Multicomponent Polymer Systems

12 Dynamic and Stress-Optical Properties

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of Polyblends of Butadiene-Styrene Copolymers Differing in Composition G E R A R D KRAUS and K. W. R O L L M A N N Phillips Petroleum Co., Research and Development Dept., Bartlesville, Okla. 74003 Dynamic viscoelastic and stress-optical measurements are reported for blends of crosslinked random copolymers of butadiene and styrene prepared by anionic polymerization. Binary blends in which the components differ in composition by at least 20 percentage units give 2 resolvable loss maxima, indicative of a two-phase domain structure. Multiple transitions are also observed in multicomponent blends. All blends display an elevation of the stress-optical coefficient relative to simple copolymers of equivalent over-all composition. This elevation is shown to be consistent with a multiphase structure in which the domains have different elastic moduli. The different moduli arise from increased reactivity of the peroxide crosslinking agent used toward components of higher butadiene content.

hen two chemically different polymers are mixed, the usual result is a two-phase polyblend. This is true also when the compositional moitiés are part of the same polymer chain such as, for instance, i n a block polymer. The criterion for the formation of a single phase is a negative free energy of mixing, but this condition is rarely realized because the small entropy of mixing is usually insufficient to overcome the positive enthalpy of mixing. The incompatibility of polymers i n blends has i m portant effects on their physical properties, which may be desirable or not, depending on the contemplated application. In many copolymerizations compositional differences arise either intermolecularly or intramolecularly (or both) as a result of the kinetics of the copolymerization. This is true i n the anionic batch copolymeriza189 Platzer; Multicomponent Polymer Systems Advances in Chemistry; American Chemical Society: Washington, DC, 1971.


190

M U L T I C O M P O N E N T P O L Y M E R SYSTEMS

tion of styrene and butadiene which allows the preparation of copolymers of almost any degree of randomness (3). Whereas it is easy to distinguish between outright block polymers and random copolymers by their char acteristic mechanical behavior ( J , 4, 5), subtle differences are likely to arise from compositional heterogeneity in random copolymers, more spe cifically copolymers free of long sequences of either comonomer i n which composition nevertheless varies along the chain. In this connection we wished to establish some limits of compatibility between molecules or molecular sequences differing i n monomer ratio only. As a first step a series of polyblends was investigated which had been prepared exclu sively from uniformly random butadiene-styrene copolymers. (The term "uniformly random" is used to denote a copolymer for which composition is independent of conversion, precluding the possibility of any sort of compositional heterogeneity on a scale of more than a few monomer units). In this report we describe the results of both dynamic and stressbirefringence measurements on these polyblends. Microheterogeneity is clearly detectable i n binary blends of components differing i n composi tion by 20 percentage units and may be present i n blends of even narrower composition distribution. The results are analyzed by alternative oneparameter equivalent mechanical model treatments, one of which is shown to be moderately successful in describing both the dynamic and stressoptical properties of the blends in terms of the properties of the components.

Experimental Polymers. The polymers used in the blending experiments were prepared by anionic polymerization using an alkyllithium initiator and a chemical randomizing agent to control monomer sequence, in the manner described by Hsieh and Wofford (3). Randomness was checked in each case by measuring the styrene content as a function of conversion. Table I gives descriptive data for these polymers. Table I.

Polymer A Β C D Ε F

~, Charge Ratio Styrene Β/8 Anal., % 9:1 8:2 7:3 6:4 5:5 10:0

9.7 19.6 29.5 39.6 49.3 0.0

Polymer Characterization Microstructure

(Β)

cis,

%

trans,

%

vinyl.

%

M /Î000

45.0 35.9 35.5 35.8 31.8 48.6

39.9 49.0 49.4 50.0 53.0 42.5

15.1 15.1 15.1 14.2 15.2 8.9

197 182 138 134 121 260

GPC w

MJ1C

Platzer; Multicomponent Polymer Systems Advances in Chemistry; American Chemical Society: Washington, DC, 1971.

