1,4 Polyisoprene a,B Relaxation

7/28/2019 1,4 Polyisoprene a,B Relaxation

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Evolution of the Dynamics in 1,4-Polyisoprene from a Nearly Constant

Loss t o a J oha r i-Goldstein -Relaxation to the R-Relaxation

C. M. Roland,*, M. J . Schroeder, J . J . Fontanella, and K. L. Ngai*,

Naval Research L aborat ory, Washi n gt on, D . C. 20375-5320, and Un i t ed S t at es Naval A cademy,

A n n a p ol i s , M a r y l a n d 2 1 40 2

Received December 1, 2003; Revised M anu scri pt R eceived J anu ar y 15, 2004

ABS TRACT: The J oha ri-G oldstein (J G ) seconda ry rela xat ion, presumed to be universa l, has n ever beenseen in 1,4-polyisoprene (PI) by dielectric spectroscopy, despite very ma ny meas urement s extendin g overthe past ha lf-century. By using a high-resolution capa cita nce bridge, we ar e able to show t he existenceof a secondary relaxation in PI that has the properties of the J G process. Measurements were also carriedout at lower temperatures, which probe the dynamics of chain units caged by neighboring segmentscomprising t he local structure. The caged dyn amics precede by decades of t ime th e J G relaxat ion an d,fr om g e ner al phy sic al pr inci pl es, ar e al so e xpec t ed t o b e a pr oper t y of a l l g l ass-for m i ng m a t e r ial s .Collectively, the caged dyna mics a nd J G relaxa tion serve as precursors to st ructural r elaxation (i.e., theg l ass t r a nsi t ion) and t hus ar e of c ent r al i m por t anc e t o und e r st and i ng vi t r i fi cat i on. The pr e sent d at ashow that the dynamics of caged PI repeat units are manifested as a nearly constant loss (NCL). ThisNCL h as been found in other gla ss-formers, both m olecular an d polymeric, a nd its temperatur e dependencein P I is similar t o tha t for other ma terials. The experimenta l results ar e consistent w ith t he predictionsfrom the coupling model.

Introduction

Su bs t a n c es h a v in g dive rse ch e mica l a n d p h y sica lstructures vitrify, with t he glass tr an sition phenomenonchara cterized by dyna mic and thermodynamic proper-ties common to all glass-formers. An immense amountof e x pe rime n t a l da t a h a s bee n a ccu mu la t e d ov er t h eyears, part icularly on the structural R-relaxa tion; nev-ertheless, a consensus regarding a theory of the glasst ra n s i t ion is la c kin g .1,2 F u n da me n t a l u n de rs t a n din gre q u ire s e x a min a t ion of t h e dy n a mics t h a t p rece de(ear lier in time) the coopera tive R-relaxa tion, since thesefaster processes serve as the precursor to structuralrelaxat ion. At early t imes, before either rotat ional ortranslat ional diffusion has transpired, molecular mo-tions are confined to a cage, defined by the intermo-lecular potential of neighboring molecules. For molec-ular glass-formers, caging is effected by the neighboringmolecules, w hile for polymers, a segment is caged bysegments from other chains a s well as r epeat units fromthe same chain. In both cases, the caging is effected byintermolecular (intersegmental) repulsive forces. Theshort t ime dy nam ics w ithin t he cage, occurring beforethe onset of structural relaxat ion, are of fundamentalinterest. One fa miliar short-time process is the second-a ry re la x a t io n , wh ich is loca l (n on coop era t iv e ) a n dthermally activated. However, at times shorter than thesecondary relaxat ion, but longer than the Boson peak

or Poley absorption,3

the m otions of the caged m oleculesare not well understood. Herein, we refer to the pro-cesses in this regime as caged dyna mics.

