464

Terminationkineticsof styrenefree-radicalpolymerizationstudiedby time-resolvedpulsedlaserexperiments

Michael Buback*,ChristopherKowollik, Caroline Kurz,Almut Wahl

Institut fur PhysikalischeChemie,Universitat Gottingen,Tammannstraße6, D-37077Gottingen,Germany

(Received:July 20,1999;revised:September7, 1999)

Intr oductionThe application of pulsed-laser techniques has enor-mouslyimprovedthe quality of ratecoefficient measure-ment in free-radical polymerization. By the pulsed-laserpolymerization (PLP) – size-exclusion chromatography(SEC) technique, propagation rate coefficients, kp, havebeenaccurately determined for an extendedset of mono-mers such as styrene1–3), a wide variety of acrylates4–7),severalmethacrylates8–11), anda few other monomers12–15).An important access to terminationratecoefficients,kt, isprovided by the single pulse (SP)–PLP experiment, inwhich the monomer conversion induced by a UV laserpulse of about 20 ns width is spectroscopically moni-tored, preferably in the near-infrared region16). Actually,both PLP techniquesare combined for kt determination:kt/kp from SP–PLP is usedin conjunction with kp fromPLP–SEC.

An attractive feature of the SP–PLP procedure origi-natesfrom the potential of point-wiseprobing the termi-nationkineticsoverextendedrangesof monomerconver-sion17). The technique is particularly well suited for kt

analysisof monomers that rapidly propagateand slowlyterminate as these characteristics are associatedwithmonomerconcentrationvs. time traces of high signal-to-noise quality. Thus SP–PLP measurementsof termina-tion ratecoefficients haveprimarily beencarriedout foretheneat high temperature and high pressure16,18–20), foracrylates21,22), for binaryandternarycopolymerizationsofacrylate and methacrylate mixtures23,24), and for meth-acrylatehomopolymerizations of monomers with largerestersize25). As wasshown in a recentpaper26), by co-add-ing individual monomerconversionvs. time tracesfromabout100 successive single pulseexperiments,the SP–PLP methodmay also be usedfor methyl methacrylate(MMA) which is high in kt and low in kp. The presentpapercontinues this kind of investigationsby extendingthe SP–PLP method to styrene which under otherwiseidentical polymerization conditions has a significantlylower kp than MMA, e.g., at 408C and 1000bar the kp

value of styrene3) amounts to 301L N mol–1 N s–1 as com-paredto the MMA kp value8) of 902 L N mol–1 N s–1. Thedifficultiesof SP–PLPexperiments on styrenearefurther

Full Paper: The singlepulse(SP)-pulsed-laserpolymeri-zation(PLP) techniquehasbeenappliedto measurekt/kp,the ratio of terminationto propagationrate coefficients,for the free-radicalbulk polymerizationof styreneat tem-peraturesfrom 60 to 1008C and pressuresfrom 1800 to2650bar. kt/kp is obtainedby fitting monomerconcentra-tion vs. time tracesthat aredeterminedvia time-resolved(ls) near infrared monitoring of monomer conversioninduced by single excimer laser pulsesof about 20 nswidth. Styrene is a difficult candidatefor this kind ofmeasurementsas conversionper pulse is small for thislow kp andhigh kt monomer. Thusbetween160to 300SPsignalswere co-addedto yield a concentrationvs. timetraceof sufficient quality for deducingkt/kp with an accu-racy of better than l20 per cent. With kp being knownfrom PLP–SEC experiments,chain-length averagedkt

valuesareimmediatelyobtainedfrom kt/kp. At givenpres-sureand temperature,kt is independentof the degreeofoverall monomerconversion,which, within the presentstudy, hasbeenashigh as20%. Thekt value,however, isfoundto slightly increasewith theamountof free radicalsproducedby a singlepulsein laser-induceddecompositionof the photoinitiator DMPA (2,2-dimethoxy-2-phenylacetophenone).This remarkableobservationis explainedby DMPA decompositionresulting in the formation oftwo free radicalswhich significantly differ in reactivity.Extrapolation of SP–PLP kt data from experimentsatrather different DMPA levels and laser pulse energiestoward low primary free-radical concentration,yieldsvery satisfactoryagreementof the extrapolatedkt valueswith recentliteraturedatafrom chemicallyandphotoche-mically inducedstyrenepolymerizations.