163 153 119 115 105 203

KRAUS A N D R O L L M A N N

191

Stress-Optical Properties

The styrene contents were confirmed analytically by ultraviolet ab sorption spectroscopy ( 7 ) . The microstructure of the contained buta diene units was determined by infrared analysis (JO). Molecular weights were determined by the gel permeation technique using a commercial Waters Associates chromatograph. The solvent was tetrahydrofuran. Since separate calibrations against light scattering molecular weights were available only for polybutadiene (of the same type as Polymer F ) and for 75:25 butadiene:styrene, the molecular weights of the copolymers were obtained from a universal calibration curve of [η]Μ vs. eluent volume, as proposed by Benoit and associates. ( 2 ) . Polymer Blending and Sample Preparation. Two methods were used to prepare polymer blends. Solution blending was accomplished by mix ing toluene solutions of the component polymers ( 5 % solids) with good agitation and coagulating the mixture i n a large excess of 2-propanol under rapid stirring. The coagulated blends were then dried at 30 °C in vacuo. Crosslinking agent ( D i - C u p 40C) was added on a two-roll labora tory mill. The amount used was 0.75%, corresponding to 0.3% of active dicumyl peroxide.

-

-

Λ

1010

-

V

ο

\δ0% \20

STYRENE"

\ 3 0 \ 40

ι


12.

-

10*

-

_

-100

Figure 1.

-80

-60

•c

-40

-20

Storage moduli of random copolymers


20

192



In preparing dry blends the peroxide was added to each component separately, and the resulting "masterbatches" were blended for 5 minutes on a roll mill at 70 °C. A l l samples were press-cured for 30 minutes at 153 °C into films approximately 0.2 mm thick. Dynamic Measurements. A Vibron direct reading viscoelastometer (Toyo Measuring Instruments Co., L t d . , Tokyo, Japan) was used to de termine viscoelastic properties. This instrument and its operation have been described i n detail by Takayanagi and Yoshino (11, 14). A l l poly mers and blends were examined at a standard frequency of 110 cps. In a few selected examples measurements were also made at 3.5 cps. Stress—Birefringence. The apparatus used to determine simultane ously stress and birefringence was of conventional design, employing compensation for the optical measurement. A l l measurements were car ried out at 24 °C. The sample chamber was a 2-liter Dewar with optically flat windows. The upper end of the sample strip was connected to a stress transducer, while the lower end could be manipulated from the outside to impose any desired strain. The actual strain was measured through the windows with a cathetometer, using gage marks stamped on the sample for reference. To measure the stress-optical coefficient, successively i n creasing strains were imposed on the sample. A t each strain the stress was recorded continuously for 5 minutes, at which time the compensator ( Babinet type, Gaertner Instrument Co. ) reading was made. Plots of bire fringence vs. stress showed good linearity. From these the stress-optical coefficients were calculated by the method of least squares.

0

ο Ν

1)

20 30

40

50% SPfRENE

-

-20

20

-

10*

-

-100

Figure 2.

-80

-60

•c

-40

Loss moduli of random copolymers


12.

KRAUS AND R O L L M A N N

193

Stress—Optical Properties

Results Dynamic Measurements. Figures 1 and 2 show the dynamic storage and loss moduli E ' and E " at 110 cps for the six component polymers, A to F . The position of the loss maximum is plotted as Tmax' vs. styrene content i n Figure 3. A good straight Une is obtained which passes through the expected values for pure polybutadiene ( 1 5 % vinyl) and polystyrene Downloaded by NORTH CAROLINA STATE UNIV on December 31, 2017 | http://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0099.ch012

1

^ 8.9% VINYL

0.5

ε ^~

0.4

0.3

20

Figure 3.

40 60 WEIGHT % STYRENE

80

100

Position of loss maximum as function of copolymer composition (circles for 15% vinyl in butadiene portion)

—i.e., —91° and 108°C, respectively. These values He slightly above the dilatometric glass transitions, as would be expected for 110-cps data. Figure 4 shows data for a mechanical blend of equal weights of Polymers A and E . The two-phase nature of this blend is immediately obvious from the observation of separate transitions for the component polymers which are almost unshifted from their positions i n Figures 1 and 2. T h e corresponding solution blend is shown i n Figure 5. The dif-


194



ferences between the dry blend and the solution blend are very small, indicating that the incompatibility is not the result of inadequate dry blending technique. The same was found also for other blends of nar rower composition distribution. F o r this reason further discussion w i l l be confined to dry blends only.