The best-known description of the ca ged dyn a mics isfrom m ode coupling th eory (MCT),4 based on nonlinearcoupling of density f luctuations in condensed matter.According t o MCT, t he ca ged rela xat ion is t he so-called

f a s t -process, which transpires at temperatures abovea crit ical temperature, Tc. When the time dependenceof this -process is Fourier transformed to a susceptibil-i t y , t h e ima g in a ry p a rt , () , has a minimum definedby t wo p o we r la ws , -b a n d a, on the respective low-and high-frequency sides. The exponents a a n d b a rerelated by the equation [2(1 - a)/(1 - 2a)] ) [2(1 +b)/(1 + 2b)], wh ere is t h e g a mma f u n ct ion . Th esusceptibility minimum ha s a frequency dependencetha t bea rs no resemblance to the loss a ssociat ed with arelaxa tion process, and hence the fa st -process of MCTis not a relaxation in the conventional sense. Note thatthe MCT-process is d istin ct from t he a bove-ment ioned

s econ da ry re la x a t ion s common ly obs erv ed in g la s s -formers; the lat ter are genuine relaxat ions, involvinglocal r otat ion and/or tr an slat ional diffusion (in MCTparla nce, these comprise the slow-process). Accordin gto MCT, the fast -process is followed by the R-relax-at ion, described by the Kohlrausch-Williams-Watts(KWW) fu nct ion

wh e re R is the R-relaxation time and KWW is a fractionl es s t h a n u n it y .5,6 Th u s , M CT re g a rds i t s p ut a t iv e-process to be the precursor of st ructural relaxat ion.

The MC T description of caged dyna mics is r estricted

t o t e mpe ra t u re s a bo ve Tc. H o we ve r , t h e re e x is t s aplethora of experimental data for both above and wellbelow Tc, which must be reconciled with a ny th eoreticaldescription. At lower tempera tures, t he durat ion overwh ic h mo le c u le s a re c a g e d is e x t e n de d be c a u s e t h eprimary a nd secondary relaxa t ions that cause decay ofthe cage a re slower. Since the caged dyna mics continuest o lo n g e r t ime s a t lo we r t e mp e ra t u re s , i t s h o u ld beexperimentally observable over a wider frequency ra ngea t T < Tc than for T > Tc. Dielectric data for both smallmolecules and polymers show7-12 tha t a t lower temper-atures the caged dynamics can be described by a slowly

Naval Research Laboratory. U n i t e d S t a t e s N a v a l Ac a d em y .* To whom correspondence should be addressed. E-mail: roland@

nrl.navy.mil.

(t) ) exp[-(t/R

)KWW] (1)

2630 M acromolecul es 2004, 37 , 2630-2635

10.1021/ma0358071 This a rticle not subject t o U.S. Copyright. P ublished 2004 by the American Chemical SocietyP ubl ish ed on Web 03/06/2004


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decreasing function of frequency, - (where is asmall posit ive exponent), or a s a logar ithmic functionof . Similar behavior is found in glassy, molten, andeven crystalline ionic conductors for temperatures atwh ich t h e ion s a re c a g ed a n d t h u s u n a ble t o mo ve t oa n ot h er s it e i n t h e e xp er i me nt a l t i m e r a n g e.7 Thevaria tion of this dispersion w ith frequency is very w eak,an d hence, in t he field of ionic conductors, it is referredto as the nea rly consta nt loss (NCL ). A good exam ple isthe glass-forming molten salt , 0.4Ca(NO3)2-0.6KNO3(C K N ), w h i ch i s b ot h a g la s s -f or m er a n d a n i on i cconductor.7

The observation of th e NC L in glass-formers is notlimited to dielectric relaxat ion measur ements. Dyna miclight scat tering experiments on polyisobutylene,13 poly-(methyl methacrylat e),14 an d glycerol14 have revealeda n early consta nt loss in the imagina ry par t of both th edepolar ized a nd polar ized susceptibilities, (), at highfrequencies (gG H z ) f or t e mp er a t u r es r a n g in g f r ombelow Tg to near or above Tc. Studies of several organicglass-forming liquids15 found a power la w decay of theoptical Kerr effect response given by t-1+c, wh e re c0. 1 a t t e mp e ra t u re s be lo w t h e Tc of MCT. Since theoptical Kerr effect signa l is the Fourier tra nsform of the

imaginary part of the susceptibility,15 t h e l a t t e r i s anearly constant loss.

