Diluent effects on viscoelastic behavior

570

Journal of Non-Crystalline Solids 131-133 (1991) 570-578 North-Holland

Diluent effects on viscoelastic behavior Donald J. Plazek, Chang Seoul

~

and Craig A. Bero

Department of Materials Science and Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA

The effects of dilution upon the viscoelastic behavior of polymers are discussed and the related results of two investigations on solvent effects are presented. The creep behavior of a 40% polyvinylacetate (PVAc) solution where the solvent, sucrose benzoate, has a higher glass temperature than the PVAc is presented. Since the glass temperature, Tg, of the solution is between that of the polymer and the solvent, it is higher than that of the neat polymer. In the second study, the viscosity and the recoverable compliance of six molecular-weight bimodal blends of a high (3.8 × 106 ) and a low (1.03 × 104) molecular-weight polystyrene were determined. The low molecular-weight component played the role of a Flory theta solvent at long times at all temperatures, enabling the determination of the steady-state recoverable compliance, Je°, of the high-molecular components as a function of concentration under theta conditions. Retardation spectra were determined from the reduced shear compliance curves for all the solutions and the neat components.

1. Introduction On dilution of a high molecular-weight polymer, several different kinds of changes occur [ 1 ] . The glass temperature, Tg, of a polymer solution is most often substantially lower than that of the undiluted polymer [2]. The Tg of the solution is normally depressed because the Tg of the solvent is usually lower than that of the polymer. The process of plasticization, which is simply Tg depression, depends on this fact. Being farther above its Tg, the solvent brings its larger fractional free volume to the solution. A second effect of dilution is the shortening of the viscoelastic rubbery plateau [3,4]. With fewer polymer molecules per unit volume, the average distance between centers of gravity is greater and the concentration of polymer chain entanglements is diminished, resulting in a shorter time for the disentanglement process, Since the stress per molecule increases with dilution, a third effect is a corresponding greater orientation of the molecules and a larger contribution to the deformation which increases the mag-

nitude of the time-dependent recoverable compliance. Instead of a Tg depression, an elevation can be incurred with a solvent that has a higher T~ than the polymer. The results for a solution where the solvent has the higher Tg are reported here. In addition to the three effects caused by dilution mentioned above, the effect of specific solvents on the shape of the viscoelastic spectrum is of value and interest. The length of the rubbery plateau is measured by the separation of the softening and the terminal peaks of the retardation spectrum L(ln ~-) [5,6] (see fig. 1). The changes in shape of -~

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Log T

1 Present Address: Department of Textile Engineering, C h o n b u k National University, Chonju, 560-756, Korea.

Fig. 1. Schematic representation of the retardation spectrum, L, of a high molecular-weight linear amorphous polymer with a narrow molecular-weight distribution, displayed as it would appear at Tg. Separation of peaks indicates that M = 400M¢.

0022-3093/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)

571

D.J. Plazek et aL / Diluent effects on viscoelastic behavior

these two main contributing peaks and the relative levels of the Andrade lines * have never been systematically studied. Figure 1 depicts the retardation spectrum of a polystyrene [7] with a narrow molecular-weight distribution and a weight average molecular weight of 3.8 × 10 6. It represents all the common features seen in viscoelastic behavior of linear polymers with a unimodal molecular-weight distribution. Moderately

low

molecular-weight

polymers

have been shown to be Flory 'theta' solvents for t h e i r h i g h e r m o l e c u l a r c o u n t e r p a r t s a t all t e m p e r a -

