comparison of the rheological properties of concentrated

Comparison of the Rheological Properties of Concentrated Solutions of a Rodlike and aFlexible Chain PolyamideD. G. Baird and R. L. Ballman Citation: Journal of Rheology (1978-present) 23, 505 (1979); doi: 10.1122/1.549530 View online: http://dx.doi.org/10.1122/1.549530 View Table of Contents: http://scitation.aip.org/content/sor/journal/jor2/23/4?ver=pdfcov Published by the The Society of Rheology

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Comparison of the Rheological Properties of

Concentrated Solutions of a Rodlike and a Flexible

Chain Polyamide*

D. G. BAIRD, Department of Chemical Engineering andEngineering Mechanics, Virginia Polytechnic Institute and State

University, Blacksburg, Virginia 24061; and R. L. BALLMAN,Monsanto Textiles Company, Pensacola, Florida 32575

Synopsis

The steady state shear rheological properties of solutions of a rodlike polyamide,poly-p-phenyleneterephthalamide (PPT), in 100%sulfuric acid have been comparedwith those of solutions of a flexible chain polyamide, nylon 6,6, in the same solvent.For solutions of similar concentration (c) and molecular weight (M), it was found thatthe primary normal stress difference (Nd and the viscosity (1J), compared at the sameshear rate (1'), werean order of magnitude greater for solutions of PPT. It was believedthat this behavior could be accounted for through the formation of an enhanced entanglement network in the PPT solutions. Plots of the zero shear viscosity (1Jo) versuscMw , where M w is the weight average molecular weight, for both systems revealed that"bends" occurred in the data corresponding to a critical entanglement molecular weight(Me) of 1180 for PPT (this corresponds to 30 main chain atoms (a) and to 5260 (z =330) for nylon 6,6. More significantly, 1Jo was found to be proportional to (CMw )6.S forsolutions ofPPT and to (cMw )3.4for nylon 6,6 solutions. 1J versus l' curves were similarin shape for both systems and could be reduced to the same master curve with the onlydifference being that the relaxation times or shifting factors were considerably greaterfor the PPT solutions. This suggested that the process of destroying entanglementsmay be similar for both polymers.

The overlap parameter el1J], where 11J] is the intrinsic viscosity, provided a muchbetter correlation of 1Jo data from the two sets of solutions than did the segment contactparameter cMw . This suggested that the structural variable controlling the onset ofentanglements may be a parameter such as the radius of gyration. Because of the inability of rodlike molecules to coil around each other, further insight into the natureof entanglements is obtained.

'Presented at the 48th Meeting of The Society of Rheology, October 23-26,1977,Madison, Wisconsin.

© 1979 by The Society of Rheology, Inc. Published by John Wiley & Sons, Inc.Journal of Rheology, 23(4), 505-524 (1979) 0148-6055/79/0023-0505$01.00


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borrego

Typewritten Text

Copyright by the American Institute of Physics (AIP). BAIRD, DG; Ballman, RL. "comparison of the rheological properties of concentrated-solutions of a rodlike and a flexible chain polyamide," J. Rheol. 23, 505 (1979); http://dx.doi.org/10.1122/1.549530

506 BAIRD AND BALLMAN

INTRODUCTION

The rheological properties of concentrated solutions and melts offlexible chain polymers point clearly to a universal physical interactionbetween chain molecules which are referred to as chain entanglements. For example, the dependence of the zero shear viscosity (770)on the 3.4 power of molecular weight (M), the change in the form ofthe steady state compliance (,r;:) from MlcRT to l/c 2RT, where cisthe concentration in g/ml, R is the gas law constant, and T is thetemperature, and the appearance of a plateau in the relaxationmodulus all depend on the Bueche segment contact parameter (eM),which is a measure of the number of intermolecular contacts permolecule.1 The concept of a physical interaction rather than intermolecular attractive forces is well documented for nonpolar, noncrystallizable, flexible molecules.f