Figure 4.

Dynamic properties of 1:1 mechanical blend of Polymers A(10% styrene) and E(50% styrene)

Figure 6 shows a blend of equal weights of Polymers Β and D . Separate loss peaks are no longer resolved, but a distinct broadening of the dispersion region is observed which suggests that the blend is twophase. A ternary blend of equal weights of Polymers B , C, and D ( F i g -



12.


Figure 5.

195


Dynamic properties of 1:1 solution blend of Poly mers A and Ε

ure 7) shows a narrower dispersion region. The dynamic properties of this blend would be difficult to distinguish with certainty from those of Polymer C, which has the same over-all composition. O n the other hand, a five-way blend of equal amounts of A , B , C, D , and Ε (Figure 8) dis plays a broad dispersion region with an interesting characteristic: the principal peaks i n E" and tan δ are displaced from each other to an unusually high degree. Obviously the maximum i n E " is weighted most heavily by the components of lower T , whereas the maximum i n tan δ is weighted predominantly by the components of higher T or higher styrene content. The behavior of the blends of Figures 4 to 8, all of which contain 3 0 % styrene over-all, is typical also of blends of other average compositions, as well as of blends of unequal amounts of the components. Results of all blending experiments are summarized i n Table II. 0

0


196

MULTICOMPONENT

P O L Y M E R SYSTEMS


Comparison of the positions of the loss maxima leads to some inter esting observations. In all binary blends, which differ by more than 20 percentage units in component composition, the E " maxima occur within a few degrees of their position in the components. The maxima in tan δ

-

-

ΙΟ»»

CM

-

Ο

\

Î3

\

9

10

ta no

8

10

-

10* •100

Figure 6.

-80

tan à

J s, ; -60

•c

-40

-20

,01

Dynamic properties of 1:1 blend of Polymers B(20% styrene) and D(40% styrene)

tend to be affected more by blending, but the behavior is not entirely consistent. In binary blends both maxima i n the loss tangent occur gen erally at lower temperatures than they do i n the components. The shift is of the order of 5-10° for the lower maximum, but varies from zero to 35° for the upper maximum. In Blend 3, representing the narrowest com-



197


position distribution tested, the maxima in E " and tan δ occur nearly at the positions indicated for a compositionally homogeneous copolymer of the same styrene content. This blend may well consist of a single phase. This is not so for the other multicomponent blends, 4 and 5. These show severe broadening of the dispersion region and two or more resolvable loss maxima. In Blend 5 (Figure 8) there is obviously significant interaction of components or partial miscibility. A n interesting aspect of broad composition distribution is the re versal with temperature of the dynamic properties relative to a narrow

-

t

10»

11 11


12.

-

Ε"

vfi

ta n*

c 45

J

V ,/ 10'

-100

.01 -80

-60

•c

-40

-20

Figure 7. Dynamic properties of 1:1:1 blend of Polymers B(20% styrene), C(30% styrene), and D(40% styrene)



198

MULTICOMPONENT POLYMER

Figure 8.

SYSTEMS

Dynamic properties of five-component blend (Poly mers A to E)

distribution polymer of the same styrene content. As an illustration we list £ ' and tan δ for Blend 5 (Figure 8) and Polymer C at two tempera tures: E dynes/cm f

-30°C Blend 5 (30% styrene, broad composition distribution) Polymer C (30% styrene, uniform composition)

tan δ

2

-70°C

-80°C

-70°C

7.5 Χ 10

8

1.3 Χ 10

10

0.48

0.125

1.6 Χ 10

8

3.0 Χ 10

10

0.98

0.035


12.