At high temperatures, NCL as a background loss cangive rise to a minimum in the susceptibility, having -b

a n d a dependences on the low- and high-frequencysides. This occurs at high temperatures (such as aboveTc), w hen R becomes short. Then, the temporal extentof t h e N C L i s r ed u ced b y t h e en cr oa c hi ng h ig h -frequency flank of the R-loss peak, which has a -KWW

dependence on the low-frequency side (viz. , the one-sided Fourier transform of eq 1), which can give rise tot he -b dependence of the susceptibility minimum. Onthe high-frequency side, there is always a contributionfrom the low-frequency flank of the Boson peak or Poley

a bs orp t ion . Th u s , t h e s t ru ct u ra l re la x a t ion a t h ig htemperatures (for which R is typically on the order ofnanoseconds), in combination with the Boson peak andthe NCL, can yield a minimum in the susceptibility, asobserved by dielectric, neutron, a nd light scat teringexperiments at sufficiently high temperatures. 4 Thisexplains why R in v a ria bly h a s t h is ma g n it u de (10-9

s ) a t Tc, wh e re Tc is obtained by extrapolat ion of theMCT scaling law s. I t is a lso obvious t hat the suscepti-bility minimum predicted by the sta ndar d MCT cannotaccount for the NC L.

At Tc an d above, with R in the ra nge of nanoseconds,all nontrivial secondary relaxat ions have merged witht he R-relaxation. Under these conditions, the claim ofMCT that the caged dynamics is the precursor of theR-relaxat ion has validity. However, at lower tempera-t u re s , t h e s e c o n da ry re la x a t io n a n d t h e R-relaxationbecome well-separated in t ime. Since the secondaryrelaxation falls intermediate in time between the fastercaged dynamics and the slower R-relaxa tion, evidentlyt h e s e c o n da ry re la x a t io n mu s t p la y s o me ro le in t h edevelopment of t he R-relaxat ion. H owever, i t is n otu n common , p a rt icu la r ly in s t u die s of p oly mers , t oregard the secondary -relaxa tions a s ha ving no role int h e g la s s t ra n s i t ion . Th is idea is ju s t i fied f or t h os e-relaxations involving intramolecular degrees of free-dom; i.e., isolated m otion of only some a toms in a flexiblechain, such a s a ny pendant groups. However, J ohar i an dG o lds t e in (J G ) s h o we d t h a t t h is is n o t g e ne ra l ly t h e

case, by t heir discovery of -relaxations in glass-formerscomprised of completely rigid molecules.16-18 This in-triguing finding implies that some -relaxa tions reflectloca l motions involving essentia lly th e entire molecule,19

and it is these secondary relaxations which are denotedJ oha ri-Goldstein (J G) relaxat ions.20-38 For polymerswithout side groups, such a s 1,4-polybutadiene, th e-relaxa tion obviously belongs to this category. In somepolymers ha ving pendant groups, for example poly-(methyl methacrylate) (PMMA) and poly(ethyl meth-acrylate) (PEMA), the secondary relaxations have beenshown to entail motion of a side group, together withs ma ll-a n g le rock ing of a p ort ion of t h e ch a in ba c k-bone;39,40 thus, essentia lly all a toms of the repeat unitpart icipat e, an d thus the motion is a J G process. J Grelaxat ions serve as the precursor of the R-relaxation,in accord with experimental data showing the existenceof var ious relat ions between the dyna mic and t hermo-dyna mic propert ies of J G relaxat ion a nd t he R-relax-at ion.8,9,23,34,41 One example is the ant icorrela tion of thefractional exponent KWW for the structural relaxat ion(eq 1) w ith (log R- log ), where is the J G r elaxat iontime.23,41

The existence of the J G relaxat ion is considered t o

be universal a mong glass-formers. 16-18 Likewise, cageddynamics, manifested as the NCL, may be regarded asa general property of glass-formers. In this work, weconsider a glass -former, 1,4-polyisoprene, for w hichn ei t her t h e J G r el a xa t i on n or t h e N C L h a s b eenreported in previous rela xat ion st udies.42-58 From broad-band relaxat ion measurements under optimal condi-t ions, we show th at these two features of the dynamicsdo indeed exist in P I. Moreover, t he respective temper-at ure dependences of the J G relaxat ion t ime a nd t hedielectric strength, , a s we l l a s t h e N CL , a re a l l inaccord with the propert ies of these processes seen inother gla ss-formers. The results a re compa red w ith t hepredictions fr om th e coupling model.7-9,19