Macromol. Chem.Phys.201, No. 4 i WILEY-VCH Verlag GmbH, D-69451 Weinheim2000 1022-1352/2000/0402–0464$17.50+.50/0

Macromol.Chem. Phys.201,464–469(2000)

Terminationkineticsof styrenefree-radical polymerization studiedby ... 465

enhancedas kt (4.9 N 107 L N mol–1 N s–1 at 408C and1000bar)27) exceeds the corresponding MMA value(2.5 N 107 L N mol–1 N s–1)26). The monomer conversioninducedby asinglelaserpulseis below 0.01%for styrene(at 408C and1000bar).Thenumber of singlepulsesthatneedsto be co-addedto yield a sufficient signal-to-noisequality undersuchconditionsexceeds onethousand.Thissituation would be in conflict with the intention of“point-wise” probing the conversion dependence of kt asthe conversion range coveredduring the collection of1000 SP–PLP signalsis well above10%.Thusthe styr-eneSP–PLP experiments of the presentstudyhavebeencarried out at temperaturesand pressures of and above608C and1800bar, respectively, wherekp is higherandkt

is lower thanat 408C/1000bar.

Experimental partThis part will be kept very brief as detaileddescriptionsofthe SP–PLP set-up and procedurehave been given else-where16,26). Theprincipalcomponentsof theSP–PLPexperi-ment are a Lextra 50 excimer laser (Lambda Physik) ofabout 20 ns pulse width (operated on the XeF line at351nm), a 75 W tungstenhalogenlamp (GeneralElectric)poweredby two batteries(12V, 180A/h), a BM 50 mono-chromator(B& M Spectronic), anda fastnearinfrared(NIR)InAs detector (EG& G Judson)of 2 ls time resolution.Monomerconversionis measuredvia theNIR absorbanceofC1H modes(at the C2C doublebond) around6140 cm–1.Thedetectorsignalis recordedon a 12 bit transientrecorder(ADAM TC 210-1, Rene-Maurer)and stored on an IBMcompatiblepersonalcomputer.

Styrene(FlukaChemie,99%)is washedseveraltimeswithaqueousNaOH andwith waterto removethe inhibitor, thendriedwith Na2SO4 anddistilled underreducedpressure.Oxy-gen is removedby severalfreeze-pump-and-thawcycles.Ina glovebox,underanargonatmosphere,thestyrene/initiatormixture is prepared,DMPA (2,2-dimethoxy-2-phenyl aceto-phenone,Aldrich, 99%) is added(to yield a photoinitiatorconcentrationmostly of about 5 N 10–3 mol N L–1), and thereactionmixture is introducedinto an internal cell28). Thisinternal cell, consisting of a Teflonm tube into which twoCaF2 windows are fitted, is insertedinto the optical high-pressurecell28). After reachingpolymerizationpressureandtemperature,excimerlaserpulsesof 351nm wavelengthareappliedat individual pulseenergiesof 2 to 3 mJ. Monomerconversioninducedby a single laser pulse is recordedviatime-resolvedonlineNIR spectroscopyat (6138l 15)cm–1.

After applying a series of single pulse experimentsinwhich, aftereachpulse,the laser-induceddecreasein mono-mer concentrationis detectedwith a time resolution ofmicroseconds(ls), absolute monomer concentrationandthusoverallmonomerconversionis measuredby introducingthe optical high-pressurecell into the samplecompartmentof a Fourier-TransformIR/NIR spectrometer(Bruker IFS-88) and recording the absorbancespectrain the 6100 to6250cm–1 range.

