Properties and Morphology of Amorphous Hydrocarbon Block

9 Properties and Morphology of Amorphous

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Hydrocarbon Block Copolymers MITCHEL SHEN Department of Chemical Engineering, University of California, Berkeley, C A 94720

The

morphologies of heterogeneous block copolymers are

determined by the block composition and by sample preparation conditions.

The

resulting

microstructures

exert a

profound influence on the properties of these materials. this review we shall first discuss the thermodynamic

In

condi-

tions under which homogeneous block copolymers can be formed. These systems are interesting because their underlying chain dynamics can be treated by the accepted molecular models. copolymer

Next we present some examples of block

morphologies.

Statistical

theories capable

of

satisfactorily explaining the observed morphologies are then briefly discussed. Finally the elastic, viscoelastic, and rheological properties of these materials are described. instances the dominant effect of the microdomain

In all

structure

on these properties is demonstrated.

T A u r i n g the past decade, there has been an upsurge of interest in studying the relation between morphology and properties of block copolymers. T h e interest is generated mainly by the technological importance of these materials, e.g., their ability to form thermoplastic elastomers or i m pact-resistant plastics. Although there are some block copolymers that are homogeneous, most of them show microphase separation.

T h e type of

structure depends on such variables as chemical composition, block configuration, solvent power, etc.

Advances in characterization techniques

such as electron microscopy and low-angle x-ray scattering now render it possible to investigate their detailed morphologies. In this chapter we shall review the morphological and property studies of both homogeneous 0-8412-0457-8/79/33-176-181$06.00/0 © 1979 American Chemical Society

Cooper and Estes; Multiphase Polymers Advances in Chemistry; American Chemical Society: Washington, DC, 1979.

182

MULTIPHASE

POLYMERS

a n d heterogeneous b l o c k c o p o l y m e r s as w e l l as t h e t h e r m o d y n a m i c theo ries i n m i c r o p h a s e s e p a r a t i o n i n these materials.

T h e r e v i e w is n o t

i n t e n d e d to b e exhaustive, rather i t w i l l focus o n t h e m o r e c u r r e n t w o r k s i n t h e field. F u r t h e r i n f o r m a t i o n is a v a i l a b l e i n t h e recent research m o n o graphs (1,2,3,4,5)

a n d r e v i e w papers c i t e d (6, 7,8,

9,10).

Homogeneous Block Copolymers T h e t h e r m o d y n a m i c c r i t e r i o n f o r the m i x i n g of t w o or m o r e systems is that t h e f r e e e n e r g y o f m i x i n g m u s t b e negative. tems, t h e e n t r o p y increases

F o r p o l y m e r i c sys

a c c o m p a n y i n g the m i x i n g

of l o n g c h a i n

m o l e c u l e s are v e r y s m a l l . S i n c e t h e e n t h a l p y of m i x i n g is u s u a l l y p o s i t i v e , i t is therefore n o t t o o s u r p r i s i n g that phase separations o f t e n o c c u r i n p o l y m e r i c m i x t u r e s . T h e t h e r m o d y n a m i c basis f o r m i c r o p h a s e s e p a r a t i o n i n b l o c k c o p o l y m e r s has b e e n p r e s e n t e d b y K r a u s e (11,12) a n d M e i e r I n t h e w o r k of K r a u s e , the e n t h a l p y change o n m i c r o p h a s e separa

(13).

t i o n is g i v e n b y t h e H i l d e b r a n d - V a n L a a r - S c a t c h a r d expression AH -

-

-kT(V/V )v v (l z

A

BXAB

(14): (1)

2/z)

w h e r e V is t h e t o t a l v o l u m e of t h e m i x t u r e , V t h e v o l u m e of e a c h l a t t i c e z

site, ζ is t h e c o o r d i n a t i o n n u m b e r , k is B o l t z m a n n constant t> a n d t ) a r e A

B

v o l u m e fractions of A a n d Β b l o c k s r e s p e c t i v e l y , Τ is absolute t e m p e r a ture, a n d XAB is the F l o r y - H u g g i n s i n t e r a c t i o n p a r a m e t e r b e t w e e n A s and Bs. T h e e n t r o p y c h a n g e a c c o m p a n y i n g m i c r o p h a s e separation is

(12)

f o r e a c h c o p o l y m e r m o l e c u l e . I n E q u a t i o n 2, m is t h e n u m b e r of b l o c k s AS/k

— (ν 1ην + Δ

Δ

VBIUVB)

-

2 (m -

1) (AS /k) d

+ In ( m -

1)

(2)

i n t h e b l o c k c o p o l y m e r m o l e c u l e . T h e e n t r o p y c h a n g e a t t r i b u t a b l e to t h e d e m i x i n g f r o m a h o m o g e n e o u s m i x t u r e to a phase-separated

system is

g i v e n b y t h e first t e r m o n t h e r i g h t - h a n d side of E q u a t i o n 2. T h e s e c o n d t e r m accounts f o r t h e e n t r o p y decrease a t t r i b u t a b l e to t h e i m m o b i l i z a t i o n of t h e segments l i n k i n g t h e A a n d Β b l o c k s ( w h e r e AS is d i s o r i e n t a t i o n d

entropy).