Experimental Section

The linear 1,4-polyisoprene (high cis), obtained from A.F.Ha lasa of the G oodyear Tire & Rubber Co., was prepared byan ionic polymerization using n-butyll i thium initiator. Thenominal molecular weight was 500 000 Da, and the calorimet-r ic Tg 203 K. Isothermal dielectric spectra were mea suredove r t he fr e q ue nc y r ang e 10 H z-100 kHz using a CGA-83capacitance measuring assembly. (This instrument is a pro-totype of the commercially available Andeen-Hagerling ca-pacitance bridge.) The measurements employed a cell similarto th at described elsewhere,59 but w ith a solid 2 mm piece ofbrass used a s t he high electrode. This cell w as mounted ona coldfinger of a Precision Cryogenics dewar, and the temper-at ure wa s controlled using a LakeShore Cryotronics DRC 82Ctemperature controller. Other measurements were made usingan IMass Inc. t ime domain dielectric spectrometer, having afrequency ra nge of 10-4-104 Hz, in combination with a DeltaDesign 9023 l iquid nitrogen cooled oven. A para llel plat egeometry (25 mm diameter with sample thickness between0.05 and 0. 15 m m ) w as e m pl oy e d , w i t h a g uar d r i ng on t hedetector side. Samples were al lowed to equil ibrate at least 1h a f t e r a t t a i n in g t h e d es ir ed t e mp er a t u r e, w i t h r ep li ca t emeasurements used to ensure thermal equil ibration.

Results and Discussion

J ohari-Goldstein Relaxation. The complex dielec-t r ic s u s ce pt ibil it y of t h e p romin en t R-relaxat ion isroutinely measured using conventional dielectric instru-ments. Shown in Figure 1 are the data obtained using

M acromolecul es, Vol. 37, N o. 7, 2004 Dyn am ics in 1,4-P olyisoprene 2631


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the IMass time domain dielectric analyzer at 216.0 (]),211.15 (0), 208.15 (O), a nd 204.15 K (3). At each of thesetemperatures, the data were obtained for frequencies

up to 104

Hz. H owever, the losses a t t he higher frequen-cies a re low a n d e xh ibi t la rg e s c a t t e r , p a rt icu la r ly a tlower tempera tures. C onsequently, no useful informa-tion is obtained for frequencies much beyond R, t h efrequency at the maximum of the R-loss peak. For thisreason, the data in Figure 1 have been truncated. Toprobe the response at higher frequencies, we employ thehigh-precision CGA-83 capacitance bridge. Note thatthese data, over the frequency range 10 Hz-100 kH z,e xh i bi t n o a p pr eci a b le s ca t t e r a t a n y t e mp er a t u r e(Figure 1). The R-relaxat ion mea surements from the tw oinstruments agree to within the experimental error.

The dielectr ic R-r e la x a t i on t i m es d ef in ed a s t h ereciprocal of the angular frequency at the loss maximum(1/(2R), which is somewha t lar ger than the R defined

by eq 1) are shown in an Arrhenius plot in Figure 2,a lon g wit h t h e f i t t o t h e Vog el-Fulcher-Tammann-Hesse (VFTH) equa tion60

The dielctric Tg, defined by R(Tg) ) 100 s, is 207.4 K.There is a small (ca. 0.5 deg) temperature differencebetween the two experiments; however, the CGA-83dat a a t 216.7 ([), 212.7 (b), 208.7 (9), and 204.7 K (1)m a t c h w e l l t h e I M a s s d a t a a t 2 1 6 . 0 (]), 211.15 (0),208.15 (O), and 204.15 K (3). These sma ll differencesare corrected by shift ing the IMass loss data for each

temperat ure horizonta lly along the frequency axis, witht h e a mo u n t o f t h e s h i f t de t e rmin e d f ro m t h e V F T He q u a t ion . F o r e x a mp le , t h e 216.0 K I M a s s da t a a reshifted 0.179 decade toward higher frequency in orderto ma tch the CG A-83 measurements at 216.7 K.