tures [8]. This is a valuable property since the steady-state recoverable compliance, Jc°, values cannot usually be measured isothermally over a large concentration range [4]. Because of this unavoidable temperature variation, the concentration dependence of Je ° is somewhat ambiguous, It should be noted the oligomers to be used as solvents are themselves viscoelastic, as are the higher molecular-weight components of such solutions. Indeed, in the neighborhood of their Tg all solvents are also viscoelastic and can be seen to additively contribute to the recoverable creep deformation of polymer solutions [3,4]. Usually the terminal retardation time of the solvent (whether it is a plasticizer or an oligomer) is much smaller than most of times of the solute polymer molecules. A typical case is exemplified by solutions of a high-molecular polystyrene ( M w = 8.6 x 105) in tricresyl phosphate where the Tg of T C P is about 1 6 5 ° C below that of the PS. In fig. 2 the retardation spectra of the polymer and the solvent are compared with that of a 40% solution of polymer. Their positions along the reduced timescale are relatively correct but unrealistic reduced times result from the T~ of the undiluted polymer being used as the reference temperature, T0 = 100 o C. Data obtained on the TCP at - 6 3 ° C only had to be shifted to - 5 0 ° C to be compared with the short-time response of the 40% solution, The terminal zone response of the solution was measured at 5 0 ° C and was shifted to 1 0 0 ° C where it overlaps with the short-time response of • The Andrade lines with slopes of 3a are seen at short times approaching glass behavior and in the entanglement plateau

region.

_

Polystyrene-TCP

_ ~ j/ ~-~o I / / k ~ [ .~rcp ~ -,z~,/ -i ~ , -as -20 -is -~b

4o%Ps

Log ~'/ar

\ /

/ r ~ ,ooo/opS

I

-~

~

To: t o o ° c , ~ to

Fig. 2. Double-logarithmic plot of the retardation spectra of tricresyl phosphate TCP a high molecular-weight (860000) polystyrene (PS), and a 40% solution of the PS in TCP shown as a function of the retardation time at a reference temperature T°°fl00°C"

the undiluted polymer. Obviously the temperature dependence equations used in the extrapolations do not hold over the 270 ° C temperature range in which the data were obtained, and the assumptions for temperature reduction fail when predictions extend to times that are shorter than the period of a molecular group vibration. However the overlap regions can be considered to be accurate on a relative basis. It is clear that the viscoelastic mechanisms of the 40% solution with reduced retardation times between 10 -as to 10 - i s s involve solvent molecule orientations. The Andrade mechanisms of the polymer show up in the solution at times which are 10 2 longer between 10 - 9 and 10-13 s. The relative rates at 100 ° C for the mechanisms of the bulk polymer and motions of the same molecular segments about 1 4 0 ° C above the T_ of the solution are different by a factor of 101~. This appears to be reasonable. Near the maximum of the first or short-time peak of L(ln ~') the solution and bulk polymer curves show similar shapes. The solution spectrum is broader below log ' r / a T of - 8 . It is possible that mechanisms found between - 8 and -14 involve solvent molecules closely associated with short polymer chain segments. In the case of T C P solutions of polystyrene where the solvent Tg of - 6 8 ° C is so much lower than that of the polymer (100°C), beyond reducing the number of polymer chains per unit volume, the effect of the solvent on the spectrum shape at log .r/ar greater than - 10 appears minimal. Only at shorter times does the TCP appear to broaden the spectrum mainly by

572

D.J. Plazek et al. / Diluent effects on viscoelastic behavior

virtue of the presence of its contribution of its own orientation.

2. Experimental

2.2. Instrumentation Creep and creep-recovery measurements were carried out in a frictionless apparatus which utilizes a magnetic bearing. Its design and operation have been described earlier [10,11].