I f t h e n u m b e r of b l o c k s i n t h e c o p o l y m e r is large (m

> 3),

t h e n it is necessary t o r e c o g n i z e t h e fact that after t h e first b l o c k - l i n k i n g segment has b e e n p l a c e d o n the interface, the p o s s i b l e n u m b e r of sites a v a i l a b l e to t h e s u b s e q u e n t l i n k s is n o w c o n s t r a i n e d . T h e e n t r o p y change f o r this effect is g i v e n b y t h e t h i r d t e r m . C o m b i n i n g E q u a t i o n s 1 a n d 2, the free e n e r g y change o n m i c r o p h a s e separation c a n b e w r i t t e n . T h e c r i t i c a l i n t e r a c t i o n p a r a m e t e r t h e n c a n b e r e a d i l y o b t a i n e d b y setting the f r e e energy change to z e r o :


9.

SHEN

(xab)

«

=

+ where n

183

Amorphous Hydrocarbon Block Copolymers

and n

A

F=îfe^ " C

2(m -

1) (AS /k)

iVAlnVA +

-

d

m(m -

VBlnVB)

1)]

(3)

a r e t h e n u m b e r s of A a n d Β units i n e a c h c o p o l y m e r

B

m o l e c u l e . C a l c u l a t i o n s o n t h e basis of E q u a t i o n 3 s h o w t h a t t h e m i c r o phase separation b e c o m e s m o r e d i f f i c u l t w i t h i n c r e a s i n g m . V a l u e s of c r i t i c a l i n t e r a c t i o n parameters c o m p u t e d f o r a m i x t u r e of h o m o p o l y m e r s are m u c h l o w e r t h a n those f o r t h e b l o c k c o p o l y m e r w i t h i d e n t i c a l c o m p o s i t i o n . T h u s i t is m o r e d i f f i c u l t f o r m i c r o p h a s e s e p a r a t i o n t o take p l a c e w h e n p o l y m e r s are l i n k e d together v i a c o v a l e n t b o n d s as b l o c k c o p o l y mers.

E x p e r i m e n t a l l y i t has b e e n f o u n d that a l t h o u g h p o l y b l e n d s of

p o l y s t y r e n e a n d p o l y ( α - m e t h y l styrene ) t e n d t o b e heterogeneous, c o r r e s p o n d i n g b l o c k c o p o l y m e r s are often h o m o g e n e o u s

the

( 15-21 ).

A l t h o u g h there are v e r y f e w h o m o g e n e o u s b l o c k c o p o l y m e r s a v a i l able they are nevertheless of interest because t h e i r viscoelastic b e h a v i o r c a n b e s t u d i e d w i t h i n t h e existing t h e o r e t i c a l f r a m e w o r k to e l u c i d a t e t h e m o l e c u l a r d y n a m i c s of b l o c k c o p o l y m e r s .

T h e most a c c e p t e d m o d e l i?

the m o l e c u l a r t h e o r y of p o l y m e r v i s c o e l a s t i c i t y p r o p o s e d m a n y years a g o b y R o u s e ( 2 2 ) , B u e c h e ( 2 3 ) , a n d Z i m m (24).

T h e R B Z model divides

the p o l y m e r m o l e c u l e i n t o Ν - f 1 s u b m o l e c u l e s w i t h Ν springs.

( beads ) h e l d together

T h e springs are stretched w h e n t h e p o l y m e r c o i l is

d i s t u r b e d b y a shear g r a d i e n t . T h e s p r i n g constant is g i v e n b y

3kT/b ,

w h e r e b is t h e average e n d - t o - e n d distance of t h e s u b m o l e c u l e .

A s the

2

2

beads m o v e t h r o u g h t h e m e d i u m , a viscous d r a g is exerted o n t h e m w h o s e m a g n i t u d e is g i v e n b y a f r i c t i o n coefficient /. A t e q u i l i b r i u m t h e viscous a n d elastic forces are e q u a l to e a c h other.

A s i m p l i f i e d f o r m of t h e

e q u a t i o n of m o t i o n c a n b e w r i t t e n as f o l l o w s : X

= σΖχ

w h e r e χ a n d χ are c o l u m n vectors of b e a d p o s i t i o n s a n d b e a d velocities, Ζ is t h e nearest n e i g h b o r m a t r i x , a n d σ =

3kT/b f. 2

I n t h e case of b l o c k c o p o l y m e r s ( 2 5 , 26, 27, 28,29), E q u a t i o n 4 m u s t b e m o d i f i e d t o take i n t o a c c o u n t t h e f a c t that n o t a l l of t h e b e a d s are t h e same (as is the case f o r h o m o p o l y m e r s ) .

F o r a triblock copolymer such

as p o l y ( s t y r e n e - b - a - m e t h y l styrene-b-styrene ), t h e e q u a t i o n of m o t i o n is (26):

X = — σ Ό Ζχ 8

_1

w h e r e σ = 3kT/b / , t h e subscripts s refer to t h e P S s u b m o l e c u l e . T h e m a t r i x D " is t h e inverse of 2

8

8

8

1


184

MULTIPHASE POLYMERS

Ο '"SA

D

(6)

Ο where δ

Α

=

a n d subscripts A refer to

2

b f /b % A

A

B

P a M S

submolecules.

T h u s t h e elements i n t h e d i a g o n a l o f this m a t r i x take i n t o a c c o u n t t h e differences b e t w e e n t h e

P S

and

P a M S

submolecules.

T h e s o l u t i o n of t h e e q u a t i o n of m o t i o n y i e l d s t h e d i s t r i b u t i o n of v i s c o e l a s t i c r e l a x a t i o n times.