Resultsand discussionIn Fig. 1, for a styrenehomopolymerization at 808C and2200bar, the NIR spectroscopically measuredchangeinrelative monomerconcentration, cM (t)/cM,0, is plotted vs.time t (after applying the laserpulseat t = 0). Actually,160 singlepulsetraces havebeenco-addedto obtain thissignal. During this particular measurement, the systemreacts from purestyreneto a mixturecontaining 3% poly-styrene.ThemonomerconcentrationcM,0, which referstothe time when a laser pulse is fired, thus graduallydecreasesfrom the initial pure styreneconcentration (ordensity) at 808C and2200barto about97%of this value.The monomerconversioninducedby a singlelaserpulseamountsto about0.008%overthefirst 150msafterpuls-ing.

Fitting of the measuredcM (t)/cM,0 vs. t datato Eq. (1)yields kp/kt (or kt/kp) andalsokt N cR,0, wherecR,0 refers tothe free-radical concentration at t = 0 that is instanta-neously produced by laser-induced decomposition of(part of) thephotoinitiatorDMPA. It shouldbenotedthatcR,0 slightly decreaseswith conversion asa consequenceof photoinitiator consumption. The initial radicalconcen-tration, which is generatedby the first laserpulseappliedto thesample,is denotedcR,00 (seelater in thetext).

cM�t�cM;0

� �2 N kt N cR;0 N t � 1�ÿkp2 N kt �1�

Fig. 1. Styrene concentration,cM (t), measuredvs. time t (afterapplication of an excimerlaserpulseat t = 0) during a styrenepolymerizationat 808C, 2200barand3% (final) overall styreneconversion. The concentration is given relative to cM,0, the sty-rene concentrationat t = 0. The signal is obtainedby co-adding160 single pulse traceseachof which is recordedwith a timeresolutionof 45 ls. Thedifferencebetweenmeasuredandfitted(Eq. (1)) datais illustrated by plotting the residuals(res) in thelowerpartof Fig. 1

466 M. Buback, Ch.Kowolli k, C. Kurz, A. Wahl

kt in Eq. (1) refersto theterminationratelaw in Eq. (2):

dcR

dt� ÿ2 N kt N c2

R �2�

In Eqs.(1) and (2), kt is considered to be independentof free-radicalchainlength.Actually, terminationin SP–PLPexperimentsprimarily occursby reactionof two freeradicalsthatarevery similar in size.In principle,a termi-nation rate coefficient kt (i,i), with chain length i beingproportional to time t after applying the laser pulse,shouldbe usedto model SP–PLP experiments (at leastunderconditionswherechain-transfer processes are notoverly important). On theotherhand,ascanbeseenfromthe plot of residuals(res) in the lower part of Fig. 1, achain-length independent kt value allows for an adequaterepresentationof themeasuredcM (t)/cM,0 vs. t trace.

During thecourseof a polymerization at constantp andT up to higher conversion,several such time-resolvedmeasurementsmay becarriedout. Each of the individualcM (t)/cM,0 vs. t traces(asin Fig. 1) originatesfrom co-add-ing a significant numberof “true” single pulse signals.SP–PLP experiments have beenperformed at the tem-peratureandpressureconditionslistedin Tab.1.

Plotted in Fig. 2 arethekt /kp valuesderivedfrom fittingthe measured cM (t)/cM,0 vs. t traces of styrenehomopoly-

merizationscarriedout at 2200barandtwo temperatures,608C (opencircles) and 1008C (full circles). Two find-ings immediately emerge from Fig. 2: (i) In the conver-sion range up to 20%, no clear variation of kt/kp withoverallmonomerconversion(or polymer content) is seenat either 60 or 1008C. This result is in full agreementwith what hasbeenobserved in a previousstudy on sty-rene27). (ii) Despite of anaveragescatter in kt/kp by aboutl40% aroundthe arithmetic mean valuesrepresentedbythe horizontal lines, kt/kp is definitely found to decreasewith temperature. For theentiresetof p andT conditionsof the presentstudy such conversion-independent kt/kp

dataareobtainedfor the initial polymerizationrangeupto 20 % conversion.Thisaveragekt/kp datais summarizedin the third columnof Tab.1. kp asa function of p andTis known from a PLP-SEC study3). The kp numberstogetherwith kt/kp directly yield kt. The literature kp dataand the calculated kt values are given in the fourth andfifth columnof Tab.1, respectively.