2.1. Materials The 40 wt% solution of polyvinylacetate (Scientific Polymer Products, Inc. 024A) in sucrose benzoate (Velsicol Chemical Corp.) was mixed by dissolving the components in redistilled reagent grade benzene so that a uniform dispersion was assured in several days. The approximately 3% solution was then freeze-dried. The polystyrene blends were prepared in the same manner using narrow molecular-weight distribution samples from Toyo Soda Manufacturing Co., Japan: F-1 ( M w = 1.03 x 104; M w / M . = 1.02) and F-380 ( M w = 3.8 x 106; M w / M ~ = 1.05). Solutions with 2.0, 5.0, 10, 20, 50, and 70% of F-380 in F-1 were made and studied. Differential scanning calorimeter (DSC) measurements to determine fictive temperatures, Tf, have been made by Zane Frund Jr. with a Perkin-Elmer DSC model 2 on the F-1 and F-380 polystyrene along with the 5, 20, and 50% blends. The specimens were all cooled at five different rates from 1 2 0 ° C down to 80 ° C and immediately heated at 20 ° C / m i n . This kind of thermal history yields fictive temperatures from the heating curves which have been identified as Tf.g [9] because it approximates the glass temperature Tg. For Tg to be a material characterizing parameter which is a function of the rate of cooling only, it must be determined from cooling experiments where Tg is the hallmark of the departure from equilibrium, because of sluggish molecular rearrangements. Heat lags during cooling in commercial instruments do not appear to be correctable because of the super-cooling of melting point standards. The Tf.g obtained following cooling at one degree per minute are: F-l, 93.4°C; 5% F-380, 93.8°C; 20% F-380, 95.2°C; 50% F-380, 99.4°C; 100% F-380, 104.6 ° C. Physical aging effects were corrected in the manner described in ref. [9]. The Te,g decreased an average of 2.6 o C with each ten-fold decrease in rate of cooling,

3. Results and discussion 3.1. Sucrose benzoate The Tg for sucrose benzoate obtained dilatometrically at a cooling rate of 0 . 5 ° C / m i n is 59.5 o C. Its viscosities between 57 and 95 ° C can be calculated from the Vogel [12], Fulcher [13], T a m m a n n and Hesse [14] equation log ~ = log A + C / 2 . 3 0 3 ( T - T~), (1) where log A = - 6.023, C = 2226 and T~ = 5 o C. The recoverable compliance curves, Jr(t), ohtained at six different temperatures between 55.8°C and 71.2°C are presented in fig. 3 as a double-logarithmic plot. The lower-temperature curves indicate an exceptionally high glassy compliance, Jg, of 3.9 x 10-10 cm2/dyn. The steadystate recoverable compliance, J eo , at 71.2°C was 2.0 x 10 -9 cm2/dyn, which is slightly more than five times greater than the Jg. However with decreasing temperatures Je ° decreased until at 55.8 ° C it was about 1.3 x 10 -9 c m / d y n , where it was only 3.3 times Jg. The log Jr(t) curves were

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.

.

Sucrose Benzoole

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, 0

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Fig. 3. Logarithm of the

~

Lo0 t recoverable

I

J

3

,

5

shear creep compliance,

Jr(t) (cm2/dyn), of sucrose benzoate measured at six temperatures as indicated as a function of the logarithmic time.

573

D.J. P l a z e k et al. / D i l u e n t effects on viscoelastic b e h a v i o r

-88/

. Sucrose

.

.

.

.

.

4

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'

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~ 878-

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Benzo

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0

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2

s

4

5

561

~__

Log f/a t

©

Fig. 4 . The reduced recoverable shear compliance, Jr,p(t), shown logarithmically as a function of the logarithm of the reduced time of recovery, t / a T . a T is the temperature shift factor of the timescale.

3 ,/d

_~© -f ~ ~

~

4 0 % PVAc

IN

SUCROSE BENZOATE

LOG t reduced to a reference temperature TO of 58.5 o C to obtain Jr.p(/)

:

[Jr(t)

_

j g ] [ ( J e ° ( T o ) _ Jg)

/(Je°(T)-Jg)]

+Jg.

(2)

Jg is insensitive to temperature and can be assumed to be constant over the small temperature range covered. Log J r , p ( t ) curves were then shifted along the timescale so as to superimpose onto the compliance curve measured at T0. The resultant reduced curve is presented in fig. 4. The temperature-dependent timescale shift factors, a 1, were fitted to log a T = - - 1 9 . 6 6 4 + -

Fig. 5. Logarithmic plot of the recoverable shear creep compliance of a 40 wt% solution of polyvinylacetate in sucrose benzoate. The temperatures of measurement for the six curves range from 53.3 up to 117.8°C as indicated.