F o r ease of c o m p a r i s o n w i t h e x p e r i m e n t a l

d a t a , m a x i m u m r e l a x a t i o n times f o r a n u m b e r of b l o c k c o p o l y m e r s w i t h different b l o c k configurations w e r e c o m p u t e d (26). T a b l e I.

T h e s e are g i v e n i n

F i g u r e 1 shows t h e s t r e s s - r e l a x a t i o n isotherms d e t e r m i n e d f o r

t w o d i b l o c k c o p o l y m e r s of styrene a n d α - m e t h y l s t y r e n e of t w o different m o l e c u l a r w e i g h t s (21).

T h e s e a r e s h i f t e d i n t o s m o o t h v i s c o e l a s t i c master

curves ( F i g u r e 2 ) . T h e i r shift factors ( F i g u r e 3 ) are seen to f o l l o w t h e W L F e q u a t i o n closely, i n d i c a t i n g the essential h o m o g e n e i t y of t h e b l o c k c o p o l y m e r samples.

Similar experiments

were

n u m b e r of t r i b l o c k c o p o l y m e r s of styrene

also c a r r i e d o u t f o r a

a n d a-methylstyrene

(19).

M a x i m u m r e l a x a t i o n times w e r e d e t e r m i n e d f r o m the master curves b y T a b l e I.

Block C o n f i g u r a t i o n s a n d M a x i m u m Times of Block Copolymers (26)

Polymer

Retardation Log

Block Configuration

α Τm ax

10% A

50% A

I. D i b l o c k c o p o l y m e r

AB

-0.42

0.65

II. T r i b l o c k copolymers

(a) A ^ B y A ^ (b) B ^ A y B j ;

0.64 -0.62

1.22 0.65

III.

A l t e r n a t i n g (segmented) block copolymers

I V . M u l t i b l o c k copolymers ° Computed for d = 185. A

X

V

(a) ΑχΈ$χΑχΒ (b) A ^ B y A j B y χ

. . . . .

(a) B AyB (b) B ^ A y B ^ A y B j ; X

Z

0.26

0.97 0.97

-0.60 0.34

0.65 1.01

—

Macromoiecules


9.

SHEN

185


10

1

1

I

BPI

1

BPI

\ \

Ν

\

~

^\II2.5°C\

\ X CM

e CD C >*

N

>y

\ll7

\

\|2I

Lu CP

7 NÔ\l44 \

\ 1-41.5

\\N\l46.5 \

ΝΛ150 154

\

I 145

1158 ι

1

ι

2

3 Log t

2 (sec)

1

3

Figure 1. Stress-relaxation isotherms for two samples of poly(styrene-b-a-methylstyrene), BPI = M = 0.8 Χ 10 ; BPII = M = 1.5 X J O . Solid curves: tensile data; broken curve: flexural data (21). w

5

w

5

P r o c e d u r e X of T o b o l s k y a n d M u r a k a m i (SO). T a b l e I I shows that t h e agreement is satisfactory b e t w e e n t h e c a l c u l a t e d a n d e x p e r i m e n t a l values (JO). Morphology

of Heterophase Block

Copolymers

F i v e f u n d a m e n t a l d o m a i n structures are p o s s i b l e f o r b l o c k c o p o l y mers c o n s i s t i n g of t w o types of b l o c k s . G e n e r a l l y l a m e l l a r structures w i l l f o r m at c o m p o s i t i o n s w i t h a p p r o x i m a t e l y e q u a l p r o p o r t i o n s of the t w o c o m p o n e n t s . A s t h e p r o p o r t i o n of o n e c o m p o n e n t increases at t h e expense of t h e other, c y l i n d r i c a l m o r p h o l o g i e s w i l l result. T h e m a t r i x p h a s e w i l l


186

MULTIPHASE POLYMERS

Table II.

M a x i m u m Viscoelastic Relaxation Times f o r B l o c k Copolymers of Styrene a n d a-Methylstyrene

log

(τ /τ °) ηι

ηχ

Sample

Wt % aMS

Exptfl

CaVd

SAS

5 17 34 42 65 73 50

0.50 0.59 0.01 0.89 1.76 2.26 1.75

0.50 0.55 1.10 1.50 1.90 2.30 1.75

ASA AS

-2

-!

0

I

2

3

4

Ref. 19 19 19 19 19 19 21

5

6

Log t (sec) Figure 2. Viscoehstic master curves of poly(styrene-b-a-methylstyrene). Solid curve: sample BPI; broken curve: sample BPII (21).


9.

sH E N


0

8

16

24 T - T

r

32 e

f

40

187

48

56

CC)

Figure 3. Viscoehstic shift factor data for samples BPI (triangles) and BPII (circles) of poly(styrene-h-a-methylstyrene). The solid curve was calculated from the WLF equation (21). b e c o m p o s e d of t h e c o m p o n e n t i n greater a b u n d a n c e .

A s the proportion

of o n e c o m p o n e n t continues to increase, e v e n t u a l l y the m o r p h o l o g y of s p e r i c a l d o m a i n s of m i n o r c o m p o n e n t e m b e d d e d i n t h e m a t r i x of t h e other

component

appears.

T h e s e structures

have

been

observed for

d i b l o c k c o p o l y m e r s of isoprene a n d styrene cast f r o m toluene (31).

