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6432 M acromol ecu l es 1996,28, 6432-6436

Viscoelastic Properties of Polymers. 4. ThermorheologicalComplexity of the Softening Dispersion in PolyisobutyleneD. J. Plazek* and I.-C. ChayDepar t ment of Materials Science an d Engineering, Universi ty of P i t t sburgh ,P i t t sburgh , P ennsy l van i a 15261K. L. Ngai and C. M. RolandNava l R esearch L abora tory , W ash i ng t on , D.C. 20375-5320Received May 17 , 1995; Re vised Manuscript Received June 29 , 1995@

ABSTRACT The viscoelastic behavior of a high molecular weight polyisobutylene has been revisited toinvestigate the unique high-frequency peak (or shoulder)seen in the loss tangent behavior in the glassto rubber softening dispersion. Creep measurements made in the temperature range -74 to f 2 7 "Cwere initially reduced to a curve,which, upon transformation from the time t o the frequency domains,yielded a loss tangent peak with no hint of any shoulder. The original creep compliance curves wererescrutinized independently, and slight variations in the derivatives of the curves revealed the elusivehigh-frequency loss peak. Additional dynamic measurements were made to connect the transformedcreep data t o some of the original Fitzgerald, Grandine, and Ferry data [ J A p p l . P h y s . 1953, 4 , 9111.The combined results cover over 9 decades of frequency. This extensive range revealed that themechanisms contributing t o the high-frequency peak have a different temperaturedependence than thatof those contributing to the main loss peak.

Historical BackgroundThe development of methods for studying the vis-coelastic behavior of polymers began during the 1940sand were pursued rather intensively into the 1950s.Polyisobutylene, a readily available saturated hydro-carbon with good stability, was the most studied poly-mer during thi s time. A problem in th e early days wascomparing da ta obtained by different laboratories. I twas unclear how results might vary from sample tosample, not due to experimental uncertainties, butbecause of a dependence on molecular weight and itsdistribution and on chain architecture. To establish a

benchmark for the comparison of results extending overa time and frequency range not available in any singlelaboratory, Robert Marvin of the US. ational Bureauof Standards obtained a 100-lb sample of a high molec-ular weight (M,= 1.56 x 109 regular productionpolyisobutylene (PIB) from the Esso Standard Oil Co.Tests were made to check the uniformity of the material,and in 1949 samples were sent to 27 laboratories inseveral countries. These labs where equipped to coverdifferent ranges of time and frequency, yielding resultswhich covered 15 decades of the time/frequency sca1e.lTimes are equivalent to the reciprocal circular frequencyw (radh), = 2nv , where v is the frequency in hertz(cycles/s).The majority of the measurements were made in anoscillatory mode, yielding complex dynamic moduli orcompliances in the frequency domain. There were alsotwo sets of stress relaxation measurements and onecreep study. The results from seven of the laboratorieswere equal within a 10% spread. These were combinedby Marvin to show for the first time how the componentsof the dynamic moduli and compliances of a highmolecular linear polymer varied from the glassy levelof response a t high frequencies to the approach tosteady-state behavior a t low frequency.At the time it was not completely known how thefeatures of the modulus and compliance curves pre-

@ Abstract published in Advance ACS Abstracts , August 15,1995.

sented in Marvin's summary paper varied with param-eters such as molecular weight and its distribution.However, earlier work on PIB by Brown and Tobolsky2established that the stress relaxation modulus in theglass to rubberlike dispersion was sensibly independentof molecular weight. For high molecular weight samplesa rubberlike plateau was observed as a function oflogarithmic time. In fu rther studies on PIB Andrewsand Tobolsky3 found the terminal relaxation time to beproportional to the 3 .3 power of molecular weight. Thesame molecular weight dependence for the viscosity hadpreviously been established by a number of ~t u d i e s , ~including those of Fox and Flory on PIB. Of course, the3 .3 or 3.4 exponential behavior has since been docu-mented to hold for virtually all linear polymers.