The exact nature of an entanglement, however, is not known. Oneview is that two chains are tightly kinked around each other bybending back on themselves in short-range contour. Another is thatcoupling involves looping of chains around each other in their longrange contour.v' Studies on the flow properties of relatively stiff andextended molecules such as cellulose derivatives.s deoxyribonucleicacid," and a helical polyamino acid? have shown these molecules toexhibit the effect of entanglement coupling even more prominentlythan do highly flexible polymers. These results have prompted Ferryand coworkers to conclude that the latter of the above two explanations is more plausible.f However, these molecules are only semirigidand may still coil or loop around each other to some degree. Aspointed out by Graessley in a recent review.s studies on the rheologicalproperties of systems of rodlike molecules are not well documented.Further studies on systems of truly rodlike molecules are needed.

In the last few years a series of rigid, rodlike synthetic polymers suchas poly-p-benzamide (PBA) and poly-p-phenyleneterephthalamide(PPT) have been synthesized and solution spun into fibers of ultrahigh strength.v-? These two polymers are believed to be highly rigidand extended for several reasons. First, Mark-Houwink exponents(0') as high as 1.7 have been reported.I-P Second, solutions of thesepolymers exhibit liquid crystalline behavior at concentrations inagreement with the predictions of Flory's theory, which is based onthe packing of rodlike molecules into solution,14,15 Finally, thestructure and physical properties of fibers and films produced fromthese polymers suggest that the molecules are rodlike.16,17


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POLYAMIDE SOLUTIONS 507

There have been only a few studies reported on the rheologicalproperties of PBA and PPT and related rigid polymers. 14,18,19 In onecase, some interesting differences between the rheological propertiesof rigid and flexible chain polymers were noted. Papkov and coworkers-! reported for isotropic solutions of PBA in N,N-dimethylacetamide that viscosity (17)-shear rate (i') curves plotted in reducedform as 17/170 versus 170i', where 170 is the zero shear viscosity, which isthe form predicted by Saito for rigid ellipsoids.i'' Furthermore, 170was observed to depend on M w 8.0 rather than M w 34, where M w is theweight average molecular weight. On the contrary, Berrylf observedfor solutions of PPT and several other polymers thought to be onlysemirigid that the steady state rheological properties in general didnot differ markedly from those of flexible molecules.

In this paper we studied the rheological properties of solutions ofPPT in 100% H2S0 4 measured in steady state shear. The concentration range was selected so that the solutions remained in the isotropic state. In order to compare the rheological properties of thisrodlike molecule with those of a flexible molecule we also report datafor solutions of nylon 6,6 in 100% H2S0 4. By selecting this systemwe are dealing with polyamides in both cases and the same complexsolvent. Hence any differences observed in the two systems shouldbe primarily the result of the polymer structure or its interaction withthe solvent. The specific objectives of this work are (1) to determinethe effect of chain stiffness on the rheological properties of polymersolutions; (2) to determine any rheological properties which arecharacteristic of rodlike molecules and which could be used to identifypolymers with the potential for forming anisotropic solutions; and(3) to provide insight into the nature of chain entanglements.

EXPERIMENTAL

Polymers

Nylon 6,6,

samples of various molecular weights were prepared by well-knownsolid state polymerization techniques. Molecular weight charac-


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teristics were determined by means of gel permeation chromatographyusing hexafluoroisopropanol (HFIP) as the solvent. Values of Mw

and the ratio Mw/Mn , where Mn is the number average molecularweight, are given in Table I.

PPT,

o 0 H H

"~I_~I(+C~-N~N-t-)

samples of various molecular weights were prepared as describedelsewhere21.22 by reacting terephthaloyl chloride with l,4-phenylenediamine in hexamethylphosphoramide. Mw of these polymerswas determined by light scattering from sulfuric acid solutions asdescribed in another paper.F Mw/Mn was assumed to be about 2.0since values of 1.8 were found for PBA, which is a similar polymersystem."! A summary of the Mw values is given in Table II.