Their

e l e c t r o n m i c r o g r a p h s are s h o w n i n F i g u r e 4. T h e d a r k regions b e l o n g to the p o l y i s o p r e n e ( P I P ) phase w h i c h w a s selectively s t a i n e d b y O s 0 . 4

T h e d o m a i n structure of t h e 20/80 styrene/isoprene

block

copolymer

( F i g u r e 4 a ) shows t i n y spheres of p o l y s t y r e n e ( P S ) b l o c k s d i s p e r s e d i n a m a t r i x of p o l y i s o p r e n e .

E l e c t r o n m i c r o g r a p h s of 40/60 a n d 50/50

c o m p o s i t i o n s ( F i g u r e 4 b a n d 4c ) a p p e a r as a l t e r n a t i n g stripes w h i c h are a c t u a l l y profiles of t h e three d i m e n s i o n a l l a m e l l a r structures. 60/40 b l o c k c o p o l y m e r , c y l i n d r i c a l d o m a i n s of t h e isoprene

F o r the

component

i n P S m a t r i x c a n b e o b s e r v e d ( F i g u r e 4 d ) . T h e d a r k dots represent

ends

of the c y l i n d r i c a l rods. T h e progressive changes i n m o r p h o l o g y w i t h c h a n g i n g c o m p o s i t i o n s also c a n b e a c h i e v e d b y a d d i n g h o m o p o l y m e r s to t h e b l o c k c o p o l y m e r ( 32, 33,34, 35 ).

T h e a d d e d h o m o p o l y m e r is s o l u b i l i z e d i n t o t h e corre-

s p o n d i n g d o m a i n s i n the b l o c k c o p o l y m e r i f t h e m o l e c u l a r w e i g h t of t h e a d d e d h o m o p o l y m e r is e q u a l to or less t h a n that of t h e c o r r e s p o n d i n g


188

MULTIPHASE POLYMERS

Figure 4. Electron micrographs of diblock copolymers of styrene and isoprene cast from toluene and microtomed normal to the surface as indicated (31).

b l o c k i n t h e c o p o l y m e r . F i g u r e 5 a shows t h e e l e c t r o n p h o t o m i c r o g r a p h of a triblock copolymer of styrene-butadiene-styrene m i x e d solvent o f T H F / m e t h y l e t h y l ketone.

( S B S ) cast f r o m a

Incorporation

of a l o w

m o l e c u l a r w e i g h t p o l y s t y r e n e ( P S ) i n t h e b l o c k c o p o l y m e r e n l a r g e d the P S d o m a i n s ( l i g h t r e g i o n s ) , as seen i n F i g u r e 5 b . H o w e v e r , i f t h e a d d e d P S has a m o l e c u l a r w e i g h t that is greater t h a n that i n S B S , t h e n separate d o m a i n s o f p u r e P S appears ( F i g u r e 5 c ) . U n d e r a p p r o p r i a t e c o n d i t i o n s i t is p o s s i b l e t o observe

long-range

o r d e r i n b l o c k c o p o l y m e r s , e.g., i f samples are p r e p a r e d b y m e l t e x t r u s i o n , t h e r m a l a n n e a l i n g , o r s l o w rate o f c a s t i n g (36-42). styrene-butadiene

A n example f o r a

b l o c k c o p o l y m e r c o n t a i n i n g 6 8 % styrene is s h o w n i n

F i g u r e 6. T h e s e structures

a r e o f t e n r e f e r r e d t o as " m a c r o l a t t i c e . "

s o m e instances i m p e r f e c t i o n s

i n the long-range

" g r a i n b o u n d a r i e s " n o r m a l l y f o u n d i n m e t a l l i c systems. m i c r o s c o p i c observations

These

a r e s u p p o r t e d b y s m a l l a n g l e x-ray

( S A X S ) a n d o p t i c a l l i g h t s c a t t e r i n g studies

In

o r d e r m a y a p p e a r as electron scattering

(39,40,41,42).


9.

SHE Ν

Theories

189

Amorphous Hydrocarbon Block Copolymers of Microdomain

Formation

T h e b a s i c d r i v i n g force for m i c r o d o m a i n f o r m a t i o n i n b l o c k c o p o l y mers is the r e d u c t i o n i n the p o s i t i v e surface free energy of the

system

r e s u l t i n g f r o m the increase o f the d o m a i n size. T h i s d o m a i n size increase gives rise to a decrease i n t h e v o l u m e f r a c t i o n o f i n t e r f a c i a l r e g i o n i n w h i c h j u n c t i o n points o f the c o p o l y m e r s m u s t b e d i s t r i b u t e d . I n a d d i t i o n , c o n f i g u r a t i o n s o f the b l o c k chains m u s t also c h a n g e i n o r d e r t o e v e n - u p the density d e f i c i e n c y i n the i n t e r i o r o f the d o m a i n s . A

number

o f statistical t h e r m o d y n a m i c theories

for the domain

f o r m a t i o n i n b l o c k a n d graft c o p o l y m e r s have b e e n f o r m u l a t e d o n t h e basis o f this i d e a . T h e p i o n e e r i n g w o r k i n this area was d o n e b y M e i e r (43).

I n his o r i g i n a l w o r k , h o w e v e r , h e a s s u m e d that the b o u n d a r y be

t w e e n the t w o phases is sharp.

L e a r y a n d W i l l i a m s (43,44) w e r e t h e

first to r e c o g n i z e that the interphase must b e diffuse a n d has finite t h i c k ness.