Viscoelastic mechanisms before and after the rubber-like plateau give rise to two peaks in the relaxation andretardation spectra, with tha t at the longer times havingthe same temperature and molecular weight depend-ences as those of the vi s~ os it y, ~, ~hile the short-timegroup of mechanisms clearly has a more intense tem-perature dependence for most linear polymers. Thisdifference in temperature dependences is minimal forPIB.7,8 For low molecular weight PIB's (e.g., 5000-50 000) Leaderman, Smith, and Jonesg found th at theshort-timeflow-temperature recoverable creep compli-ance showed only one apparent dispersion from theglassy level (at ca. Pa-l) up to a steady-state levelPa-l). Only a single peak in the retardationspectrum was observed. The entanglement networkwas not sufficiently developed to give rise t o a delayedgroup of mechanisms following a transient rubberyplateau. Leaderman, Smith , and WilliamslO discoveredthat the molecular weight distribution has an enormouseffect on the terminal viscoelastic effect. At the timePIB samples with narrow molecular weight distribu-tions could not be made, so the dependence of thesteady-state recoverable compliance J , on molecularweight could not be established.

Dynamic mechanical measurements made on thewidely distributed U.S. National Bureau of Standards0024-929719512228-6432$09.00100 1995 American Chemical Society

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Macromolecules, Vol.28, No. 19, 1995 Viscoelastic Properties of Polymers. 4 6433(iii)Notwithstanding the large stretch exponent fo rthe segmental relaxation function determined from lightand quasi-elastic neutron scattering, the dispersion inPIB s dynamic mechanical loss modulus or recoverablecreep compliance is quite b r ~ a d . l l J ~ J ~ , ~ ~n analysis ofthe behavior of PIB in the glass transition zone led t othe suggestion2" tha t other modes, transpiring overlonger length scales than that of the segmental motion,were contributing o the observed mechanical response.In fact, in a low molecular weight PIB new modes

situated in the time scale between the Rouse modes andthe locaI segmental motion were directly observed byphoton correlation spectroscopy in the retardation timespectrum obtained by the inverse Laplace transforma-tion of the time correlation f~ n c t i 0n . l~(iv) The glass-rubber transition zone of PIB issignificantly broader than that of most other polymers.This is reflected by the small value of 0.65 of it s"steepness index", defined as the maximum (absolute)value of d log(G(t)) vs d log(t) in the glass-rubbertransition region.21 For most polymers steepness indi-ces are larger, for example, 1.57 for polystyrene.(v) The terminal and the segmental relaxations ofmany high molecular weight polymers, including PS,when investigated in a common temperature range havedifferent temperature dependence^.^^-^^ However, thisdifference is not present in the behavior of PIB.8Moreover, in many polymers of low molecular weightthe steady-state compliance J, has been found t odecrease drastically as temperature decreases towardTg.13326The size of this effect is much reduced in PIB.8(vi) Polymers generally exhibit a single maximum intheir loss tangent versus either frequency o r tempera-t ~ r e , ~ ~owever, as first discovered by Fitzgerald, Gran-dine, and Ferryl1J2 FGF), he dynamic mechanical losstangent of PIB has an additional shoulder on the high-frequency (o r low-temperature) side of the peak. Thistwo-peak structure of ta n 6 is likely related t o the twopeaks found in the retardation spectrum obtained byphoton correlation spectroscopy mentioned in iii.Item vi is the focus of the present study. Additionalmechanical measurements at longer timesAower fre-quencies have been made by us on PIB, in order t oclarify the origin of the unique two-peak structure oftan 6 previously seen a t higher frequencies by FGF. Asreferred to in v, among amorphous polymers PIB showsthe least degree of departure from thermorheologicalsimplicity. In this paper we address the question ofwhether the (unusual) shape of the loss tangent versusfrequency curve from PIB is sensitive to temperature.Experimental Section

The P IB use d in t h i s s tudy w a s f rom the o r ig ina l 1940sbatch d ist r ibuted by Marvin f rom the U.S. Nationa l Bureauof Sta nda rds , N BS (now N IST). Th i s i s t he sa m e P IB a sstudied by Fi tzgera ld , Grandine , and Ferry . The sample wi ll ,henceforth, be referred to as NBS-PIB. The absence ofunsa tu ra t ion m a ke s t h e po lyme r qu i te r e s i s t a n t t o de g ra da -t ion . Creep measure ments of i t s te rmina l zone behaviorver i f ied tha t the mater ia l has not changed over the past 50ye a r s . In a ny c a se , ou r i n t e re s t i n t he p re sen t w ork is l imi tedto t he g l a ss t o rubber sof tening d ispersion .The c reep exper iments were carr ied out wi th a magnet icbear ing torsiona l c reep appara tus tha t has been descr ibede lsewhere .28 The dynamic mechanica l measurem ents wereobta ined wi th a Bohl in VO R rheometer . A parallel plategeometry was used for both exper iments .Results