1052

(3) T-5" The T~ is 5 ° C which is the same as for the viscosity temperature dependence in fig. 1, but C = 2423 here, which indicates that the temperature dependence of the recoverable compliance is slightly greater than that of the viscosity. However, viscosity values were not adjusted with the magnitude reduction as the Jr(t) were with eq. 2. Such a treatment increases the slope of the viscos-

from a glassy level of 2.3 x 10 - t ° up to 1 0 - 4 cmZ/dyn. A nascent entanglement rubbery plateau is seen in the 71.2°C and the 87.8°C curves. Only timescale shifts were necessary to reduce these curves to single curves at To = 56.1°C. The results of the successful reduction are shown in fig. 6. It can be seen that twelve orders of magnitude of time is required for the recoverable compliance curve to climb from the glassy level to the terminal Je° level. The Tg ( 0 . 5 ° C / m i n cooling) was estimated to be 4 9 ° C which is almost midway between that for the sucrose benzoate ( 6 0 ° C ) a n d undiluted PVAc (37°C).

4

ity curve to within 2% of that of eq. 3.

40% PVAc IN ,UCROSEBENZOATE ,_--¢~-6~ , , ~ . R T

3.2. 40 % Polyoinylacetate in sucrose benzoate

~-8

_ ~ ' ~ -

.~-~ °-

=56.1°C The recoverable compliance, Jr(t), curves of a 40 wt% solution of PVAc in sucrose benzoate are shown logarithmically in fig. 5. Six log J r ( t ) c u r v e s in the temperature range 5 3 ° C to 1 1 8 ° C cover nearly a million fold variation in magnitude rising

-1¢

~

0

I

2

I

4 LOG t/a.,

,

6

8

Fig. 6. Data from fig. 5 reduced to a reference temperature of

56.1° c.

574

D.J. Plazek et al. / Diluent effects on viscoelastic behavior

3.3. Comparison o f retardation spectra

-

Retardation spectra were determined from the r e d u c e d log J r ( t ) c u r v e s from figs. 4 and 6. These are shown in fig. 7 reduced to 60 °C where the vari°us L(ln ~') f°r the sucr°se benz°ate' SB and the 40% PVAc-SB solution are compared with a previously determined spectrum for an undiluted PVAc [16]. Only that portion of the latter spectrum which is insensitive to the molecular-weight distribution is reproduced here. By contrast with the PS-TCP example shown in fig. 2 where the spectrum for the solvent, TCP, w a s found at the shortest times, here because of its relatively high Tv at corresponding L(ln ~') levels, the spectrum of the sucrose benzoate is found at the longest times and the contribution of the SB to the deformation is largely hidden by the polymer molecules contributions. Since the response of the SB is believed to be accelerated by the presence of the lower T~ polymer, these results do not yield sufficient information to allow a quantitative separation of contributions to the deformation. The relative portions of the spectra show that the polymer solution is more turgid at a given temperature than the undiluted polymer. The time-dependent recoverable deformation of the solution

' -5 PVAc-SucroseBenzoole -6

' ~' ~

~

/440% PVAc

' . POLYSTYRENE F-1. ~111.6°C

~ ~

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M=lO3xlO '

6

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2

1

3

4

5

LOG t Fig. 8. Double logarithmic plot of Jr(t) vs. t of a low molecular-weight polystyrene, F-l, ( M = 1.03 × 104) determined at six temperatures between 91.0 and 111.6 ° C.

just above the glassy level can be deduced to be an order of magnitude slower than that of the PVAc. The temperature dependence for the recoverable deformation and the viscous flow of this solution of PVAc in SB have been found to differ in a manner similar to that found for polystyrene, polyvinylacetate and polypropylene (PP). The recoverable compliance temperature shift factors referred to T0=56.1°C were fitted by log a t = - 1 2 . 4 4 3 + 511.4/(T-15) and the viscosities were fitted to

(4)

log ~/= -2.125 + 886.2/(T+ 10).