Solutions

100% H2S0 4 was used as a solvent for both polymers. Althoughthis is a rather complex solvent because of its ability to dissociate intomany complex ions,23 it was selected because PPT is soluble only instrong acid solvents. PPT solutions of 0.004 g/ml to 0.16 g/ml wereprepared (see Table II). For concentrations (c) above 0.16 g/ml thesolutions became anisotropic for the highest-molecular-weight sample(Mw = 40,100) and were not considered here. Nylon 6,6 solutions inthe concentration range of 0.11-0,46 g/ml were prepared (see TableI). In order to observe any nonlinear rheological behavior for thenylon 6,6 solutions, the concentrations had to be considerably higherthan for the PPT solutions.

Rheological Properties

Shear stress (T) and primary normal stress (NI ) data were obtainedunder steady shear conditions at 24 and 600 C using the cone-and-plategeometry of the Rheometries mechanical spectrometer (RMS). Theplates were 5 em in diameter and the cone angle was 0.04 rad. Thetorque and normal force measurements were reduced to the shearstress and primary normal stress difference, respectively, followingwell-known methods.v'


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14:48:07

POLYAMIDE SOLUTIONS

RESULTS AND DISCUSSION

511

Comparison of Rheological PropertiesThe steady state shear rheological properties of nylon 6,6 and PPT

solutions having the same polymer concentration and similar M w arecompared in Figs. 1 and 2. The zero shear viscosity (1)0) values ofthePPT solutions are at least one order of magnitude higher than valuesof the nylon 6,6 solutions of similar c and Mw . The onset of nonNewtonian behavior occurs at a l' about one decade lower for the PPTsolutions. Likewise N 1 values measured at similar l' are about oneorder of magnitude higher for the PPT solutions.

10

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SHEAR RATE (SEC·')

Fig. 1. Comparison of viscosity-vs-shear rate curves for solutions of nylon 6,6 andPPT in 100% H2S0 4 both at a concentration of 0.117 g/ml and of similar molecularweights. For nylon 6,6: (e)"M'w = 14,500, (e)"M'w = 25,100, 1e-J"M'w = 35,200 (,)"M'w= 42,300. For PPT, (O)Mw = 12,800, (6)Mw = 20,200, (oiMw = 27,600, (<;l)Mw =32,000.


14:48:07


Goc!>cr ()-

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C, • •103

Cf •<!> • •10° 10'

SHEAR RATE (SEC-')

Fig. 2. The primary normal stress difference versus shear rate for solutions of nylon6,6 and PPT in 100% H2S04 both at a concentration of 0.11 g/ml and of similar molecular weights. The symbols are the same as in Fig. 1.

The manner in which chain stiffness contributes to the observedrheological properties of the PPT solutions is not clear. If we aredealing with dilute solutions, then the observed behavior could beaccounted for (e.g., compare the predictions of the rigid and flexibledumbbell models'"), We are, however, dealing with conditions inwhich considerable coil overlap occurs. According to Frisch andSimha,26 the product of c and the intrinsic viscosity [11] is a measureof the degree of coil overlap in a solution. The onset of coil overlapbegins near c[11] = 1 and free draining behavior starts near c[1J] = 10.2

For the nylon 6,6 solutions, 8 <C[l1] < 17,while for the PPTsolutions16 < c[1]] < 47. On the other hand, the number of intermolecularcontacts as measured by the Bueche parameter cMw lie in the samerange for both solutions, i.e., 1500 < cMw < 5000. Thus, in order toaccount for the differences in the rheological properties of the flexibleand rigid polymers it becomes necessary to understand the nature ofintermolecular contacts or "entanglements," what parameters controlthe onset of these entanglements, and whether there is any similarityin the nature of entanglements for rigid and flexible molecules.