In recent years the creep compliance behavior ofseveral PIB samples with differing molecular weights

2 1 , , , , , , , , 1

" 1

0 1 2 3 4 5 6 7 8 9Log oa rFigure 1. Reduced loss tangent , tan 6 ( G / G = J"/J'),as afunction of reduced frequency obtaine d by Ferry , Gra ndin e,and Fi tzgera ld . lG Reference tempe ra tu re 20 = 25 "C .PIB sample by Fritzgerald, Grandine, and Ferryshowedl1J2 a feature tha t remains unique even todayamong linear polymers. Their reduced dynamic datarevealed an asymmetrical loss tangent peak with aprominent shoulder at high reduced frequencies. Thisresult, being of central importance to our present work,is reproduced in Figure 1. Interestingly, this shoulderis not indicated in the recoverable creep compliancecurves obtained by Leaderman et U Z . ~ J " It should benoted that, along with the stress relaxation data ofAndrews and T~b ol sk y, ~he dynamic compliance resultsof Fitzgerald, Grandine, and Ferryl1J2 represent theearliest and best evidence fo r the time-temperaturereduction process, which yields a n extended frequencyor time scale curve.Recently, in the first two papers of this s e r i e ~ , ~ , ~ J ~einvestigated thoroughly the thermorheological proper-ties of both high molecular weight and low molecularweight PIB and compared them with tha t of polystyrene(PS), another well-studied amorphous polymer. Thesemeasurements were motivated by the contrasting ther-morheological properties of PIB and PS. A large dif-ference of viscoelastic responses of PIB and PS isexpected by the coupling theory7s based on the differ-ence in their capacities for intermolecular coupling. Theexperimental data obtained in refs 7 and 8 were inagreement with these expectations and have sincespurred on continued study of PIB.Introduction

Polyisobutylene exhibits several properties whichdistinguish it from other flexible-chain polymers. Thisis ironic given the many contributions, as describedabove, PIB has made to o u r general understanding ofpolymer viscoelasticity. The most conspicuousof PIB'speculiarities include the following:(i) The segmental relaxation dispersion of PIB isunusually narrow. When the relaxation function mea-sured by dynamic light scattering14 is fitted to theKohlrausch function15

The stretch exponent ,L? is found to be equal t o 0.55,whereas fo r most polymers /3 < 0.50. The large valueof /3 for PIB is also deduced from quasi-elastic neutronscattering experiments.16(ii) A comparison of the temperature dependence ofthe local segmental relaxation time z of polymers wasmade17J8by plott ing log t against TdT where Tgis thetemperature at which z attains a value of 100 s. Amongamorphous polymers PIB exhibits the weakest normal-ized temperature (TdT)ependence. A strong inversecorrelation between the (TdT) ependence and j317-20also indicates tha t PIB has a large p.

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6434 Plazek et al.

- -6.55 -7.0mU$ -7.55 -8.0Ym3 -8.5s -9.0

Macromolecules,Vol.28, No. 19, 1995

------

-5.5-6.0- -6.5

5 -7.0Fmi -7.5H -8 .0--m3 -8.53 -9.0

NBS PIB.................... ' 27.3"b, 11.1 -t 1

-9.5-10.0- 1 0 1 2 3 4 5 6 7Lo g (t /s)

Figure 2. Double-log arithmic plot of th e recoverable com pli-ance J,(t) (cm2/dyn) of the Nat iona l Bureau of S t a n d a r d spolyisobutylene samp le measured as a func t ion of t ime at si xt e mpe ra tu re s a s i nd ic a t ed .-5.5-6.0F

Ba" iBa "Q-"

-10.09.5 ~0 2 4 6 8 1 0 1 2 1 4Lo g (Va, i s )