K a w a i a n d c o - w o r k e r s (31 ) t r e a t e d the p r o b l e m f r o m the p o i n t o f

v i e w of m i c e l l e f o r m a t i o n . A s the solvent evaporates f r o m a b l o c k c o p o l y m e r s o l u t i o n , a c r i t i c a l m i c e l l e c o n c e n t r a t i o n is r e a c h e d .

A t this p o i n t ,

the d o m a i n s are f o r m e d a n d are a s s u m e d to u n d e r g o n o f u r t h e r w i t h c o n t i n u e d solvent e v a p o r a t i o n .

change

M i n i m u m free energies for a n A B -

t y p e b l o c k c o p o l y m e r w e r e c o m p u t e d this w a y . H e l f a n d ( 45,46 ) u s e d a m e a n field a p p r o a c h t o treat t h e p r o b l e m of m i c r o d o m a i n f o r m a t i o n ( F i g u r e 7 ) . F o r a d i b l o c k c o p o l y m e r w i t h a h i g h d e g r e e of p o l y m e r i z a t i o n , the f o l l o w i n g free-energy expression c a n b e w r i t t e n (46) :

· · ·· ·· ·· ·· ·· ······· ·V·A· *· · ·ν···/ ν -

Figure 6.

Electron micrograph of diblock copolymer of styrene and butadiene cast from xylene (courtesy of M . Hoffman)


9.


SHEN

Β DOMAIN \ INTERPHASE

A DOMAIN

link i n a m i x e d homogeneous

193

state to that i n the m i c r o d o m a i n s . T h e

w i d t h of t h e i n t e r f a c i a l r e g i o n is g i v e n b y a, a n d is g e n e r a l l y of the o r d e r r

of nanometers.

A n o t h e r c o n s e q u e n c e of t h e c o n f i n e m e n t of t h e l i n k t o

the interphase is t h e density d e f i c i e n c y i n t h e i n t e r i o r of t h e d o m a i n . T h e system tends to statistically r e d u c e t h e c o n f o r m a t i o n s w h i c h l e a d t o the i n h o m o g e n e o u s

d e n s i t y a n d f a v o r t h e rarer c o n f o r m a t i o n s i n t h e

center of the d o m a i n . T h e loss of c o n f o r m a t i o n a l e n t r o p y w i l l increase w i t h i n c r e a s i n g size of t h e d o m a i n , w h i c h is r e p r e s e n t e d b y t h e t h i r d t e r m of E q u a t i o n 7. T h e s y m b o l b i n this t e r m is the statistical l e n g t h of a m o n o m e r u n i t . T h e last t e r m i n t h e e q u a t i o n is i n d e p e n d e n t of d o m a i n sizes a n d fixes t h e s t a n d a r d state of t h e s y s t e m as that of a h o m o g e n e o u s m i x e d state.

H e r e a is a m e a s u r e of t h e r e p u l s i o n b e t w e e n A a n d Β

b l o c k s . B y m i n i m i z i n g E q u a t i o n 7, d c a n b e c a l c u l a t e d . T a b l e I I I s h o w s that t h e c o m p u t e d values of ds are i n satisfactory a g r e e m e n t w i t h a v a i l able e x p e r i m e n t a l d a t a f o r a n u m b e r of b l o c k c o p o l y m e r s of styrene a n d butadiene. I n t h e i r statistical m o d e l f o r m i c r o p h a s e s e p a r a t i o n of b l o c k c o p o l y mers, L e a r y a n d W i l l i a m s (43) temperature T . B

p r o p o s e d the c o n c e p t of a s e p a r a t i o n

It is d e f i n e d as the t e m p e r a t u r e at w h i c h a

first-order

t r a n s i t i o n occurs w h e n t h e d o m a i n s t r u c t u r e is at e q u i l i b r i u m w i t h

a

h o m o g e n e o u s m e l t , i.e., AG

=

AH

- Τ AS =

0

(8)

or

Γ.=

(AH/AS)

demix


(9)

194

MULTIPHASE POLYMERS

T a b l e III. M i c r o d o m a i n Repeat Distances Copolymers of Styrene a n d Butadiene Mol Wt (kg/mol)

Polymer Lamellar morphology S-B

B-S-B

S-B-S

32-48 35.5-54.5

(nm)

51 55 63 49

44.5 49

71-46

74 46

19.4-72-19.4

40

24-72-24

44

37.5-72-37.5

48

73-72-73

66

38 41 48 64 24 38 25

27-30

17-68-17

30

14-30-14

26

7.2-33

8.6

8-40

10.7

11-47

S-B-S

dexp

(nm)

48.9-32.4

14.1-27.9-14.1

Spherical morphology S-B

i n Block (46)

8.4 9.3 11.1 11.6 11.4 12.4 14.3 13.8

10.8

12-147

11.2

12-163

10.9

13-59

12.8

15-^32

11.2

15-83

12.2

13-75-13

13.5

10-71-10 7-35-7 14-63-14 21-98-21 120-660-120

10 9.3 11.6 17.0 21

13.1 10.7 8.5 13.5 18.1 58

Polymer Engineering and Science

V a l u e s o f t h e s e p a r a t i o n t e m p e r a t u r e f o r a series o f p o l y ( s t y r e n e - b - b u t a diene-b-styrene ) were determined b y light transmission, calorimetry, a n d electron

microscope

observations

A comparison between

(44).