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Evidence for Entanglements

The most characteristic behavior cited as evidence for the onset ofan entanglement network for concentrated polymer solutions is therather abrupt change in the dependence of 1)0 on (eMw ) to (eMw) 3.4.

In Fig. 3, In 1)0 is plotted against In eMw for both polymer solutions.Within each system the parameter eMw provides a reasonable superposition of data obtained from solutions of varying e and M w .

Bends occur in both sets of data, indicating the onset of an entanglement network. The critical value (eMw)c for PPT is about 1700while for nylon 6,6 it is about 6000. We note also that this value forPPT is independent of temperature as data measured at 60°C yield(eM)c = 1800. From these values of (eMw)c and using

(eMw)e = pMe, (1)

where Me is the critical molecular weight required for the formationof an entanglement network in undiluted polymer, it is estimated thatMe = 1180 (p = 1.44g/cm'') for PPT and 5260 for nylon 6,6. For PPTthis corresponds to 30 main chain atoms and to 326 for nylon 6,6,which is in the range of 300-700 main chain atoms observed for otherflexible polymer systems for the onset of an entanglement network.27

Furthermore, above (eMw)e rJo becomes proportional to (eMw)3.4 3 fornylon 6,6 solutions and to (eMw )6.8 for PPT solutions. Thus, it appears that in stiff chain systems the entanglement network is enhanced.

In the next sections we attempt to determine whether the effectsof an enhanced network are reflected in the.y dependence of 1), therelaxation times, and the fluid elasticity.

Viscosity-Shear Rate Behavior

The shape of rJ versus 'Y curves is similar for many flexible chainpolymers and when the curves are shifted parallel to the coordinateaxes, they are found to fall on a single master curve. 2 One interpretation of this behavior is that the process of breaking up intermolecular interactions in a constant shear field is similar for many polymersystems.

We next compare the rJ versus .y behavior of PPT and nylon 6,6solutions. Because the shape of the master curve depends on themolecular weight distribution, we have selected a theoretical mastercurve proposed by Graessleys'' for polymers with MwfMn = 2 with


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10~,- --"'T'"-----""'-----"""

w(f)

(5a..

10

101

100~ ~ ........~ ......

102

Fig. 3. Zero shear viscosity (710) versus the segment contact parameter (cMw ) forsolutions of nylon 6,6 (0) and PPT (0) in 100% H2S0 4 at 24°C. Data taken fromTables I and II and consist of different concentrations and molecular weights. (6)710measured at 60°C and shifted vertically to show that (cMw ) is independent of temperature.

which to compare our data. Although there are several questionsabout the origin and derivation of Graessley's theory, it has provensuccessful in several instances29,3o and for this reason willbe used here.Representative TJ versus l' data for nylon 6,6 solutions presented inFig. 4 are shown shifted for best fit with the master curve in Fig. 5.


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104r-------r------,------,.-----.....,

0-

10'~----.......-----""'------I.-----.....10" 100 101 102 103

SHEAR RATE (SEC-I)

Fig. 4. Shear rate dependence of viscosity as a function of molecular weight fornylon 6,6/100% H2S0 4 solutions. The data were obtained on samples all of the sameconcentration of 0.204 g/ml and at a temperature of 24°C. (O)lilw = 35,200, (6)lilw

= 42,300, (D-)lilw = 54,300, (9)lilw = 66,900, (-0) lilw = 73,200.

Likewise the TJ versus l' data for PPT solutions shown in Fig. 1 areshifted for best fit with the master curve and results are shown in Fig.6. For both systems excellent agreement with the Graessley mastercurve was observed not only for the representative data shown above,but for other solutions of differing c and Mw. The main differencewas that the shifting factor or the relaxation time (Tp) was considerably larger for the PPT solutions (see Tables I and 11). Apparently,the enhanced network of the PPT solutions does not affect the shearrate dependence of 1]. In fact, these results suggest there may be somesimilarity in the breakup of entanglements for rigid and flexiblemolecules.