I t is e v ide n t f rom t h e s e s pe ct ra t h a t a s e con da ryrelaxation is present on the high-frequency side of theR-peak. This secondary relaxation appears as a shoulderat 212.7 K and becomes a broad peak at 208.7 K andlower temperatures. Note that given the weakness ofthe secondary relaxat ion in PI , i ts observation wouldbe very difficult using a conventional dielectric instru-m en t . Th is e xp la i n s w h y i t w a s u n d et e ct e d i n a l lprevious dielectric studies of PI, including our own.42-58

Alt h ou g h t h e da t a a t 216. 7, 212.7, a n d 208.7 Kindicat e a secondary r elaxa t ion is present , a chara cter-istic frequency cannot be deduced from t he broadshoulder in (). At low er t emperat ures, below Tg, thes h ou ld er e vol ve s i nt o a d is t in ct p ea k w i t h a p ea kfrequency

. The peak relaxation times,

) 1/(2

),

a r e pl ot t ed i n F ig ur e 2, a l on g w i t h t h e f i t t o t h eArrhenius equation

The act ivat ion enthalpy E ) 38.2 kJ /mol. The onlyp en d a n t m oi et y i n P I i s t h e m et h y l g r o up , w h o serotat ion is very fast at temperatures above Tg, wi t h a na ctivat ion entha lpy much sma ller tha n th e 38.2 kJ /molwe find herein.61 A mechanical secondary r elaxation w asreported for PI ,62 wit h a re la x a t io n t ime 3 o rde rs o fma g n it u de fa s t e r t h a n t h e in F ig u re 2 a n d h a v in g amuch w eaker t emperat ure dependence. This process ist h u s more lo ca l a n d n ot t h e J G re la x a t ion , s in ce t h eslower motion involves all a toms of the repeat unit. TheE determined herein for PI is nearly the same as thevalue of 35.7 kJ /mol reported for t he s econdar y relax-ation of 1,4-polybutadiene,24 wh ich is known to be a J G-re la x a t io n . A ll in dica t io n s a re t h a t t h e s econ da ryrelaxation of PI involves motion of the entire repeat unita n d t h us ca n b e cl a ss if ied a s a J oh a r i-Goldstein-relaxation.

The J G process is rela ted t o the R-relaxat ion, a s canbe demonstrated by a relat ionship from the couplingmodel (CM).8,9,63-65 Simila r t o t h e J G re la x a t io n , t h eprimit ive (independent) relaxat ion of the CM entailsmotion of the entire molecule and is not cooperat ive.Thus, the primitive relaxation time, 0, of the model is

Figure 1. Dielectric loss spectra of PI . The da ta a t 216.0 (]),211.15 (0), 208.15 (O), and 204.15 K (3) were obtained usingthe IMa ss t ime domain dielectric ana lyzer. All the other data ,which sta rt a t 10 Hz an d continue up to 100 kHz, were takenwit h t he CG A-83 capa citan ce bridge. There is good agreementof the CG A-83 data at 216.7 ([), 212.7 (9), 208.7 (b), and 204.7K (1) with t he IMass da ta at 216.0 (]), 211.15 (0), 208.15 (O),and 204. 15 K (3) , r e spe c t i ve l y , a f t e r t he l a t t e r have b e e nshifted horizontally by an amount determined from the VFTH

(eq 2) temperature dependence of the R-relaxation frequency(see Figure 2) to account for the slight differences in temper-ature. The other eight spectra were obtained only using theCG A-83. The spectra tha t show R-loss ma xima correspond(from right to left) to T ) 236.7 (*), 232.7 (2), 228.7 (+), and224.7 K (4). The lower t hree C GA-83 curves, w hich sh ow-losspe aks, w e r e t ake n (st ar t i ng fr om t he b ot t om ) at 169. 7 (4),181.7 (+) , and 200. 7 K (*) . T he ve r t i c al ar r ow s m ar k t heloca tions of the calculated primitive relaxa tion frequencies, 0,at (from right to left) 212.7 (9), 208.7 (b), and 204.7 K (1).The locations of th ese 0 should be compared with the second-ar y r e laxat i on peaks at t he se t e m pe r at ur e s.