199



These reversals are a direct consequence of the multiphase structure and occur throughout the entire series of blends studied. Similar reversals would be expected with frequency at fixed temperature. Stress Birefringence. Confirmation of the multiphase nature of the polyblends described may be obtained b y stress-optical measurements. Since this technique apparently has not been used before to demonstrate incompatibility in polyblends, a brief description is given of the rationale behind the method. The stress-optical coefficient, Κσ, of an elastomer network is a con stant, independent of extension ratio and crosslink density. It is directly proportional to the difference between the longitudinal and transverse polarizabilities of the statistical chain segment ( bi — b ) : 2

Ko = 2τ ( η + 2) (J* - 6 )/45 nkT 2

2

2

(1)

Here η is the average refractive index, k is Boltzman's constant, and Τ is absolute temperature (13). If a polyblend were to form a homogeneous network, the stress would be distributed equally between network chains of different composition. Assuming that the size of the statistical seg ments of the component polymers remains unaffected by the mixing process, the stress-optical coefficient would simply be additive by compo sition. Since the stress-optical coefficient of butadiene-styrene copoly mers, at constant vinyl content, is a linear function of composition ( Figure 9), a homogeneous blend of such polymers would be expected to exhibit the same stress-optical coefficient as a copolymer of the same styrene content. Actually, a l l blends examined show an elevation of Κσ which increases with the breadth of the composition distribution (Table I I I ) . Such an elevation can be justified if the blends have a two- or multiphase domain structure i n which the phases differ i n modulus. If we consider the domains to be coupled either in series or in parallel (the true situation w i l l be intermediate), then it is easily shown that Κα = Και \\ + Koo Γ, · · · (series)

(2)

or Κα = (Κοι \\E + Ko2 V E )/(V E X

2

2

1

+

l

VE) 2

2

. . . (parallel)

(3)

assuming linear elasticity. Here V i , V are volume fractions, and Eu E are Youngs moduli. Extension to more than 2 components is obvious. O f the two equations only the second is capable of accounting for an elevation in Κσ. Predictably, it overestimates the stress-optical coefficient since simple parallel coupling is an obvious exaggeration. Values calculated b y Equations 2 and 3 are shown i n the fifth and sixth columns of Table III. 2


2

200


Table I I .

Loss

Composition, Wt %


Blend No.

A (9:1)

Β (8:2)

C (7:3)

Ε (δ:δ)

D (6:4)

F (10:0)

50

—

50

—

—

33.3

33.3

—

—

33.3

—

33.3

—

20

—

33.3

—

1

50

—

—

2

—

50

—

3

—

33.3

4

33.3

—

5

20

6

—

7

.

—

20

20

66.7

—

—

—

—

—

75

—

25

8

33.3

—

—

66.7

—

—

9

—

—

—

—

60

40

10

—

50

—

—

—

50

11

—

—

—

50

—

50

12

66.7

—

—

33.3

—

—

13

—

—

50

—

50

—

14

25

75

—

20

Column 9 identifies corresponding loss maxima of the components (C) with those observed in the blend (B). β

The elastic moduli of the component polymers were obtained by extrapo lating M o o n e y - R i v l i n plots (8,9) of the stress to zero strain: Polymer Ε Χ 10- , dynes/cm β

2

A

B

C

D

E

F

26.7

24.9

18.0

13.2

12.3

30.0

The variation in modulus appears to be caused by increased reactivity of the dicumyl peroxide crosslinking agent toward butadiene-rich polymers. The last column i n Table III shows a weighted mean, using empirical weight factors of 0.73 and 0.27 for parallel and series coupling, respec tively. These values fit the observed stress-optical coefficients within experimental error. The elevation of the stress-optical coefficient, together


12.

201

Stress-Optical Properties


Maxima i n Blends* Over-all % Styrene

Col. 9*

30

C Β C Β C Β C Β C Β C Β C Β C Β C Β C Β C Β C Β C Β C Β


30 30 30 30 30 30 30 30 10 20 20 40 40 b e

E

! l

Maxima, °C

-81 -28 -76; - 3 0 -67; -46 -64; -48» -67; - 5 7 ; - 4 6 -62, - ; - 4 8 » -81 -57;-28 -73, -52»;-19 -81, -67;-57;-46;-28 -65, -44»;-20» -67, - 2 8 -70 -23 -104:-46 -93 -59 -81 -46 -77 -54 -104:-28 -93 -30 -104;-67 -93;-70 -104;-46 -97 ;-41 -81 ;-46 -82 ;-52 -57 ;-28 - 5 4 ;-30» -81 ;-28 -84 ;-32

tan

IMaxima, °C

-69;+5 -70;-2 -50;-17 -30< -50;-33;-17 -;-37;-69;-33;+5 -70»;-37»-7 -69;-50;-33;-17;+5 -57;-;-17 -50;+5 -65;-3 -86;-17 -92;-29 -69;-17 -72;-20 -86;+5 -89;+6 -86;-50 -92;-70 -86;-17 -89;-39 -69;-17 -70;-52 -33;+5 -34»;-4 -69;+5 -79;+l

