ma50002a045

210Macromolecules1981,14,210-211DiscussionTheproductshavingunsaturatedendgroupswerenotdetected,whichindicatesthatathightemperaturescy-clizationofthepropagatingcation(eq1)occursinpref-erencetodirectP-protontransfertomonomer.(1)IH3r3M,-w~-c-cH~-c+-IIII1I1+M-M,-CHz--CH,CH,+MH+(2)r3\/Ineq1and2Mdenotesmonomerandn,thenumberofmonomerunits.Cyclizationresultsincessationofprop-agationbycationI,andthedecreaseinmolecularweightwithincreasingtemperatureshouldbeduetotheincreaseintherateofcyclization.Intheoligomerizationofstyrenederivativesbycationiccatalystsithasbeenconcludedthatcyclizationpredom-inatesoverP-protoneliminationwhenthecation-anioninteractionisweakenedonthebasisoftheeffectsofcounteranionsandsolventsonthecompositionofdimers.%Thepropagatingionofradiation-inducedpolymerizationisknowntobeafreeion,landtheresultofthepresentstudyindicatesthatP-protoneliminationcannotcompetewithcyclizationinthecaseofthefreecation.Thedimerisproducedbyreactions1and2aswellashigheroligomers.Anotherpossibleprocessofdimerfor-mationistheeliminationofTMPIfromcation11,whichhasbeenproposedintheradiation-induceddegradationofpoly(a-methylstyrene)athightemperature.6y311-TMPI+M,,-cH~-~(3)AThereactionistheprotolysisoftheC-Cbondbytheprotonderivedfromthearomaticringtogivetheneutralproductandthestabletertiarycarboniumionandcom-peteswiththeprotontransfertomonomer(eq2).Thedimerisformedbyachainreaction(reactions1and3)whencationIhasalongchain.Itisworthnotingthatoligomersotherthanthedimerwerenotproducedintheradiation-induceddegradationofpoly(a-methylstyrene).Itseemsreasonabletoassumethatdegradationcontributestodimerformationatlowertemperatures,wheredimerformationhasthehigheractivationenergy(Figure1).Incontrast,athighertemperaturestheconcentrationofthepropagatingcationhavingasufficientlylongchaintoyieldthedimerbydegradationislimited,andthedimerispredominantlyformedbyreactions1and2.ReferencesandNotes(1)Williams,F.“FundamentalProcessesinRadiationChemistry”;Ausloos,P.,Ed.;Interscience:NewYork,1968p515andreferencescitedtherein.(2)Chawala,A.S.;Huang,R.Y.M.J.Polym.Sci.,Polym.Chem.Ed.1975,13,1271.(3)(a)Sawamoto,M.;Masuda,T.;Nishii,H.;Higashimura,T.J.Polyrn.Sci.,Polym.Lett.Ed.1975,13,279.(b)Higashimura,T.;Nishii,H.J.Polym.Sci.,Polyrn.Chem.Ed.1977,15,329.0024-9297/81/2214-0210$01.00/0(c)Nishii,H.;Higashimura,T.Ibid.1977,15,1179.(d)Hi-gashimura,T.;Hiza,M.;Hasegawa,H.Macromolecules1979,12.217.Ibid.1979.12.1058.(4)Best,J.V.F.;Bates,T.’H.;Williams,F.Trans.FaradaySOC.1962,58,192.(5)ThechaintransferisalsoknowntooccurinthecatalyticDO-lymerization;forexample,see:Dainton,F.S.;Tomlinson,-R.H.J.Chem.SOC.1953,151.(6)Yamamoto,Y.;Miki,M.;Havashi,K.Macromolecules1976.~.9,874.Ibid.1977,10,1316.(7)TheassignmentwasbasedoncomparisonofthepeakpositionswithauthenticTMPIandstandardstyreneoligomers;thepeakpositionsofstyrenedimer,trimer,tetramer,andpen-tamerwere25.1,22.2,20.5,and19.3counts,respectively.(8)Brandrup,J.;Immergut,E.H.,Eds.“PolymerHandbook”,2nded.;Wiley:NewYork,1975;p11-437.(9)TheGvalueisthenumberofmoleculesoftheproductorthemonomerconsumedper100eVofenergyabsorbed.TranslationalDiffusionandHydrodynamicRadiusofUnperturbedFlexibleChainsMANFREDSCHMIDT*andWALTHERBURCHARDZnstitutfuerMakromolekulareChemiederUniuersitaetFreiburg,0-7800Freiburgi.Br.,WestGermany.ReceivedSeptember29,1980Rapiddevelopmentofquasi-elasticlightscatteringtechniqueduringthepastfewyearshasfurnishedhighlyaccuratemeasurementsoftranslationaldiffusioncoeffi-cients,makingpossibleafairlyrigoroustestofdynamictheoriesforflexiblemacromoleculesinsolution.Inthisnotewesummarizealltheexistingexperimentalresultsforpolystyrenein8solventsandfindsignificantdis-agreementwiththewell-knownexpressionsofKirkwood’orZimm2forthediffusioncoefficient.Atpresentnosatisfactoryexplanationisknownforthisdiscrepancy,whichhasbeenpointedout3-’previouslyonthebasisofmorelimiteddata.Followingcommonpractice,wemaydefineanaveragereciprocalhydrodynamicradiusintermsoftheStokeslawexpression(1/Rh)z=(~TVO/~BT)D~(1)whereV~issolventviscosity,kBTthethermalenergy,andD,themeasurablez-averagetranslationaldiffusioncoef-ficient.Thehydrodynamicradiusmaythenbecomparedtotheobservableroot-mean-squarez-averageradiusofgyration(S2),ll2intermsofthedimensionlessnumberp=(S2),’/2(1/Rh),1/2(2)whichisindependentofchainlength.ofKirkwood1p8Formonodispersepolymers,accordingtotherelationD=k,T/(vJ‘(6S2)’/2)(3)withP=(3~)~/~/2~/~=5.115p=:1.504whiletheZimmtheory(whichpreaveragesthehydrody-namicinteractions)leadstoP=(3/2)1/2~r(3/4)/r(y4)=5.202=1.479(4)thedifferencebetweenthetwoexpressionsbeingduetocouplingbetweeninternalandtranslationalmotions(im-*TowhomcorrespondenceshouldbeaddressedattheDepart-mentofChemistry,DartmouthCollege,Hanover,N.H.03755.01981AmericanChemicalSocietyMacromolecules1981,14,211-212211,yi'441(I/Rh)i'105106IO'108M.Fire1.Hydrodynamicradius,(I/Rh);l,andradiusofgyration,(g1I2,forlinear,nearlymonodispersepolystyrenein8solvents.Datasources:CurveA:(e)ref4;(V)ref10;(0)ref11;(A)ref3;(m)ref12.CurveB:(0)ref15;(a)ref19;(0)ref20;(+)ref13;(X)ref17;(0)ref16;(0)ref4;(V)ref18;(A)ref14;(V