(5)

Since T g = 4 9 ° C (and A = Tg- T~, the A(ar) is 34°C and A ( n ) = 59°C. For polystyrene [16] the corresponding values are 29 and 60 o C; for PVAc [15], 47 and 57°C and for PP [17], 30.5 and 50"5°C"

-7

3.4. Polystyrene a n d blends -8 d

~-9 -10 -II

%= 60°C

Log ~'/a,

Fig. 7. Logarithmic presentation of the retardation spectra of sucrose benzoate, a polyvinylacetate and 40% solutionof polyvinylacetate in sucrose benzoate at To = 60 o C.

Recoverable creep compliance curves for the narrow distribution low molecular-weight polystyrene F-1 were determined at six temperature between 91 and 111.6°C. They are presented in fig. 8 and clearly show the strong decrease in Je° with decreasing temperature which has been observed repeatedly for low molecular-weight polystyrene [16,18,19] and more recently for a low molecular-weight polymethylphenylsiloxane [20]. In a number of cases it is clear that the underlying retardation spectrum is diminishing at long times

575

D.J. Plazek et al. / Diluent effects on viscoelastic behavior 111.6 POLYSTYRENE

F 1

~

~.

~

x ~

o~)

I

~ ~~-/ s-- -~' j _g ~_- ~~ 7 1046

~

-I

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in

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934

~-so-

i

I

"-. "-....

~97o

~'~--oe~/91°~c

to

I F-380

- " ' ~

t/a~

LOG

-'-

Fig. 9. Jr(t) curves from fig. 8 plotted against the reduced timescale, logarithmically. Shift factors, a T, obtained from the

-6

short-time asymptotic portions of the curves.

I

-2.5

I

-2.0

I

I

I

-I.5 -I.0 -0.5

I

0.0

Log C

with decreasing temperature and those associated viscoelastic mechanisms are lost and cannot contribute to the deformation near and below Tg. In these cases magnitude-reduction, as was described above for the sucrose benzoate, is not applicable. The result of a reduction attempts by superposing the short-time portions of the curves which appear to follow a high-temperature asymptote is shown in fig. 9. A twenty to thirty-fold decrease in are° over the 20 ° C temperature range is indicated as an apparent consequence of the loss of polymeric modes of motion. This presumption is based on the observation that at and below Tg the retardation spectrum that remains is quite similar to that found for non-polymeric organic glass-formers [4,7,21]. The recoverable compliance curves of the polystyrene blends and the F-380 sample, which were obtained, all reduced successfully. Each curve is reduced to its respective Tg and they are shown in

-2

i

i

F-580 r~t~,

i

in F-I

-4

:

~-8

f

/

i

i

i

i

- - - z~ /1" / ........... ,o ~z -. zo ....... 50 ................. ::.:.-:........ ,o

............... o "~ "

-10 . ~ 7 0

,

2

,

4

,

6

,

8

Log

,

t/o r

I0

,

12

,

14

16

Fig. 10. Double logarithmic plot of J r ( t ) - J ~ vs. t / a r for the polystyrenes F-I and F-380 and five blends, are indicated, Each curve is reduced to its own Tg (see table 1).