Shoulder. Single broad maximum.

with its successful (if empirical) description by a calculation based on a heterogeneous model, seems to us ample confirmation of the multiphase nature of these blends. Discussion In the present section an attempt is made to describe both stressoptical and dynamic properties of blends i n terms of those of the com ponents, using a more detailed, but simple equivalent mechanical model. W e consider a (binary) blend as consisting of domains of Polymer 2 dispersed i n Polymer 1. These domains are thought to be coupled i n series-parallel fashion. The simple analysis of the stress-optical coeffi-


202

MULTICOM PONENT

P O L Y M E R SYSTEMS

, 8 X VINYL


3

15% VINYL

b

0

.1

.2

.3

MOL FRACTION STYRENE

Figure 9.

Stress-optical coefficients for component polymers

Table III. „

n

Stress-Optical Coefficients for Blends K i X

10"

Κσ Χ 10

Over-all No." 1 2 3 4 5 6 7 8 9 10 11 12 13 14 β

10

(calc.)

%

06s. cm /dyne

Additivity cmï/dyne

Series

Parallel

Weighted Mean

30 30 30 30 30 30 30 30 30 10 20 20 40 40

2.05 1.98 2.02 2.04 2.01 2.01 2.12 2.00 2.41 3.12 2.79 2.52 1.41 1.51

1.90 1.90 1.90 1.90 1.90 1.90 2.00 1.90 2.04 2.98 2.55 2.38 1.36 1.36

1.82 1.88 1.89 1.84 1.86 1.84 1.93 1.87 1.91 2.96 2.48 2.36 1.32 1.29

2.20 2.01 1.98 2.09 2.10 2.07 2.29 2.10 2.51 3.13 2.88 2.55 1.44 1.64

2.10 1.98 1.96 2.03 2.03 2.01 2.19 2.03 2.35 3.09 2.77 2.50 1.41 1.55

Content,

2

For composition of blends see Table II.



12.


σ


203

σ Figure 10.

The Takayanagi model

outlined above suggests that the model should be capable of emphasizing parallel coupling, particularly i n systems of approximately equal component volumes. Physically, such a system resembles an inter locking network of two phases rather than a dispersion of one phase i n the other. One model which incorporates the desired features and which has been used with some success to describe the behavior of polyblends is that of Takayanagi and associates (12). This model is illustrated in F i g ure 10. The parameters λ and φ represent the state of mixing, and their product equals the volume fraction of the disperse phase. A n equally plausible arrangement for coupling the elements of the model would be a series combination of " 1 " and "2," in parallel with " 1 . " Takayanagi rejects this alternative on the grounds that it leads to poorer fits of experi mental data. The ambiguity i n the arrangement of the series and parallel elements is an inherent difficulty with all such models. Another difficulty is conceptual. The Takayanagi model is anisotropic i n the sense that it gives different mixing laws depending on how the cube of Figure 10 is oriented with respect to the stress. This would be appropriate for de scribing the properties of fibers or laminates, but for isotropic blends the apparent difficulty can only be overcome by letting λ = φ, which does not produce good fits to experimental data. A model which removes this difficulty without introducing additional parameters is shown i n Figure 11. It seems particularly suitable for describing the idea of interpene-

dents


204

M U L T I C O M PONENT P O L Y M E R SYSTEMS

trating networks. Its geometric parameters a and b are uniquely related to V by the equation 2

V

2

= a (36 2

2a)

(4)


Two ways of arranging the various elements are shown in Figure 11; still others are possible. However, only the two cases shown, which represent

σ COUPLING Β

Figure 11.