log R) -14.35 +

721.3

T - 163.24(2)

Figure 2. Temperature dependence of the R-relaxat ion (9)an d J G -relaxation (b) t imes in P I, a long w ith t he respectiveVFTH and Ar r he nius f i t s . The si ng le ope n c ir c le i s t hecalculated primitive relaxat ion t ime at 204.7 K.

log ) -13.5 +1995

T(3)

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expected to be close to the most proba ble relaxa tion tim eof the J G relaxat ion for a ny given t empera ture. TheCMs conception of th e evolution of th e dyna mics8,9

differs from the conventiona l view t hat the J G relax-ation is comprised of a broad symmetric distribution ofre la x a t io n t imes , a ddit ion a l t o t h e R-relaxation. At agiven temperature and pressure P

wh e re 0 is ca lculat ed from the R-relaxa tion time by theCM relat ion 8,9,63,64

wh e re KWW (eq 1) describes the time dependence of theR-relaxat ion and tc (2 10-12 s) is t he chara cterist ict ime for the onset of intermolecular cooperat ivity.65

Previous works on various glass-formers have shownthat for genuine J G -relaxat ions 0.7-9,19,66 Thisrelation between a nd 0 is striking, in tha t th e formeris a n e x p e rime n t a l ly de t e rmin e d q u a n t i t y , wh ile t h elat ter is calculated via eq 5 using only parameters oft he R-relaxation, e.g. , R a nd KWW.

Eq uat ion 4 can be tested aga inst the data for PI . First,we f i t t h e a s y mme t ric R-loss peaks at 212.7 and 208.7K (Figure 1), a nd tw o other temperatures, 207.15 a nd209.65 K (not shown), to the one-sided Fourier trans-form of eq 1. This yields KWW ) 0.47 independent oftemperat ure (a s shown for 212.7 a nd 208.7 K as da shedlin e s in F ig u re 1) . I n t e re s t in g ly , t h e R-lo s s p e a k a thigher temperatures broadens on the low-frequency sideto become nearly symm etric. This beha vior is anoma lous(in the absence of a conductivity contribution) and isnot seen in the dielectric spectra of other polymeric ornonpolymeric glass formers. The broadening is repro-ducible, both herein using either inst rument (Figure 1)and as seen in previous measurements on other 1,4-polyisoprene sa mples.67 The cause of this behavior is

unclea r, but it ma y be relat ed to the presence of a dipolemoment pa ra llel to the P I chain backbone. I t is knowntha t sub-Rouse modes 68,69 ca n i n t ru d e o n t h e l oca lsegmental mode (i .e. , the R-relaxat ion), affect ing theapparent shape of the lat ter. However, this would notexplain why the effect is noted herein at higher tem-perat ures only.

Focusing on the fits to the KWW function at 212.7and 208.7 K, which yield KWW ) 0.47, 0 is calculatedusing eq 5 from the R a t 212.7, 208.7, a nd 204.7 K. Thefrequency 0 ) 1/(20) for each temperature is indicatedin Figure 1 by a vert ical arr ow. For T ) 212.7 and 208.7K, the calculated 0 is located on the broad shoulder ofthe J G -relaxation. For T ) 204.7 K, 0 i s n e a r t h esecondary relaxat ion peak ma ximum. This a greementbetween 0 a n d at 204.7 K is shown in Figure 2 bythe location of the single datum (open circle), represent-ing the logarithm of the calculated 0 for this temper-ature. The equivalence of a n d 0 is consistent withthe prediction of the coupling model and supports thedesignat ion of the observed secondar y r elaxat ion in P Ias a J G relaxat ion. Thus, it serves as t he precursor tot he R-relaxation.