Figure 3. D a ta f rom F igu re 2 reduced to a common curve a tt he r e fe re nc e t e mpe ra tu re To of -73 "C.has been determined. Compliances from the glassylevel out t o the terminal (steady-state) zone weremeasured. Only some of the results have been pub-l i ~ h e d . ~ ~urprisingly, when the results were trans-formed to the loss tangent, no high-frequency peak orshoulder was found. However, for at least a very highmolecular weight PIB (> 10 9 ts existence was certain.It had been observed not only by FGF but by one of us30at the U S . Naval Research Laboratory and much earlierby DeWitt, Zapas, and Markovitz a t the Mellon Insti-t ~ t e . ~ lll of these results were obtained by nonreso-nant forced-oscillation measurements. In a n attemptto elucidate this dilemma, creep measurements weremade on an available sample of the NBS-PIB. Therecoverable compliance J& ) esults obtained at sixtemperatures, from f 2 7 "C down to -74 "C, are shownin Figure 2. Simple temperature reduction of the logJ ,( t ) curves t o a reference temperature TO Tg -7 3"C was accomplished with only time-scale logUT shifts.Vertical shifts, in this temperature range, have beenshown to be unne ces~ ary. ~~he resulting reduced curveis presented in Figure 3. It appears t o be as successfulas any such curves presented in the literature. Thisreduced recoverable compliance curve was analyzed bymeans of an iterative interaction scheme6 o obtain theretardation spectrum L shown in Figure 4. Repeatedestimates of L are made until the input JAt) curve canbe calculated by numerical integration.

The iteration is stopped when the calculated curvefits within the scatter of the input data. Beyond thispoint no further information can be extracted from thereduced curve. With the optimizedL other viscoelasticfunctions were calculated. A logarithmic presentation

NBS-PIB-7

?-l0I11 /l 1 I 1 I I 1 I0 2 4 6 8 1 0 1 2 1 4Lo g ( r , s )Figure 4. Logari thmic presenta t ion of the re ta rda t ion spec-tru m obtained from the reduced curve of Figure 2 as a functionof the reduced re ta rda t ion t im e r,.

-6.01 1 . 1 I-6.5 --7.0 -c -7.5 -

6 -8.0 -6 -8.5 -3 -9.0i: -9.5 -

CN. -m:::::I l \ f 5

-11 o 0. 0-12 -10 -8 -6 -4 -2 0Lo g (w/s')Figure 5. Logarithmic plot of the re al, J', and imaginary , s',components of the complex dynamic compliance as a functionof the an gular f requency w = 2 n v , where v is the frequency inher tz (cps) . The l inear loss tangent curve is shown as afunction of log w a t -73 " C. These curves were ca lcula tedus ing the L show n in Figu re 4.of the storage J' and loss J" dynamic compliances isgiven in Figure 5 along with a l inear loss tangent curveas a function of the logarithmic reduced frequency w(rad s). The tan 6 peak, centered at log o = 3 .7 , showsno high-frequency shoulder. Chagrined at this result ,we reexamined the original unreduced recoverablecompliance curves. Derivatives of the log J A t ) vs log tm were obtained manually and from a cubic splinefunction fit of the data poipts of the curves that areprincipally in the softening dispersion (i.e. log J,(t)

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Macromolecules, VoE.28, No. 19, 1995 Viscoelastic Properties of Polymers. 4 6435maximum, occurring at the lower frequencies in Figure1,with the Rouse modes, which are known to dominatethe viscoelastic response in the glass-rubber transitionregion.z7 Rouse dynamics transpire over a length scaleshorter t han tha t associated with topological interac-tions (entanglements)but involve chain segments suf-ficiently long t o be "Gaussian" (i.e., have a statisticalen d- be nd separation described by a Gaussian distribu-tion function). It has been suggested that these chainsegments contain on the order of 50 or more backbonebonds.Identification of the higher frequency modes contrib-uting t o the loss tangent curves in Figure 1 s problem-atical. Segmental relaxation, associated with the glassto liquid transi tion, primarily involves correlated localmotion of only a few backbone bond^.^^,^^ From pub-lished data on local segmental motion in PIBI4 inanother high molecular weight sample and consideringthat all but the lowest temperature curve in Figure 2are a t temperatures above the glass transition temper-ature (= -7 3 "C) f PIB, we expect local segmentalrelaxation t o prevail at much higher frequencies thanthose associated with the satellite peak in Figure 7.Therefore, the mechanism giving rise t o this high-frequency shoulder is neither Rouse nor segmentalrelaxation. Evidently, a thi rd mode must be present .Such intermediate dynamics, involving on the orderof 10backbone bonds, have previously been designatedz0as "sub-Rouse modes" to convey th at the motion involvessegments, while larger than the couple of conformersinvolved in local segmental relaxation, containing fewerchain units than the shortest of the Gaussian submol-ecules described by the Rouse model. The actua lnumber of backbone bonds involved in sub-Rouse modesis not known a t this time. We assign the satellite peakin Figure 7 to these sub-Rouse dynamics. Of course,the length scales associated with the sub-Rouse modesare present in all polymers. The prominenceof the sub-Rouse modes in PIB is due t o the unusual circumstancethat the retardation times of its segmental motions havethe weakest normalized temperature dependence amongamorphous polymers (see ii in the Introduction). As aresult, the encroachment of the PIB local segmentalmotions toward the Rouse modes occurs to a lesserdegree than in other polymers.8 As a result, theseparation in time scale between the segmental motionand the Rouse modes (which is a measure of the widthof the softening dispersion) is considerably broader inPIB. The broad softening dispersion of PIB makes iteasier for the sub-Rouse modes, situated in time withinthe dispersion, t o be resolved as a shoulder in the losstangent. In the usual circumstance (i.e., for otheramorphous polymers), encroachment in time is moresevere, which causes the width of the softening disper-sion t o become narrower. This narrower width makesthe sub-Rousemodes more difficult to resolve in the losstangent spectrum.The anomalies of PIB listed in the Introduction, aswell as the thermorheological complexity describedherein, are experimental facts. Although clearly theremust exist motions intermediate in length scale t o theRouse and local segmental modes, a detailed charac-terization, as well as identification, in polymers otherthan PIB, is lacking. Reflecting on the fact tha t recentinvestigations of PIB have contributed so greatly tounderstanding polymer viscoelasticity, one must con-clude that after more than 50 years continued study ofthe viscoelastic behavior of amorphous polymers is stilla worthwhile endeavor.