Comparison of Experimental and Rouse Relaxation Times

Graessley and Segal29 reported for highly entangled solutions ofpolystyrene that experimental relaxation times (TO) obtained byshifting TJ versus 'Y data to a theoretical master curve were no longer


14:48:07


10',...----......----......----.,....-----,----,

10'

101-lL:---_.l.- --l. ...J..,. J.- --'10-3

Fig. 5. Data of Fig. 4 shifted for best fit with Graessley's theoretical master curvefor polymers with MwflJn = 2. Symbols are the same as in Fig. 4. Solid line representstheory.

simply related to the Rouse relaxation time T R but residual variationswere noted which depended on ¢M in a form shown below:

To/TR = ad(l + fJl¢M), (2)

where al and fJl are constants and ¢. is the volume fraction of polymer.Following the same procedure, values of TO were obtained for bothPPT and nylon 6,6 solutions and are summarized in Tables I and II.Values of To/TR are plotted versus ¢Mw in Fig. 7 for both systems,where ¢Mw is proportional to the entanglement density.? Althoughthere is considerable scatter in the data, there is no tendency for ToITRto depend on ¢Mw for PPT solutions. Only at large values of ¢Mwis there any indication that To/TR depends on ¢Mw for nylon 6,6 solutions.

The fact that TO is in general simply related to TR for both systemsis rather puzzling. We are dealing with solutions for which values ofcMw are considerably greater than those of (cMw)c. Furthermore,since rJo is so strongly dependent on cMw for PPT solutions, one mightexpect values of TO to no longer be simply related to TR. It may be thatalthough we are above (cMw)c, a residual dependence on cMw mayonly arise for polymers of very high molecular weight. Graessley andSegal were dealing with very-high-molecular-weight polystyrenes,some of which had values of M w as high as 3,370,000.


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10' ,.....------,r--------,-----...,-----....,

100

~<,

r- G-

10.1

10-'l L- L- ...l'-- .....l .......

IO~ 10~ 10.1 100 101

'6"1;./2

Fig. 6. Viscositydata of Fig. 1 for PPT solutions shifted for best fit with Graessley'smaster curve for polymers with MwlMn =2. Symbols are the same as in Fig. 1. Solidline 'represents theory.

Elastic Properties

Finally, the onset of an entanglement network should be reflectedin the elastic properties of the solutions. The steady state compliance(J~) is used as a measure of fluid elasticity, since it is related to therecoverable shear strain 'Yrand the shear stress (7) by the followingrelations":

'Y r = J~7. (3)

Values of JZ were obtained by plotting NdT/2 versus i'2 and using thefollowing relation:

JO = .!min d In(NtiT/2

) (4)e 2 i'~O d In i'2 .

Such plots consistently gave straight lines over a fairly large i' range,as illustrated in Fig. 8. The linearity of such plots is a consequenceof Hooke's law in shear.32

As suggested by dilute solution molecular theories, J~ is analyzedin reduced form for polydisperse systems as follows:


14:48:07


1.2

1.0

0.8

~ 0.6<,

1/' /::,. &0.4 0

c9 /::,. /::,.(fX>/::,.

0.2 OOCOo'-- --J. ....L. ...L- ......I.........

403010o 2.0¢Mw X 10- 4

Fig. 7. Viscosity time constant ratio versus the product of the volume fraction andMw: (0) PPT data from Table II; (.0.) nylon 6,6 data from Table I.