Fig. 11. Logarithmic plot of the steady-state recoverable compliance, Je°, for the polystyrene F-380 and six blends with F-1 as a function of the logarithm of the concentration, C (g/cm3), of F-380.

fig. 10 with a log Jr(t) for F-1 (0% F-380) which corresponds to the shape found at 99 ° C. This is the temperature at which the terminal mechanisms of F-1 contribute most to the short-time portion of curve for the 2% F-380 blend. All of the curves have been shifted to their positions at T~ and their Jg contributions have been subtracted to show the correspondence of the shortest time portion of the time-dependent recovery. The weight average molecular weight of the samples and blends are presented in table 1 along with the Jg and the Tg, which were calculated using the equation of A1tares [22], 1.02 x 10 s Tg = 98.0 M. ' which was determined dilatometrically with a cooling rate of 1 o C / h . Since the pure F - I is not thermorheologically simple, it must be fortuitous that the data on the 2% blend of F-380 in F - I appear to reduce successfully. More closely spaced measurements possibly over a wider timescale or frequency range should reveal changes of shape in the Jr(t) curves with temperature for blends with a high concentration of a low molecular-weight c o m p o n e n t . The values obtained for the steady-state recoverable compliance of six blends are presented in fig. 11 along with value for the F-380. All of the values

were

obtained

in

the

temperature

range

576

D . J . P l a z e k et al. / D i l u e n t e f f e c t s o n v i s c o e l a s t i c b e h a v i o r

~

~ ~

~ ~ ~ :~ ~

U

o, E

2 "~ ~

~ ~ d d

~ ~ ~ ,~ ~ ,-4

_

b e t w e e n 162 a n d 2 0 2 ° C . W i t h the e x c e p t i o n of the F-1 s a m p l e no v a r i a t i o n of Je ° with t e m p e r a ture was observed. A t c o n c e n t r a t i o n s b e t w e e n 0.0492 g / c m 3 (5% F-380) a n d 0.984 g / c m 3 (100% F-380), the slope d log J ° / d log C is 2.13. Since the m o l e c u l a r weight p e r e n t a n g l e d unit M e (ass u m i n g two units p e r e n t a n g l e m e n t since there are two cross-linked units p e r c r o s s - l i n k a g e in a cross-linked n e t w o r k with f u n c t i o n a l i t y o f 4) is 16000, there should b e a b o u t 12 e n t a n g l e m e n t s p e r F-380 m o l e c u l e in the 5% b l e n d . This is the s a m e level of e n t a n g l e m e n t w h e r e the first deviation from the a p p r o x i m a t e s q u a r e - p o w e r - l a w beh a v i o r was f o u n d in P S - t r i c r e s y l p h o s p h a t e solution s t u d y [3] where the M w o f the solute was 8.6 × 105. T h e same degree of e n t a n g l e m e n t a p p e a r s to h o l d for o t h e r solvents a n d even lower m o l e c u l a r weights [23].

I

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,~,.~,.~~ ~ N N I

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3.5. Retardation spectra

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R e t a r d a t i o n s p e c t r a were d e t e r m i n e d f r o m all the J r ( t ) curves shown in fig. 10 a n d are p r e s e n t e d in fig. 12. T h e y are r e d u c e d to the references t e m p e r a t u r e s i n d i c a t e d in the figure. T h e t e m p e r a tures chosen were those that b r o u g h t c o i n c i d e n c e with the s h o r t - t i m e A n d r a d e region of the F-380 sample. These p o s i t i o n s for all the b l e n d s corres p o n d to t e m p e r a t u r e s that are within 2 ° C of the various Tg's c a l c u l a t e d above. T h e p r i n c i p a l c h a n g e in s h a p e of log L with

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94.8

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-

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in F-I

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Fig. 12. Logarithmic presentation of the retardation spectra obtained from the recovery curves s h o w n in fig. 10. Reference temperatures are indicated.

577

D.J. Plazek et al. / Diluent effects on viscoelastic behavior

, 8 ~6 tzD

• Blends (this study) *Blends(SJQ) oM0nod0sperse

__.~4

®TCP .Soln.(ER)

•

<3

,

Polystyrene

®TCP Soln.(N.R,)

weight tail. It is reassuring that separation between the peaks goes zero at a molecular weight which is ( M ~ ) ¢ within experimental uncertainty. This is the break point of the log ~ versus log M ~ dependence. This indicates that the molecular entanglements m a n i f e s t t h e m s e l v e s simultaneously in the viscosity and the recoverable creep compliance as a function of chain length and concentration.