these

e x p e r i m e n t a l a n d c a l c u l a t e d v a l u e s o f T is g i v e n i n T a b l e I V . F u r t h e r s

e v i d e n c e f o r t h e existence o f s u c h " s t r u c t u r e d - u n s t r u c t u r e d " transitions t h r o u g h r h e o l o g i c a l measurements w i l l b e g i v e n i n a later section. Elasticity

of

Heterophase

Block

Copolymers

T h e s t r e s s - s t r a i n b e h a v i o r o f heterogeneous

block copolymers de-

p e n d s o n t h e i r c h e m i c a l c o m p o s i t i o n . T h o s e c o n s i s t i n g o f a soft r u b b e r y c o m p o n e n t a n d a h a r d glassy c o m p o n e n t m a y e i t h e r b e r u b b e r l i k e o r


9.

195


SHEN

plasticlike.

I n t r i b l o c k c o p o l y m e r s w h e r e t h e f o r m e r is t h e m a j o r c o m

p o n e n t , t h e s t r e s s - s t r a i n curves w o u l d e x h i b i t h i g h e l a s t i c i t y u p to n e a r l y 1000%

before fracture.

T h e r u b b e r l i k e e l a s t i c i t y arises f r o m t h e f a c t

that t h e p l a s t i c d o m a i n s " a n c h o r " the r u b b e r y n e t w o r k c h a i n s as p s e u d o c r o s s l i n k s . I n a d d i t i o n , these d o m a i n s also h a v e t h e r e i n f o r c i n g effect o f fillers

(47). / —

L e o n a r d (48) d e r i v e d a n e q u a t i o n of state f o r s u c h systems: (NBT/v ^L ) R

0

(1.0

+

2.5 μ

ρ

14.1

+

^ ) p

(λ -

2

1/λ )

(10)

2

w h e r e / is the elastic force, R is t h e i d e a l gas constant, Τ is t h e a b s o l u t e temperature, L

0

is t h e u n s t r e t c h e d l e n g t h , v a n d t> a r e v o l u m e fractions r

p

of t h e r u b b e r y a n d p l a s t i c c o m p o n e n t s , r e s p e c t i v e l y , Ν is t h e n u m b e r o f r u b b e r chains a n c h o r e d b e t w e e n 2N d o m a i n s , a n d λ is t h e e l o n g a t i o n ratio. T h e t h e o r y w a s d e r i v e d f r o m e n t r o p y c o n s i d e r a t i o n s of t h e hetero geneous system a l t h o u g h the r e s u l t i n g e q u a t i o n is i d e n t i c a l to t h e classi c a l s t a t i s t i c a l t h e o r y of r u b b e r e l a s t i c i t y f o r filled systems. Block copolymers i n w h i c h

the plastic component

is s u f f i c i e n t l y

a b u n d a n t to f o r m c o n t i n u o u s regions c a n b e r e g a r d e d as m i c r o c o m p o s i t e materials.

T h e d i s p e r s e d d o m a i n s i n these m a t e r i a l s

rather than macroscopic i n dimensions.

are m i c r o s c o p i c

A n u m b e r of e x i s t i n g theories

f o r t h e e l a s t i c i t y of composites has b e e n s u c c e s s f u l l y a p p l i e d t o c a l c u l a t e the elastic m o d u l i of these m a t e r i a l s .

T a k a y a n a g i (49) a n d K a w a i (50)

a n d t h e i r c o - w o r k e r s w e r e a m o n g t h e first t o treat the elastic m o d u l i as composites.

T h e y chose a n e q u i v a l e n t m o d e l to represent

composites,

u s i n g t h e d e g r e e o f m i x i n g ( λ ) of t h e d i s p e r s o i d s a n d t h e c o m p o s i t i o n ( φ ) of t h e d i s p e r s o i d s a n d m a t r i x as i n d e p e n d e n t v a r i a b l e s . P e r f e c t m a t e r i a l c o n t a c t b e t w e e n t h e phases is a s s u m e d . W h e n t h e e q u i v a l e n t m o d e l is s t r e t c h e d , t h e elastic f o r c e c a n b e b o r n e b y t h e m a t r i x a l o n e o r b y b o t h the m a t r i x a n d t h e d i s p e r s e d phases.

T h e m o d u l u s of t h e e q u i v a l e n t

m o d e l c a n b e c a l c u l a t e d b y either the Series M o d e l o r t h e P a r a l l e l M o d e l . F o r t h e Series M o d e l , t h e m o d u l u s of the c o m p o s i t e i s :

a n d for the Parallel M o d e l :

(12)

w h e r e s u b s c r i p t s d a n d m refer to d i s p e r s e d a n d m a t r i x phases respec t i v e l y , u are t h e v o l u m e fractions of t h e t w o phases, a n d λφ = s


v. d

The

196

MULTIPHASE POLYMERS

Table IV.