kt of styrenehomopolymerization is almost insensitivetoward temperature,but clearly decreaseswith pressure.The Arrhenius plot for kt at 2200 bar is shown in Fig. 3.Theactivation energy is estimatedto beEA(kt) = (0.4 l 8)kJ N mol–1. This value is close to EA(kt) = (4.3l 4.0)kJ N mol–1 deducedfrom the expression for kt (p,T) inref.27) The literaturedata is from chemically and photo-

Tab.1. Collection of experimental kt/kp valuesfrom SP–PLPfor styrenebulk polymerizationsat severaltemperatures,H, andpres-sures,p. Thekp valuesfrom ref.3) andthekt datacalculatedfrom kt/kp andkp arealsogivenasis thedeviation from theliteraturedata,Dkt = (kt,SP– PLP– kt,lit)/kt,SP– PLP, wherekt,SP– PLP is thekt valuefrom thepresentstudyandkt,lit thecorrespondingvaluefrom ref.27)

H/ 8C p/bar log (kt/kp) log (kp/(L N mol–1 N s–1)) log (kt/(L N mol–1 N s–1)) Dkt/%

60 2200 4.73 2.96 7.69 42.080 2200 4.46 3.20 7.66 31.8

100 2200 4.28 3.42 7.70 32.780 1800 4.63 3.14 7.77 32.780 2650 4.29 3.28 7.57 32.9

Fig. 2. kt/kp of styrenebulk polymerizations at 608C, 2200bar(opencircles)andat 1008C, 2200bar (full circles)measuredasa function of overall monomer conversion. The abscissa valueof overallstyreneconversionrefersto thearithmeticmeanvalueof initial and final concentrations(conversions) of a particularexperimentconsisting of a largernumberof individual SP–PLPmeasurements (seetext)

Fig. 3. Arrheniusplot of kt for styrenebulk polymerizationsat2200barandtemperaturesof 60,80 and1008C. Eachdatapointis obtainedas the meanvalue of kt datadeterminedwithin theinitial polymerizationrangeup to about20% overall monomerconversion(seeFig. 2). The dashedline representskt datafromPS–PLPexperiments(seeref.27))

Terminationkineticsof styrenefree-radical polymerization studiedby ... 467

chemically induced styrene homopolymerizations withazo-bis-isobutyronitrile (AIBN) usedastheinitiator27). Ascanbe seenfrom Fig. 3, literature kt (dashedline) agreeswith the presentdata in temperature dependence,butclearly differs, by about 30%, in absolute value. Thisfinding will bediscussedbelow.

Thepressuredependenceof kt of bulk styrenepolymer-ization at 808C is shownin Fig. 4. From the slope of thestraightline in Fig. 4 an activation volumeof DVm (kt) =(16 l 6) cm3 N mol–1 is calculatedaccording to Eq. (3).

ÿDVm�kt� � q lnkt

qp

� �T

NR NT �3�

The dashedline in Fig. 4 represents kt datafrom ref.27)

Again, the formula for kt (p, T) in ref.27) is usedto deriveDVm. The activation volumeassociatedwith the literaturedatais DVm (kt) = (15 l 3) cm3 N mol–1. TheDVm (kt) valuesderived by the two fully independent procedures are inexcellent agreement. The absolutevalues of kt from thetwo sourcesare howeverdifferent, as could alreadybeseenin Fig. 3.