/4¢/ ®. ~ 4 o/// ® ~-~

So

®-,'°~t"

~ 2 0

4

t

5 Log (M@) 6

Fig. 13. Length of the entanglement rubbery plateau as measured by the separation of the peaks of the retardation spectra on the logarithmic time-scale, A log ~m, as a function of the logarithm of the product of the molecular weight, M, and the volume fraction of the polymer, 4. (E.R.) refs. [3] and [4l;

(N.R)[5]; (S.J.O.)[27]; Monodisperse[16].

dilution is obviously the shortening of the entanglement plateau. The two peaks arising from the orientation of the F-380 chain-like molecules merge to one at a concentration between 2 and 10%. The increasing magnitude reflects the greater orientation of the diminishing number of the high molecular-weight molecules per unit volume due to the increase in the stress per molecule. The shoulder in the L(ln ~-) of the 2% blend between log r / a r of 3 and 6 is the contribution from the low molecular-weight polymeric solvent F-1. The length of the entanglement plateau is objectively determined by the separation of the maxima in L(ln ~-) as seen in fig. 12. The value obtained from the various L(ln ~') in fig. 12 are presented in fig. 13 with previously reported resuits on 'monodisperse' polystyrenes and blends and solutions of such polystyrenes. The peak separation, A log ~'m, is shown as a function of the logarithm of the product of the molecular weight, M, and the solute volume fraction, ~. The line which has a slope of 3.4 is close to the most dependable datapoints. Any contamination of the samples with high molecular-weight tails swells the terminal peak enormously and moves its maxim u m toward longer times. The point at l o g ( M ~ ) = 6 which is the farthest from the line represents j • o f a s o l u t i o n o f P r e s s u r e Chemicals sample 14A which is known to have a high molecular-

the

7

3.6. Dependence of oiscosity on molecular weight The viscosity of most linear polymers with broad molecular-weight distributions have long been known to be a function of the weight average m o l e c u l a r weight, M [24]. This empirically e s t a b lished dependence has been shown to fail for binary polystyrene blends with molecular-weight ratios of 8 [25] and 27 [26]. The viscosities of the blends were found to be as much as five times lower than the corresponding polystyrene with a narrow molecular-weight distribution. The viscosities of binary blends being described here with a molecular-weight ratio of 380 have values that are

7 - - - ,

-

]C

,/

160oc/~ _/

/

8 / gz9(3 ~ 4

2

100

~¢

5/ 4J

5[

6i

L_©G M,,s Fig. 14. Logarithmic values of the limiting low rate of shear viscosities ~ of polystyrene plotted as a function of the logarithm of the weight average molecular weight, Mw, at 160°C and at Tg + 100 ° C. Datapoints for monodisperse samples: (O), ref. [16]; ~, [261. Points for blended samples: ~, [26]; ~, [28];

(~),[6]; (to), this study.

578

D.J. Plazek et al. / Diluent effects on viscoelastic behavior

as much as three times lower than the value of the established 3.4 slope line. The current results are shown in fig. 14 along with those for the blends of Montfont, et al. [26] and those for the blends of Orbon [27]. Values for polystyrenes with narrow distribution are also shown from Allen and Fox [28] a n d refs. [16] and [26].

4. Conclusions (1) The Tg o f a 45% polymer solution of polyvinylacetate in sucrose benzoate (SB) was shown to be 49 o C at 0.5 o C/min rate of cooling. This is below the corresponding value of 59.5 ° C for the S B a n d higher than t h a t o f t h e P V A c (37 o C).

(2) The SB was determined to have an exceptionally high glassy compliance Jg = 3.9 × 10-10 cm2/dyn. (3) T h e S B e x h i b i t e d a Je ° w h i c h d e c r e a s e d i n magnitude upon cooling toward T~. (4) The form of the recoverable compliance Jr(t) of the SB w a s a terminating Andrade creep, where at short times Jr(t) was a linear function of 11/3.