0.8 I I I I I 10.7 -0.6 -.-3 0. 5 -5 0.4 -

2 0.30.2

15

V0. 1 -74.20.0

--1 0 1 2 3 4

Log ( WFigure 6. Derivatives obtained from the curves in Figure 2.

NBS-PIS

1.5roc+1 .o0.5

n n.- -5 -4 -3 -2 -1 0 1 2 3 4 5log (w / S ' )Figure 7. Loss tangent of NBS-PIB as a function of realfrequency at the four indicated temperatures. The highestfrequency data (open circles at T = -35.8 "C) are fromFitzgerald,et d . 1 5 The intermediate frequency results (openand filled triangles, respectively at T = -52.0 and -35.8 "C)are from dynamic mechanical spectroscopy, while the low-frequency data (filled, open, filled, and open squares respec-tively at T = -74.2, -66.9, -52.0, and -35.8 "C) representcreep measurements.nonresonant forced-oscillation measurements (Fitzger-ald-Ferry in~trument~~).he intervening gaps be-tween the creep data points and those of FGF wereobtained from forced-oscillation measurements madewith a Bohlin VOR dynamic mechanical rheometer(filled triangles at -52.0 "C and open triangles at -35"C).

The softening dispersion determined over a realfrequency range of about 9 decades and over a widetemperature range (Figure 7) clearly confirms theexistence of the two-peak structure. Moreover, the twomechanisms responsible fo r the main peak and theshoulder of ta n 6 do not have the same temperatureshift factors. The mechanisms contributing to the mainpeak have a weaker temperature dependence than theother mechanisms tha t give rise t o the shoulder. Thehigh-temperature peak o r shoulder moves to lowerfrequencies faster t han the main peak with decreasingtemperatures. It is obvious that the high-frequency losstangent peak was reduced out of existence, by theapparently successful superposition process.Conclusion

From the data in Figure 7 we conclude that at leasttwo groups of viscoelastic mechanisms, with differenttemperature dependences, contribute to the softeningdispersion of the NBS-PIB. We can identify the primary

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6436 Plazek et al. Macromolecules, Vol.28, No. 19, 1995It has been made clear that superposition of vis-coelastic data to an apparently successful reduced curveis not sufficient proof of thermorheological simplebehavior. Data extending over 8-10 decades of timeand/or frequency appears to be necessary for a reason-able proof. The narrower frequency range of 2%decades enabled Ferry, Grandine, and Fitzgerald12 toachieve apparently successful reduction of their data onthe NBS-PIB.Acknowledgment. The work a t NRL was supportedby the Office of Naval Research. K.L.N. is supportedin part by ONR Contract N000149520203.