In the last column of Tab.1, the relative deviationbetweenthe two setsof kt values is given. The SP–PLPdataaresystematically abovethecorrespondingliteraturevalues, by about 30%. This discrepancy is not easilyunderstood, in particular as part of the literature valueshave also been measuredby photochemically inducedinitiator decomposition. In theseexperiments, however, adifferent type of initiator (AIBN) hasbeenused.More-over, laserpulsesof lower energy were applied. Unfortu-nately, AIBN is no suitableinitiator for SP–PLP experi-ments at temperaturesabove 608C that have to beemployed to achieve a satisfactory signal-to-noisequalityof the conversion vs. time trace.At theseelevatedtem-

peraturesa significantthermal decomposition of AIBN isobserved,which interfereswith the photochemical initia-tion process.The differences in kt values (Fig. 3 and 4)maybedueto the type of initiator. In particular, the frac-tion of propagatingprimary freeradicalsmaybedifferentand even non-propagating radicalsmay be produced inthe photo-initiation step. Such processes are notaccountedfor in thekinetic schemeunderlying Eq. (1).

To addressthis issue in more quantitative terms,SP–PLP experiments for styrenehavebeencarriedout at ahigher primary free-radical concentration, cR,00 =2.3 N 10–5 mol N L–1, than used in the experiments pre-sentedin Tab.1 wherecR,00 wasalwayscloseto 9.6 N 10–6

mol N L–1. cR,00 is estimated from pulse energy, initiatorconcentration, initiator absorption cross-section at thelaser wavelength, and efficiency of free-radical produc-tion21). Thesurprising resultfrom this additional measure-ment for 808C and2200bar is that thekt value (deducedfrom fitting the experimental cM (t)/cM,0 vs. t trace)increases with cR,00. Becauseof signal intensityproblemsin the styreneSP–PLP experiments,suchmeasurementstoward significantly lower primary free-radical concen-trations can not be carriedout. SP–PLP experiments atsubstantial variationof cR,00 may, however, be performedon methyl acrylate(MA) with DMPA acting asthephoto-initiator. For this rapidly propagating monomer, SP–PLPsignalsof goodquality mayberecordedevenat low cR,00.The resulting kt/kp datafor MA homopolymerizations at408C and 1000bar taken from ref.21,25) are plotted (asopen circles) in Fig. 5. A clear increasein kt/kp (andthusin kt) is seen. Linear fitting of log (kt/kp) vs. cR,00 yieldsthe curved log (kt/kp) vs. log cR,00 relation represented bythefull line in Fig. 5.

Fig. 4. Pressuredependenceof kt for styrenebulk polymeriza-tions at 808C andpressuresof 1800, 2200 and2650bar. Eachdatapoint is obtained as the meanvalue of kt datadeterminedwithin the initial polymerization rangeup to about20% overallmonomerconversion (seeFig. 2). The dashedline representskt

datafrom PS–PLPexperiments(seeref.27))

Fig. 5. kt/kp datafrom SP–PLPexperimentswith DMPA asthephotoinitiator obtainedat different (initial) radical concentra-tions,cR,00, generated by the first laserpulsein free-radical bulkpolymerizationsof methylacrylate (MA) at 40 8C and1000bar(open circles)21) andstyrene(STY) at 808C and2200bar (opentriangles).The (dotted)horizontal line representsthe styrenekt

valuefor 808C and2200bar from a recentstudy21) with chemi-cal initiation usingAIBN astheinitiator.

468 M. Buback, Ch.Kowolli k, C. Kurz, A. Wahl

Assuming that the variation in observedkt is mainlydueto the initiator DMPA, thecurvefor MA is shiftedinlog (kt/kp) direction suchasto passthrough the log (kt/kp)dataof the two styreneSP–PLP experiments both beingcarried out at 808C and 2200bar, but at different cR,00.The resulting dashedline at low cR,00 coincideswith thehorizontal (dotted) line that representsliterature kt atidenticalp andT. At low levels of free-radical concentra-tion thekt datafrom thepresentinvestigation thusarenotin conflict with thevaluesfrom recentliterature27).