Caged Relaxation: The Nearly Constant Loss.For glass-formers such a s P I t ha t h ave a resolved J Grelaxat ion, t he combined dispersions of t he R- a n d-processes for the equilibrium liquid occupy ma nydecades of frequency. Hence, measurements a t frequen-cies much higher tha n a vaila ble herein would be neces-

s a ry t o s t u dy t h e s h o rt er-t ime c a g ed dy n a mics in P I .Accordingly, to probe the caged dynamics, measure-ments w ere made a t lower temperatures, below Tg, forwhich the R- and -relaxations have moved beyond thelowest available frequencies. The dielectric loss at theselower temperat ures is small, necessitat ing aga in the useof the CGA-83. The main part of Figure 3 shows thedata collected at 169.7 K and several representat ivelower temperatures. The dispersions are so f lat thatthey a re appropriat ely referred to as the nea rly consta ntloss. The data collected at the three lower temperatures,85.5, 79.5, and 73.5 K, show some scat ter. These d a t ashow a slight increase with frequency, rather than thede cre a s e , a s s e en a t h ig h er t e mpe ra t u re s . E v ide nt ly ,there is another process contributing at high frequenciesat these lower t empera tures. Nevertheless, the varia tionof is so weak that the loss reflects mainly the NCL.Overall, the weak frequency dependence of of the dat ain Figure 3 is similar to the NCL found in molecularglass-formers.7,8,10,12,29,70-72

F ro m t h e da t a t a k e n a t di f f e re n t t e mp e ra t u re s , wedetermined of the NCL a t t hree frequencies: 0.1, 1,

a n d 10 k H z. T h e s e v a lu e s a re p lo t t e d a s lo g vst e mp e ra t u re in t h e in s e t t o F ig u re 3. T h e s o l id l in erepresents the least-squares f it of all the data points,suggesting that the NCL has a temperature dependencegiven by

i n t h e t e mp er a t u r e r a n g e of F i gu r e 3 . Th i s w e a kv a r ia t i on w i t h t e m pe ra t u r e o f t h e N C L i n g l a s s y P Irecalls similar behavior found in small molecule glass-formers at temperatures below Tg. T h e N CL f o r t h elat ter has a temperature dependence of

Figure 3. The nearly constant loss measured by the CGA-83i n P I a t r e pr e sent at i ve t e m pe r at ur e s b e low Tg. Fr om t op t obottom: 169.7 (4), 151.7 (9), 139.7 (3), 85.5 ([), 79.5 (2), an d73. 5 K (O) . T he i nse t show s t he ne ar l y c onst ant l oss as afunction of tempera ture a t 0.10, 1, and 10 kHz. The l ine is aleast-squa res fi t to al l data points, which has a slope equal to-184 K-1.

(T) ) 0.456 exp( T79.8) (6)

(T,P) 0(T,P) (4)

0 ) (tc)1-KWW(

R)KWW (5)



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wit h Tf 33 K.29,70 The same temperature dependence(e q 7) h a s b ee n f o un d f or t h e N C L i n g la s s y i on i cconductors 73 an d explained 7,73 in the framework of thecoupling model. A similar explanation when applied toca g e d molecu la r dy n a mics re a di ly a c cou n t s f or t h et e mp e ra t u re de p e n de n c e o f t h e N CL in P I a n d s ma llmolecule glass-formers,as given by eqs 6 and 7.

Recently, Sokolov and co-workers74

carried out dy-n a m i c l ig h t s ca t t e r in g m ea s u r em en t s on P I i n t h eg ig a h er t z t o t e ra h e r t z r a n g e, a t t e m pe ra t u r es f r omabout 153 K to about 240 K. The spectral range is muchh ig he r t h a n t h a t of t h e die le ct r ic in s t ru men t s u s edh e rein , a n d a c cordin gly t h e me a s u red t e mpe ra t u reran ge wa s higher. Sokolov et a l .74 observed the NCL inthe susceptibility spectra of the glassy state (T < Tg),having a frequency dependence of () -0.15 a n d aweak temperature dependence. These results are con-sistent wit h the behavior at lower temperatur e reportedherein, supporting our identificat ion of the dielectr ic lossin F ig u re 3 a s o r ig in a t in g f ro m t h e c a g e d dy n a mic sma nifested a s the NCL . At t empera tures a bove Tg, theNCL is m uch more sensitive to tempera ture, suggesting

t h a t i t s en s es t h e g la s s t ra n s i t ion . S u ch in t ere st in gbehavior can be interpreted using the coupling model.75