The "isotropic' model

the extremes series-parallel (coupling A ) and parallel-series (coupling B ) , have been evaluated. W h i l e the "isotropic model" may be mentally more satisfying, it must be recognized that all such models merely furnish phenomenological descriptions by providing essentially empirical sets of combination rules. The advantage of one or the other model can be demonstrated only by its ability to represent data.


12.


205


The equations describing the moduli are as follows: Takayanagi model:

E

=

[ λ £ + (1 - λ ) # ! 2

~ê/\

+

(5)


Isotropic model (coupling A ) :

E

" (1 -

b/E

6 ) / £ +

+

2

"

t ( 1

2a (b -

a ) 2

+

2 a

( 1

"

6 ) 1

^

+

a)

(1 - α)/Εχ +

( 6 )

a/Ε

2

Isotropic model ( coupling Β ) : F

(

=

a

\a(2b -

a)E

2

, + (1 -

, 1 ~ b)

b - a

a) ^ ^ aE 2

2

2

+ (1 -

α*)Ε ^ λ

E

)

x

1

(

) w

In all three equations E and E are now the complex moduli; the storage and loss moduli for the blend are obtained by direct substitution into these equations and separation of the real and imaginary parts to obtain separate mixture rules for each. Analytical expressions have been ob tained for these, but they are lengthy and cumbersome. A l l the calcula tions described, therefore, were carried out by computer. The substitu tion of complex moduli into the solution of the equivalent purely elastic problem is justified by the correspondence principle of viscoelastic stress analysis ( 6 ) . 2

x

Table IV.

Parameters for Equations 5 and 6 Equation 5

α

Equation 6

Blend No."

λ

Φ

α

b

1 2 6 7 8 9 10 11 12 13 14

.490 .555 .395 .900 .347 .889 .559 .527 .405 .604 .267

.990 .887 .820 .290 .990 .470 .880 .920 .800 .800 .980

.490 .505 .390 .335 .394 .445 .495 .490 .390 .509 .335

1.000 .980 .969 1.000 1.000 1.000 1.000 1.000 .969 .961 1.000

For composition of blends see Table II.



206

MULTICOMPONENT POLYMER

Figure 12.

SYSTEMS

Data on Blend 8 fitted by equivalent models

Expressions for the stress-optical coefficient based on the above models are written easily. One assumes that the birefringences con tributed by the various elements of the model are additive by volume and are given by the product of the stress i n the element and the stress-optical coefficient of the appropriate component. The resulting equations are:

Takayanagi model: Κ K.=

Π

(l-

φ ) * , ,

+

ι

φ

λ

* ^ £ χ 2

2

+ +

φ

Ε

(

ι

~

(1-

1

°>

X)K

El

λ)


(8) (

8

)

12.


207


Isotropic model (coupling A ) :

'

" |_(1 -

(1 - α)/Ει + α/Ε,] ~ ~ l

2

[ { U - a ) + 2 a ( l - 6)} & +

K

2

ai


+ 6/£

(1 -

β

*

( 1

"

6 )

+ b/E

2

+

2a(6 - a) (1 - a) 1 a/E, + (1 - «O/JSJ

,, Q

W

The corresponding expression for coupling Β of the isotropic model is not given as it was not used i n the final analysis of the stress-optical data.

•

-

< _

ISOTW)PIC MODIEL

_ TAKAYAiNAGI 1» OBSEWtiD

\

V

\ \ \\ \\ Λ\\« \\

-

-

>

V\

V

8

10

i V

-

SCALE FOR Ε-100

-80

-60

SCALE FOR E"-80

-60

-40

-40

-20

0

-20

0

20

•c Figure 1 3 .