Separation Temperatures in Triblock

Molecular Polymer

M, -

M

B

Weight — - Μ,

Volume Fraction Styrene (φ )

X 10'

3

M

n

8

K r a t o n 1101

12.5-75-12.5

100

0.245

K r a t o n 1102

5.4-32.3-5.4 9.4-56.2-9.4 7-36-6 16-78-16

43 75 49 112

0.245 0.245 0.25 0.275

58

0.463

TR-41-1647 TR-41-1648 TR-41-1649

14-30-14

u n p r i m e d λ a n d φ refer t o t h e Series M o d e l a n d t h e p r i m e d ones t o t h e P a r a l l e l M o d e l . T h e t w o m o d e l s are i n fact e q u i v a l e n t , i f λ ' =

1 — v

d

—

φ (51, 5 2 ) . E q u a t i o n s 11 a n d 12 h a v e b e e n u s e d b y a n u m b e r of authors (51,52,53) t o c o m p a r e w i t h e x p e r i m e n t a l l y d e t e r m i n e d elastic of heterophase

block copolymers.

moduli

H o w e v e r , the S e r i e s - P a r a l l e l

Model

is o n l y v a l i d f o r soft dispersoids i n h a r d m a t r i x i n c o n c e n t r a t i o n ranges w h e r e g e o m e t r y of the d i s p e r s e d phase is n o t i m p o r t a n t . F o r t h e inverse case of h a r d d i s p e r s o i d s i n soft m a t r i x , t h e m o d u l i d a t a c a n n o t b e ade quately predicted b y the model.

Halpin

(54)

a n d Nielsen

(55,56)

p r o p o s e d a m o r e g e n e r a l e q u a t i o n that covers the c o m p l e t e c o m p o s i t i o n range.

B u t as t h e c o m p o s i t i o n of t h e b l o c k c o p o l y m e r changes, a phase

i n v e r s i o n c a n o c c u r at a certain p o i n t . F o r s u c h a s i t u a t i o n , t h e use of some e m p i r i c a l m i x i n g rules is necessary.

R e c e n t l y , F a u c h e r (57)

o u t that b y u s i n g t h e " p o l y a g g r e g a t e " m o d e l of K e r n e r (58) necessary to postulate the existence of t h e m a t r i x phase. m o d e l i m p l i e s t h e e q u i v a l e n c e of t h e t w o phases.

pointed i t is n o t

I n fact, t h e

Since n e i t h e r one c a n

b e r e g a r d e d as the m a t r i x f o r the other, t h e d i f f i c u l t y of t r e a t i n g the phase i n v e r s i o n is c i r c u m v e n t e d . T h e r e s u l t i n g equations are l e n g t h y , b u t the p r e d i c t i o n s a p p e a r to agree w e l l w i t h literature d a t a . F o r p l a s t i c - l i k e heterophase

b l o c k c o p o l y m e r s , the stress-strain b e

h a v i o r is s t r o n g l y d e p e n d e n t o n m o r p h o l o g y . K a w a i a n d c o - w o r k e r s

(59)

f o u n d that f o r a 50/50 d i b l o c k c o p o l y m e r of styrene/isoprene cast f r o m a m i x e d solvent system of toluene a n d m e t h y l e t h y l ketone, t h e stressstrain c u r v e shows regions of y i e l d i n g a n d d r a w i n g . T r a n s m i s s i o n elec t r o n m i c r o g r a p h s s h o w that there is extensive e l o n g a t i o n of the p l a s t i c d o m a i n s i n t h e r e g i o n of d r a w i n g . T h e s e authors h y p o t h e s i z e d t h a t s u c h


9.


SHEN

197

Copolymers of Styrene and Butadiene (44) T

s

(K) Method

Model

Observed

590

583-593 > 343 373-423 > 340 < 310 > 600 > 347 < 530 > 500 573-598

265 430 298 735 515

light transmission calorimetry light transmission calorimetry calorimetry light transmission calorimetry electron m i c r o s c o p e calorimetry light transmission Journal of Polymer Science, Polymer Physics Edition

m o r p h o l o g i c a l changes c a n b e a t t r i b u t a b l e t o heat t r a n s f o r m e d f r o m t h e s t r a i n energy, t h e r e b y c a u s i n g t h e flow t o take p l a c e u p o n s t r e t c h i n g . U n d e r appropriate conditions of sample preparation, the phenomena of " s t r a i n - i n d u c e d p l a s t i c - r u b b e r t r a n s i t i o n " c a n b e o b s e r v e d . F o r b l o c k c o p o l y m e r s e x h i b i t i n g y i e l d i n g a n d d r a w i n g regions i n t h e first s t r e s s s t r a i n c y c l e , t h e r e is u s u a l l y c o n s i d e r a b l e s t r a i n - s o f t e n i n g i n t h e s e c o n d a n d s u b s e q u e n t d e f o r m a t i o n (60, 61, 62, 63). T h e d r a w i n g process o c c u r s w h e n t h e n a r r o w i n g o f t h e cross-sectional a r e a o f t h e s a m p l e s u d d e n l y appears at o n e p o i n t i n t h e s a m p l e a n d s u b s e q u e n t l y propagates the entire s a m p l e is t r a n s f o r m e d .

until

S u c h p h e n o m e n a a r e s i m i l a r t o that

i n c o n v e n t i o n a l plastics e x c e p t that i n this instance t h e n e c k e d r e g i o n s a r e not plastic b u t rubbery.

A f t e r t h e n e c k i n g process

has p r o p a g a t e d

t h r o u g h o u t , t h e s a m p l e w h i c h w a s i n i t i a l l y a p l a s t i c has n o w b e c o m e a r u b b e r . T h e e l e c t r o n m i c r o g r a p h s s h o w that there is extensive d i s r u p t i o n of t h e c o n t i n u o u s p o l y s t y r e n e d o m a i n s i n t h e s t r e t c h e d s a m p l e .

