1t2h])o. se calculated using quantum chemical calculations
(within a factor of 2–3 of those reported in [12]).
(withinaAfftaecrt o2r50o fm2i–n3 oof fptohlyomseerreizpaotirotend atin 14[102 a]n).d 160 °C, respectively, the conversion is less than 3%
(FAigfuAterfert e12r)5 2a05nm0d milnesinos fothpf aponoly l8ym%me (erFriizigzauatrtieoio n2n) a.a Ttth 11e44s00e asa nninddd 11ic66a00t e°˝C Cth,, arrete stsphpeee cnct-itBvivAeel yslye, t,lfht-hein eciotcinoavtnieovrnes riroseinao cintsi iolsensl sies st sshlatohnwa 3an%t 3 %
(Figure 1) and less than 8% (Figure 2). Theses indicate that the n-BA self-initiation reaction is slow at
160 °C or a lower temperature. However, as temperature increases (Figures 3–5), the contribution of
(Figure1)andlessthan8%(Figure2). Thesesindicatethatthen-BAself-initiationreactionisslowat
1s6e0l f°-Cin oitri aat iloonw teor ttheme ppoelryamtuerreiz. aHtioowne ivnecrr,e aass etesm (cpoenrvaetrusrioe nin ocfr meaosrees t (hFaingu 2r5e%s 3a–t 51)8,0 t h°Ce c, aobnotruitb 4u0t%io na to f
160˝Coralowertemperature. However,astemperatureincreases(Figures3–5),thecontributionof
s2e0lf0-i °nCit,i aantido na btoo utht e6 0p%ol aytm 2e2r0i z°aCt,i oanft einr c2r5e0a mseisn ( ocfo rnevaecrtsioionn) .o Af tm 1o6r0e ° tCh,a cno n2v5%er saito 1n8 i0n c°rCe,a asbeos ulitn 4e0a%rly a t
self-initiationtothepolymerizationincreases(conversionofmorethan25%at180˝C,about40%at
2f0r0o m°C 2, .a5n%d t aob 6o.5u%t 6 b0e%tw aete 2n2 505 ° aCn, da f2t2e0r 2m5i0n .m Aitn 1 o8f0 r °eCac, tthioen c)o. Anvte 1r6s0io °nC i,n ccorneavseerssi toon 2 i5n%cr aefatseers 2 l2i0n emairnly,
200˝C,andabout60%at220˝C,after250minofreaction). At160˝C,conversionincreaseslinearly
fraonmd t2h.5e% ra ttoe 6o.f5 i%ts binetcwreeaesne 5is5 salnigdh 2tl2y0 h migihne. rA itn 1it8ia0l °lyC., A tht e2 c0o0n °vCe,r as i2o5n% in ccornevaesressi oton 2is5 %ac ahfiteevre 2d2 a0f tmeri n,
a1n1d0 tmhein r.a Ateg oafi nit, st hinec croenasvee rissi solnig ihntclrye ahsigehs efra sinteitri ainlliyti. aAllty 2 a0t0 2 °0C0, °aC 2. 5A%t c2o2n0v °eCrs, lieosns i sth aacnh i5e5v emdi naf itse r
1s1u0f fmiciine.n At tgoa ainch, itehvee c ao 3n0v%er csoionnv einrsciroena.s Feisg ufarsetse 1r– i5n iitnidailclya taet t h20a0t a°tC 1. 4A0t– 222200 °°CC t, hlees cso tnhvaenrs 5io5n m doine si s
snuoffti lceivenelt otoff a dcuhriienvge tah 3e0 2%5 0c omnivne,r ismiopnl.y Finiggu trheast 1 t–h5e ipnodliycmateer tizhaatti oant 1c4a0n– c2o2n0t °inCu teh be ecyoonnvde r2s5io0n m dione. s
n ot level off during the 250 min, implying that the polymerization can continue beyond 250 min.
Processes2016,4, 15 10of16
from2.5%to6.5%between55and220min. At180˝C,theconversionincreasesto25%after220min,
andtherateofitsincreaseisslightlyhigherinitially. At200˝C,a25%conversionisachievedafter
110 min. Again, the conversion increases faster initially at 200 ˝C. At 220 ˝C, less than 55 min is
sufficienttoachievea30%conversion. Figures1–5indicatethatat140–220˝Ctheconversiondoesnot
leveloffduringthe250min,implyingthatthepolymerizationcancontinuebeyond250min. Figure7
showsthehighsensitivityoftheconversionpredictionstotheself-initiationratecoefficient,implying
tPhroecelsosews 2u01n6c, e4r, 1ta5i ntyoftheestimateoftheratecoefficientateachofthetemperatures. 11 of 16

FFiigguurree 77.. MMooddeell pprreeddiiccttiioonn aanndd mmeeaassuurreemmeennttss ooff ccoonnvveerrssiioonn aass wweellll aass tthhee sseennssiittiivviittyy ooff pprreeddiicctteedd
ccoonnvveerrssiioonn ttoo 1100%% cchhaannggeess iinn k a tatt htheefi fviveet etmempepreartautruerse.s.
i
𝑘𝑘𝑖𝑖
5. Concluding Remarks
An experimental study of the self-initiation reaction of n-BA in free-radical polymerization was
presented. The frequency factor and activation energy of the monomer self-initiation reaction were
estimated from batch-reactor monomer-conversion measurements from spontaneous polymerization
of n-BA in the absence of oxygen, using a macroscopic mechanistic mathematical model of the reactor.
A comparison of the estimated monomer self-initiation reaction rate constant with estimates obtained
via quantum chemical calculations showed satisfactory agreement. These experimental estimates
quantify, for the first time, the sole contribution of the monomer self-initiation to the initiation of n-
BA polymerization.