References and Notes(1) Marvin, R. S. In Proceedings of the 2nd InternationalCongress on Rheology; Har riso n, V. G. W., Ed.; Oxford, U.K.,July 1953; Butterw orths: London, 1954.(2) Brown, G. M.; Tobolsky, A. V. J . Polym. Sci. 1951, , 165.(3) Andrews, R. D. ; Tobolsky, A. V. J . Polym. Sci. 1951, , 221.(4) Fox, T. G.; Loshaek, L. J . Appl . Phys . 1955,26, 080.(5) Plazek, D. J. J . Phys. Chem. 1965, 9, 480.(6) Orbon, S. J. ; Plazek, D. J . J . Polym. Sci . , Polym. Phys . Ed .1979, 7, 871.(7) Plazek, D. J. ; Zheng, X. D.; Ngai, K. L. Macromolecules 1992,25, 920.( 8 ) Ngai, K. L.; Plazek, D. J.; Bero, C. A. Macromolecules 1993,26, 065.(9) Leaderman, H.; Smith, R. G. ; Jones, R. W. J . Polym. Sci.1954, 4, 7.(10) Leaderman, H.; Smith, R. G.; Williams, L. C. J . Polym. Sci .1959, 6, 33 .

(11) Fitzgerald, E. R. ; Grandine, L. D. , Jr. ; Ferry, J. D. J . A ppl .Phys . 1953,24, 50 .(12) Ferry, J. D. ; Grandine, L. D., Jr.; Fitzgerald, E. R. J . A ppl .Phys . 1953,24,11 .(13) The third paper in this series was published as: Plazek, D.J. ;Bero, C. A.; Neum eister, S.; Floudas, G.; Fytas, G.; Ngai,K. L. Colloid Polym. Sci. 1994, 72, 430.

(14) Rizos, A. K.; Jian , T.; Ngai, K. L. Macromolecules, in press.(15) Kohlrausch, R. Pogg. Ann . Phys. (3) 1847,12,393;ogg. Ann .Phys. (4) 1854, , 56, 179.(16) Ngai, K. L.; Colmenero, J. ;Alegria, A .; Arbe, A. Macromol-ecules 1992, 5, 727.(17) Plazek, D. J. ; Ngai, K. L. Macromolecules 1991, 4, 1222.McGrath, K.; gai, K. L.; Roland, C. M. Macromolecules 1995,28, 825.(18) Bohmer, R.; Ngai, K. L.; Angell, C. A.; Plazek, D. J. J . C h e m .Phys. 1993,99, 201.(19 ) Ca tsiff, E.; Tobolsky, A. V. J . Colloid Sci. 1955, 0, 375.(20) Santangelo, P. G.; Ngai, K. L.; Roland, C. M. Macromolecules(21 ) Aklonis, J . J. ;Rele, V. B. J . Polym. Sci. C 1974, 6, 27 .(22) Plazek, D. J . J . P hys . Chem. 1965, 9, 480.(23) Plazek, D. J. Polym. J . 1980, 2, 3.(24) Plazek, D. J.; Plazek, D. L. Macromolecules 1983, 6, 469.(25) Ngai, K. L.; Plazek, D. J. J . Polym. Sci. , Polym. Phys. Ed .

1993,26, 682.

1986.24. 19 .(26) Plazek, D. J.; ORourke, M. V. J . Polym. Sci. , Polym. Phys.Ed. 1971, , 09 .(27) Ferry, J. D. Viscoelastic Properties of Polymers; Joh n Wiley& Sons: New York, 1980.(28) Plazek, D. J. I n Methods of Experimental Physics; Fava, R.A., Ed.; Academic Press : New York, 1979; Vol. 16C, Cha pter11.(29) Plazek, D. J. ; Chay , I.-C., unpublished re sults.(30) Roland, C. M., unpublished results .(31)DeWitt, T. W.; Zapas, L. J. ; Markovitz, H ., unpublished(32) Plazek, D. J. ;Chelko, A. J. , J r . Polymer 1977, 8, 5.(33) Plazek, D. J. ; Raghupathi, N.; Orbon, S. J. J . Rheol. 1979,23, 77 .(34 ) Fitzgerald, E. Phys. Rev. 1957, 108, 690. F itzgerald , E.;Ferry, J . D. J . Colloid Sci. 1953, , .(35) Adolf, D. B.; Ediger, M. D. Macromolecules 1992, 5, 074.(36) Bahar, I.; Erm an, B.; Krem er, F.; Fischer, E. W. Macromol-

result s an d personal communications.

ecules 1992,25, 16 .MA950676S