JeR = J~cRTM~ . (5)MwMzMz+ 1

For MwlMn = 2,MzMz+1/M~ =3. Values of J~ and JeR are given inTables I and II and plotted in Fig. 9 for both systems as a function ofcMw. For nylon 6,6 solutions, JeR rises from a value of about 0.2 tovalues of about 0.7-0.8. The dependence of JeR on cMwat low valuesof cMw presumably reflects the change from Zimm to Rouse-likebehavior. The values of 0.7-0.8 are somewhat higher than the valueof 0.4 predicted by the Rouse theory, but are definitely independentof cMw. The higher values of JeR can probably be accounted for bythe difficulties encountered in determining J~ and the polydispersityof the samples. On the other hand, for PPT JeRvaries from 0.4 to 1.3,but no dependence on cMw is observed for either low or high valuesof cMw. However, this is to be expected for low values of cMw sincedilute solution theories for rigid macromolecules predict JeR to be0.6.25

Again, although we are well above (cMw)c, and apparently an entanglement network exists, J~ is still of the form M/cRT rather than1/c2RT. The only explanation for this is that the change in behaviorof J~ occurs at values of cMwapproximately 3-4 times (cMw)c, 2 andwe are only approaching these values with our data.


14:48:07

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0=----l_.....J.._....L..._J.........J._-L._~_.L_.....I

o 2.0 4.0 6.0 80 100 12.0 14.0 160 18.0'(2

Fig. 8. The ratio of primary normal stress difference to the square of viscosity(Ndl'}2) versus 1'2 for solutions of PPT in 100% H2S0 4. Concentration; 0.117 g/ml;T, 24°C. (J~.)Mw = 32,000; (O)Mw = 20,700.

FURTHER DISCUSSION

The contact parameter (eM) has been found to produce a bettersuperposition of 110 data within the same flexible chain polymer systemthan does the overlap parameter, c[1J].2 This result has promptedGraessley to conclude that this was evidence for interactions whicharise from ropelike coupling of chains.2 However, if this is the case,then one wonders why eM does not reduce 110 values obtained fromboth flexible and rigid polymers to a common curve. Corrections fordifferences in the segmental friction factor (D, plus replacement ofM with z, the number of main chain atoms, provide a better reductionof data for flexible chain polymers. With these corrections taken intoaccount, Fox and Allen27 found for a number of flexible chain poly-


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520

10'

'" 10°-!

BAIRD AND BALLMAN

Fig. 9. Reduced compliance versus cMw. (LI.)PPT/100% H2S04, and (0) nylon6,6/100%H2S0 4• All data were obtained at 24°C and are presented in Tables I andII.

mers that the critical number of main chain atoms (zc) for the onsetof an entanglement network was between 300 and 700. Yet there isstill considerable scatter in the values of z.: The idea of using cM oreven cz still neglects the importance of polymer structure and configuration. It would seem that the onset of physical contacts betweenmolecules would certainly depend on the hydrodynamic volume sweptout by a given molecule and hence on the radius of gyration (82 ) 1/2

of a molecule. Furthermore, it would seem that the number ofphysical contacts would also be related to (82 ) 1/2 since the larger thehydrodynamic volume swept out by a molecule, the more chances forcollision with neighboring molecules. It would seem that a parameterwhich reflects the shape of a molecule could possibly account fordifferences in 710 data for flexible and rigid chain polymers.

With these thoughts in mind we used c[7J] as the reducing parameter, with results presented in Fig. 10, rather than cMw , which hadbeen used in Fig. 3. Values of [1]] for PPT in 100%H2S04 were determined by well-known methods and results are given elsewhere. 12

For nylon 6,6 solutions, values of [1]] were estimated using the following relation given by Burke and Orofino33:

[1]] = 11.5 X 1O-4M~·67 (6)

for solutions of nylon 6,6 in 96%H2S04. c[1]] provides a much better


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oo

OffiJ

104 r------,...------::r-------,

10~ -

o cPOo

00o

§Ooo

o 0

-

o

10° ~-----~-----~----~10°

c C'PFig. lo. Zero shear viscosity versus the overlap parameter (C[l1)) for solutions of

nylon 6,6 (0) and PPT (0) in 100%H2S04 at 24°C.

superposition of 110 data onto a single plot. Although c(11] does notaccount completely for differences in 110 data for the flexible and rigidchain polymers, it at least suggests the importance of selecting a parameter which reflects the configuration of polymer molecules.