Data on Blend 13fittedby equivalent models


208



3.2

1.4

1.6

1.8 Κ

2

2.2 10

σ

2

2.4

x10 , C M / D Y N E

2.6

2.8

3.0

(CALC)

Figure 14. Observed and calculated stress-optical coefficients (calculation by Equation 9 with parameters producing bestfitto dynamic data) Both Equations 8 and 9 assume linear elements. The calculations have also been performed (by computer) for neo-Hookean elements. This leads to a slight dependence of Κσ on strain. The predicted dependence is so small, however, that i t would be difficult to detect experimentally. Application of Equivalent Models to Dynamic Data. Equations 5, 6, and 7 were applied to the data on a l l binary blends i n this study. Equation 7 showed no advantage over the simpler Takayanagi Equation 5. Equation 6 produced slightly better fits than 5 i n most cases. Table I V gives the parameters for the Takayanagi and Isotropic (coupling A ) models fitting the data most closely. In each case the component present in excess b y volume was chosen as the continuous phase. It is interesting that the isotropic model consistently gives the best fit with b « 1—i.e., the situation idealizing an interlaced network of the two phases. In no case could an exact fit be obtained; examples of the quality of fit produced to the experimental data are shown i n Figures 12 and 13.



12.



209

Analysis of Stress-Optical Data. The slight, if indeed real, improve ment of the isotropic model over the Takayanagi model would be of little consequence were it not for a more pronounced difference between the two models in their ability to describe the stress-optical data. When the parameters obtained from the dynamic data (Table I V ) are substituted into Equations 8 and 9, Equation 8 produces results which are uniformly too low. Equation 9 also underestimates the magnitude of Κσ but only by an average 7% (Figure 14). F o r most blends the discrepancy is less than 5 % , and all calculated values show the characteristic elevation of the birefringence attributed to the multiphase structure. It is difficult to assess to what extent the imperfect fits obtained by the equivalent models are the result of partial miscibility. This is because the models do predict minor shifts i n the loss maxima, which are i n the same direction as the shifts expected from partial miscibility. Thus the major cause of the deviations may well be the inability of the models to describe a complex morphology with a single adjustable parameter. Conclusions In the molecular weight range of 120,000-200,000 butadiene-styrene random copolymers form multiphase blends when they differ by 20 or more percentage units in composition. The precise limits of compatibility have not been determined but may lie substantially below this figure. The multiphase structure of these polyblends is indicated by both dynamic and stress-optical properties. As a result of this structure polyblends of broad compositional distribution exhibit a temperature reversal of their dynamic properties relative to narrow distribution polymers of the same average composition: above a certain temperature a broad distribution blend w i l l have higher storage moduli and loss tangents, while at low temperatures the behavior w i l l be reversed. Another reversal occurs in the glassy region. Acknowledgment The authors are indebted to R. J . Sonnenfeld for preparing the polymers used in the blending studies and to N . W . Tschoegl for several helpful discussions. Literature Cited (1) (2) (3) (4)

Childers, C. W., Kraus, G., Rubber Chem. Technol. 1967, 40, 1183. Grubisic, Z., Rempp, P., Benoit, H . , J. Polymer Sci., Β 1967, 5, 753. Hsieh, H . L., Wofford, C. F., J. Polymer Sci., A-1 1969, 449, 461. Kraus, G., Childers, C. W., Gruver, J. T., J. Appl. Polymer Sci. 1967, 11, 1581.


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(5) (6) (7) (8) (9) (10) (11)

Kraus, G., Gruver, J. T., J. Appl. Polymer Sci. 1967, 11, 2121. Lee, Ε. H . , Quart. Appl. Math. 1955, 12, 183. Meehan, E. J., J. Polymer Sci. 1946, 1, 175. Mooney, M., J. Appl. Phys. 1940, 11, 582. Rivlin, R. S., Saunders, D. W., Phil. Trans. Roy. Soc., A243 1951, 251. Silas, R. S., Yates, J., Thornton, V., Anal. Chem. 1959, 31, 529. Takayanagi, M . , Proc. Intern. Congr. Rheology, 4th, 1965, Part 1, 161187. (12) Takayanagi, M . , Uemura, S., Minami, S., J. Polymer Sci., C 1964, 5, 113. (13) Treloar, L . R. G., "The Physics of Rubber Elasticity," p. 138, Oxford University Press, London, 1949. (14) Yoshino, M . , Takayanagi, M., J. Japan Soc. Test. Mat. 1959, 8, 330. RECEIVED December 31,

1969.


Multicomponent Polymer Systems

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