Conclusions

Amon g a mo rph ou s p oly mers , P I h a s bee n wide lystudied, both dielectrically a nd m echa nically, by ma nyworkers.42-58 The spectra show only the local segmentalmode (i.e. , the R-peak in the dielectric spectrum) andthe normal modes. No evidence of the presence of asecondary relaxa tion ha s been reported (note the trivia lmethy l group rota tion is dielectrically ina ctive). On theother ha nd, the w orks of J ohari a nd G oldstein16-18 a n dothers 20-38 indicate that a secondary relaxat ion of theJ ohari-G oldstein kind is universal, existing in a ll glass-

formers. This apparent conundrum is resolved from ourdielectric loss measurements with greater sensit ivityan d resolution th a n heretofore, leading t o the discoverytha t a wea k J G relaxat ion is indeed present in P I . Ourconclusion that this -rela xat ion is a genuine J G processis consistent with the fact that its act ivat ion enthalpyin the gla ssy sta te is quite close to the va lue for t he J Grelaxa tion in 1,4-polybuta diene (a polymer w ithout sidegroups, whereby the secondary relaxat ion necessarilyinvolves th e entire r epeat unit). Additiona l support forthe identification of the -peak in P I a s a J G process isthe correspondence betw een the most probable r elax-at ion t ime, , an d the primit ive relaxa t ion t ime of thecoupling model, 0. Conforma nce to eq 4 ha s been shownpreviously for J ohari-Goldstein relaxat ions in otherglass-formers.8,9,19,66

At t imes prior to , t h e P I s eg men t s re ma in ca g e d,a n d t h e dielect r ic s p e ct ra re flect t h e dy n a mics con -stra ined within the cage, which ha s the form of a NCL.Recent experiments using dielectric relaxat ion,7-12,72

scat tering,13,14 a n d t h e o p t ic a l K e rr e f f e c t 15 h a v e a l ls h ow n t h a t t h e N C L i s q u i t e g e ne ra l , h a v in g b ee nobserved in inorgan ic, polymeric, an d small moleculeglass-formers. We find herein that the intensity of theN C L i n P I a t t e m pe ra t u r es b el ow Tg h a s a w ea ktemperature dependence, in accord with eq 7 and thebehavior of other glass-formers and glassy ionic conduc-tors. Our identifica tion of the NCL in P I is corroboratedby recent dyna mic light scattering mea surements in the

gigahertz t o terahertz ra nge on the sa me polymer.74 Atthese higher frequencies, the light scattering da ta revealthat the NCL exists not only in the temperature rangeof the present experiments but also at temperatures upto ca. 20%above Tg.

Notes Added in Proof. After the present paper wasin the publicat ion stage, an extension of the standardMC T a ppea red [G otz e, W.; Sper l, M., cond-ma t/0401536;htt p://lan l.arXiv.org], w ith a nea rly logarit hmic decayof the correlat ion function obtained for temperaturesn e a r t h e M CT cri t ica l t e mpe ra t u re Tc. Although thisextension addresses the NCL phenomena near Tc, MCTstill does not account for the NCL at temperatures wellbelow Tc, a s observed herein for P I .

We recently becam e aw ar e of a review ar ticle by Ra ult[Rault , J. No n - Cr yst. S o l i d s 2000, 27 1, 177] reportinga secondary -process in PI. Although ref 62 herein wascited by Rault as the source for this information, theoriginal work wa s actua lly by Pechhold a nd B lasenbrey[Pechhold, W.; Blasenbrey, S. K a u tsch . G u mm i K u n stst.1972, 25, 195], who found a -relaxation in mechanicalmeasurements on semicrysta lline P I .

Acknowledgment. The research at NRL was sup-

ported by the Office of Nava l Research.

References and Notes

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