The questionthat needsto be answered is: Why doesthe kt value derived from SP–PLP experiments via Eq.(1) vary with free-radical concentration?Beforedoing so,it should also be noted that, as a consequenceof theincreasein observedkt with cR,00, the monomerconver-sionperpulsedecreasestowardhigherprimary free-radi-cal concentration.This ratherunexpectedobservation hasfirst beenmadeby Kurz during the courseof her SP–PLP studiesinto methyl anddodecyl acrylate bulk poly-merization kinetics21). The most plausible explanationthatwe canpresentlyoffer for theseobservationsis basedon the assumption that the two primary free-radical spe-cies (seeScheme1) that are formeduponphoto-inducedDMPA decomposition largely differ in their reactivitytoward the monomer. Fischeret al.29) showed that fromthe two types of primary free radicals produced fromDMPA, PhCO9 and Ph(OCH3)2C9, the Ph(OCH3)2C9 spe-cies is only involved in termination reactions. Increasingthe initiator concentration is thus associatedwith a sub-stantial enhancementof non-propagating, but terminatingradicals. The chain-terminating efficiency ofPh(OCH3)2C9 should be responsible for the observedincreasein kt. Accordingto this argument, thevariation inkt suggestedby Fig. 5, is not necessarily indicativeof anychangein kt, but most likely resultsfrom the applicationof an incompletekinetic schemewhich doesnot considertheformation of a lessreactiveprimary free-radicalinter-mediate from DMPA. The literature data27), which arefrom chemically andphoto-chemically inducedpolymeri-zationswith AIBN asthe initiator, arenot influencedbythe formation of two typesof primary free radicalswithoneof thembeing unableto propagate. Thuskt is a truebimolecular (chain-length averaged) termination ratecoefficient, which should not dependon cR,00.

An explanationalong theselines is consistent with theentiresetof experimental observations madein SP–PLPexperiments with DMPA acting asthephotoinitiator. Themodelling of such pulsed laser polymerizationsvia the

programpackage PREDICIm 30) is currently underway31).It is beyondthe scopeof this article to presentthe earlyresultsof this study.

It is important to note that the kt value from SP–PLPexperiments with DMPA asthe initiator, after extrapola-tion to low levels of cR,00, nicely agreeswith the termina-tion rate coefficient obtained from both chemicallyinduced and pulse sequence-PLP experiments (carriedout at low levels of free-radical concentration). Thevalueof kt at low levels of cR,00 may be looked upon as the“true” (chain-length averaged) bimolecular terminationrate coefficient. The very satisfactory agreement of sty-renekt data(at low cR,00) determinedfrom differenttypesof experiments,providesstrong support for thevalidity ofthe kt values reported in ref.27) Thus the expression forkt (p,T) from ref.27) is recommendedfor usein estimatingstyreneterminationratecoefficients asa function of pres-sureandtemperature:

lnkt�p;T�

L Nmolÿ1 N sÿ1

� �� 20:785ÿ 1:050N10ÿ3 N

pbar�

�5:2 N10ÿ8 Np2

bar2ÿ 753

T=K� 0:1060

T=KN

pbar

�4�

A separatefit hasbeencarriedout for theambientpres-surekt data27). Theresulting expressionreads:

ln�kt=�L Nmolÿ1 N sÿ1� � 21:37ÿ 958T=K

�at ambientpressure�

In conclusion: The SP–PLP method may be appliedtowardmeasuringthe terminationratecoefficient of sty-rene bulk polymerization. The resulting kt values, afterextrapolation to low levels of free-radical concentration,are in excellent agreement with the corresponding datafrom recent studies. SP–PLP experiments carriedout atextendedvariationof the primary free-radical concentra-tion(s) produced by DMPA decompositionstrongly indi-catethat free radicals of distinctly different reactivity areformed.

Acknowledgement:The authorsare grateful to Prof. HannsFischer (Zurich) and to Dr. M. Busch for helpful discussions.Financial support by the Fonds der Chemischen Industrie isgratefullyacknowleged.

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