Fox and Allen'? first recognized the importance of chain structureand configuration in accounting for differences in Me values for different polymer systems. Following Bueche's theory for short chains!they proposed an empirical law:

= No [(S5)AV Ze] (Zw)";-110 6 M v z, ~,

(7)


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(8)

where (S6}AV is the unperturbed mean square radius of gyration, Nois Avogadro's number, v is the specific volume, r is the segmentalfriction factor, and a = 3.4 for Zw ~ Z; or a = 1.0 for Zw ::s: Ze. Designating

and

x, = (stAV (~e),

Eq. (7) can be written as

no = ~ NoXc (;J at,

where a = 3.4 for X~ Xc and a = 1 for X~ Xc' Based on data for anumber of flexible chain polymers, they observed a value of Xc = 4.7X 10-15 ± 20% and proposed that Xc is approximately a universalconstant for flexible chain polymers. Berry and Fox34 further confirmed this value Xc with additional data obtained from other flexiblechain polymers.

Values of Xc were calculated for both PPT and nylon 6,6 to determine whether this concept could be extended to rigid macromolecules.Using M; = 5260 from the data in Fig. 1, Z' = 14, where Z' is thenumber of chain atoms per repeat unit, r = 1.14g/cm" and (S6)Av/M= 96 X 10-10 ern mop/2 g-1/2,35 we estimated Xc to be 5.70 X 10-15 fornylon 6,6. This is in reasonable agreement with the universal valueof Xc and is similar to the value reported for nylon 6 (Xc = 5.0 X10-15) .34

Calculating Xc for PPT is a more difficult task since values of(86) A viM are not defined for rod like molecules. In place of(S6) A viM we used the value of (S2} at Me estimated from data ofArpin and Strazielle-" for values of M w up to 40,100. From theirdata,

(S2}IMw = 1.93 X 1O-2M~514, (9)

with (S) IMw having dimensions of cm'' gig mole. With M; = 1180,(S2)/Me becomes 7.31 X 10-17 em? gig mol. The phenylene ringswere considered to be long bonds, as is generally accepted.r' and thuscounted as only one chain atom. With Z' = 6, Me = 1180, r = 1.44


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POL YAMIDE SOLUTIONS 523

g/cm'' and {S2)/Mc = 7.31 X 10-17, Xc was estimated to be 3.13 X10-15• Although this value is some 33% lower than the universalvalue, it is in agreement with the range of values reported for flexiblechain polymers.v-

CONCLUSIONS

The following conclusions can be drawn from this study:1. The effect of chain stiffness on the rheological properties of

concentrated polymer solutions is to promote the onset of intermolecular interactions or entanglements at much lower values of c, Mw,

and z than for flexible chain polymers.2. The dependence of 710 on {cMw )6.8 distinguishes solutions of PPT

from solutions of linear flexible chain polymers, and hence this maybe indicative of polymer systems with the potential to exhibit liquidcrystalline behavior.

3. The structural variable controlling the onset of entanglementeffects seems to be a parameter which reflects the shape and configuration of the molecule such as the radius of gyration.

4. "Entanglements," at least in the case of rigid molecules, may notrequire any notion of molecular looping or bending at all. Just theaction of one molecule encountering a neighboring molecule duringthe deformation process and thereby limiting the number of pathsavailable to this molecule may serve as an entanglement.

It would seem that further studies of the rodlike systems underdynamic or transient flow conditions (i.e. start of shear flow) or inextensional flow would be well worthwhile in that they would providefurther insight into the nature of entanglements for rodlike moleculesthat cannot be obtained under steady flow conditions.

We are grateful to the Monsanto Company for permission to publish this work andto Dr. J. H. Saunders for his support and interest. We also appreciate the assistanceof J. A. Burroughs and J. K. Smith in the preparation of samples and rheologicalcharacterization of the polymer solutions.