(5) The low molecular-weight polysystryene (F1) showed a decreasing Je° with decreasing ternperature as did the SB but the F-1 data could not be reduced to a single curve as could all of the solution data. (6) The usual effects of dilution, shortening the length of the rubbery entanglement plateau and increasing the Jr(t) values with increasing diluent concentration were observed. (7) At the higher concentrations of the higher molecular-weight PS component, J~° cc C -2-13. (8) The viscosity of the PS blends was found n o t t o be a function of the weight average molecu-

lar weight. The authors wish to acknowledge the support of the National Science Foundation through the G r a n t MSS-8517120.

References [1] J.D. Ferry, Viscoelastic Properties of Polymers, 3rd Ed. (Wiley, New York, 1980). [2] E. Jenckel and R. Heusch, Kolloid-Z. 130 (1953) 89. [3] E. Riande, H. Markovitz, D.J. Plazek and N. Raghupathi,

J. Polym. Sci. Polym. Symp. 50 (1975) 405. [4] D.J. Plazek, E. Riande, H. Markovitz and N. Raghupathi, J. Polym. Sci. 17 (1979) 2/89. [5] N. Raghupathi, PhD thesis, University of Pittsburgh

(1975).

[6] S.J. Orbon and D.J. Plazek, Ed. 17 (1979) 1871. [7] G.C. Berry and D.J. Plazek, nology, Vol. 3, eds. D.R. (Academic Press, New York,

J. Polym. Sci. Polym. Phys. in: Glass Science and TechUhlmann and N.J. Kreidl 1986) ch. 6.

[8] J.R. McAdams and M.C. Williams, Marcromolecules 13 (1980) 858. [9] D.J. Plazek and Z.N. Frund Jr., J. Polym. Sci. Part B Polym. Phys. 28 (1990)431.

[10] D.J. Plazek, J. Polym. Sci. A-2 6 (1968) 621. [11] D.J. Plazek, in: Methods of Experimental Physics, Vol. 16c, ed. R.A. Fava (Academic Press, New York, 1979) ch. 11. [12] H. Vogel, Phys. Z. 22 (1921) 645. [13] G.S. Fulcher, J. Am. Chem. Soc. 8 (1925) 339, 789. [14] G. Tammann and W. Hesse, Z. Anorg. Allg. Chem. 156 (1926) 245. [15] D.J. Plazek, Polym. J 12 (1980) 43. [16] D.J. Plazek and V.M. O'Rourke, J. Polym. Sci. Part A-2 9 (1971) 209. [17] D.L. Plazek and D.J. Plazek, Macromolecules 16 (1983) 1469. [18] R.W. Gray, G. Harrison and J. Lamb, J. Polym. Sci. Polym Phys. Ed. 14 (1976) 1361. [19] K.L. Ngai, D.J. Plazek and S.S. Deo, Macromolecules 20 (1987) 2047. [201 C.A. Bero and D.J. Plazek, unpublished results. [21] D.J. Plazek and J.H. Magill, J. Chem. Phys. 45 (1966) 3038. [22] Timothy Altares Jr., unpublished results obtained at the Mellon Institute. [23] Y. Einaga, K. Osaka, M. Kurata and M. Tamura, Macromolecules 4 (1971)87. [24] G.C. Berry and T.G Fox, Adv. Polym. Sci. 5 (1968) 261. [251 H. Watanabe, T. Sakamoto and T. Kotaka, Macromolecules 18 (1985) 1008. [26] J.P. Monfort, G. Marin and P. Monge, Macromolecules 17 (1984)1551. [27] S.J. Orbon, PhD thesis, University of Pittsburgh (1978). [281 V.R. Allen and T.G Fox, J. Chem. Phys. 41 (1964) 337.