References

1. F. Bueche, J. Chern. Phys., 20,1959--1964 (1952).2. W. W. Graessley, Adv. Polymer s«, 16,158 (1974).3. W. W. Graessley, J. Chern. Phys., 43,2696 (1965).4. S. F. Edwards, Proc. Phys. Soc., 91,513 (1967).5. R. F. Landel, J. W. Berge, and J. D. Ferry, J. Colloid Sci., 12,400 (1957).


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6. F. E. Helders, J. D. Ferry, H. Markovitz, and L. J. Zapas, J. Phys. Chern., 60,1575 (1956).

7. N. W. Tschoegl and J. D. Ferry, J. Amer. Chern. Soc., 86,1474 (1964).8. J. D. Ferry, Viscoelastic Properties of Polymers, Wiley, New York, 1970.9. S. L. Kwolek, U.S. Pat. 3,671,542 (1972).

10. H. Blades, U.S. Pat. 3,767,756 (1972).11. J. R. Schafgen, V. S. Foldi, F. M. Loguillo, V. H. Good, L. W. Gulbrick, and F.

L. Killian, Paper presented at American Chemical Society Meeting, 1976; Polym.Prepr., 1769 (1976).

12. D. G. &iiird and J. K. Smith, J. Polymer Sci., 16,61 (1978).13. M. Arpin and C. Strazielle, Makromol. Chem., 177,581 (1976); C. R. Acad. Sci.

(Paris), C280, 1293 (1975).14. S. P. Papkov, V. G. Kulichikhin, V. S. Kalmykava, and A.Ya. Malkin, J. Polymer

Sci.: Polymer Phys. Ed., 12,1753 (1974).15. P. J. Flory, Proc. R. Soc., A234, 73 (1956).16. P. W. Morgan, Paper presented at American Chemical Society Meeting, 1976;

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cayne, Florida, 1976.19. D. G. Baird, in Liquid Crystalline Order in Polymers, edited by A. Blumstein,

Academic Press, New York, 1978; Chap. 7.20. N. Saito, J. Phys. Soc. Jpn., 6, 297 (1951); 1,554 (1952).21. T. I. Bair, P. W. Morgan, and F. L. Killian, Paper presented at American

Chemical Society Meeting, 1976; Polym. Prepr., 17,59 (1976).22. T. 1.Bair and P. W. Morgan, U.S. Patent 3,673,143, June 1972.23. R. A. Cox, J. Amer. Chem. Soc., 96,1059 (1974).24. A. S. Lodge, Elastic Liquids, Academic Press, London, 1964.25. R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids:

Vol. T, Fluid Mechanics, John Wiley, New York, 1977.26. H. L. Frisch and R. Simha, Rheology, edited by F. R. Eirich, Academic Press,

New York, 1956, Vol. I, Chap. 14.27. T. G. Fox and V. R. Allen, J, Chern. Phys., 41,344 (1964).28. W. W. Graessley, J. Chern. Phys., 47,1942 (1967).29. W. W. Graessley and L. Segal, Macromolecules, 2,49 (1969).30. D. R. Paul, J. E. St. Lawrence, and J. H. Troell, Polymer Eng. Sci., 10,270

(1970).31. R. A. Stratton and A. F. Butcher, J. Polymer Sci.: Part A·2, 9, 1703-1717

(1971).32. J. G. Brodynan, F. H. Gaskins, and W. Philippoff, Trans. Soc. Rheol" 1, 109

(1957).33. J. J. Burke and T. A. Orofino, J. Polymer Sci.: Part A.2, 7, 1 (1969).34. G. C. Berry and T. G. Fox, Adv. Polymer Sci., 6, 1 (1969).35. P. R. Saunders, J, Polym. Sci.: Part A, 3, 1221 (1965).

Received September 27,1978Accepted as revised January 11, 1979


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comparison of the rheological properties of concentrated

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