If the

s a m p l e is a n n e a l e d at e l e v a t e d t e m p e r a t u r e , t h e n t h e s a m p l e returns t o t h e p l a s t i c state (63). T h e s e m o r p h o l o g i c a l changes also c a n b e o b s e r v e d b y small-angle x-ray scattering sample

( S A X S ) i n F i g u r e 8. T h e u n s t r e t c h e d

of a p o l y ( styrene-b-butadiene-b-styrene )

blended

with 20%

p o l y s t y r e n e shows a r a t h e r s h a r p p e a k b u t b e c o m e s b r o a d e n e d u p o n stretching.

T h e scattering c u r v e f o r t h e a n n e a l e d s a m p l e , h o w e v e r , is

m o r e s i m i l a r t o that o f t h e u n s t r e t c h e d

sample,

indicating a partial

r e s t o r a t i o n o f t h e o r i g i n a l m o r p h o l o g y (64). T h e m e c h a n i c a l p r o p e r t i e s of a m a c r o l a t t i c e o f S B S has b e e n i n v e s t i g a t e d ( 6 5 ) . T h e s a m p l e consists of a h e x a g o n a l a r r a y o f p o l y s t y r e n e c y l i n d e r s e m b e d d e d i n t h e p o l y b u t a d i e n e m a t r i x . T h e stress-strain c u r v e s


198

MULTIPHASE POLYMERS

10

ο α> Φ

Ν

Φ C

3 Ο Ο

«Γ

5

g χ

~0

0.20 Scattering

0.40 Angle

Figure 8. Small-angle x-ray scattering (SAXS) data for poly(styrene-b-butadiene-b-styrene) blended with 20% polystyrene and cast from THF/methyl ethyl ketone (after Ref. 64) of t h e m a c r o l a t t i c e s h o w a d e c i s i v e a n i s o t r o p y . T h e m o d u l i d a t a w e r e f o u n d to b e i n excellent agreement w i t h t h e T a k a y a n a g i - K a w a i m o d e l i f t h e l o n g i t u d i n a l s a m p l e is r e p r e s e n t e d b y p a r a l l e l c o u p l i n g a n d t h e transverse s a m p l e b y series c o u p l i n g . Yiscoelasticity

of Heterophase

Block

Copolymers

I n a n e a r l i e r section, w e h a v e s h o w n that t h e viscoelastic b e h a v i o r of h o m o g e n e o u s b l o c k c o p o l y m e r s c a n b e t r e a t e d b y t h e m o d i f i e d R o u s e B u e c h e - Z i m m m o d e l . I n addition, the T i m e - T e m p e r a t u r e Superposition P r i n c i p l e has also b e e n f o u n d to b e v a l i d f o r these systems.

However, if

t h e b l o c k c o p o l y m e r shows m i c r o p h a s e s e p a r a t i o n , these c o n c l u s i o n s n o l o n g e r a p p l y . T h e basic tenet of t h e T i m e - T e m p e r a t u r e S u p e r p o s i t i o n P r i n c i p l e is v a l i d o n l y i f a l l o f t h e r e l a x a t i o n m e c h a n i s m s are affected b y t e m p e r a t u r e i n t h e same m a n n e r .

M a t e r i a l s o b e y i n g this P r i n c i p l e are

s a i d t o b e t h e r m o r h e o l o g i c a l l y s i m p l e . I n other w o r d s , r e l a x a t i o n times at o n e t e m p e r a t u r e are r e l a t e d to t h e c o r r e s p o n d i n g r e l a x a t i o n times at a reference

temperature

b y a constant

ratio

(the shift factor).


For

9.

SHEN

199


heterogeneous systems, the constituent p o l y m e r s exist i n separate phases a n d m u s t u n d e r g o r e l a x a t i o n processes i n d i v i d u a l l y .

Such

heterogeneous

b l o c k c o p o l y m e r s therefore d o n o t satisfy t h e s a i d s t i p u l a t i o n a n d s h o u l d b e c o n s i d e r e d t h e r m o r h e o l o g i c a l l y c o m p l e x (66,67,68, 69). T h e i r m a s t e r c u r v e s a r e i n f a c t different i n s h a p e at d i f f e r e n t t e m p e r a t u r e s b e c a u s e t h e r e l a x a t i o n times o f t h e t w o different phases a r e affected b y t e m p e r a t u r e d i f f e r e n t l y . H o w e v e r , t h e e x p e r i m e n t a l l y accessible r a n g e ( w h i c h F e s k o a n d T s c h o e g l (66) c a l l " t h e e x p e r i m e n t a l w i n d o w " ) is s m a l l . W i t h i n t h i s w i n d o w the n e i g h b o r i n g isotherms appear to b e superposable b y simple h o r i z o n t a l s h i f t i n g a l o n g t h e l o g a r i t h m i c t i m e axis, b u t t h e result o f s u c h s h i f t i n g w o u l d g i v e rise t o a n erroneous master c u r v e . A u s e f u l w a y t o represent t h e v i s c o e l a s t i c i t y o f heterogeneous system is t h e c o n t o u r p l o t , a n e x a m p l e f o r w h i c h is s h o w n i n F i g u r e 9. S u c h a p l o t shows s i m u l -

-80

-60 -40 -20

0

TEMPERATURE

20

40

60

80

- *C

Transactions of the Society of Rheology

Figure 9. Contour plot (70) of dynamic loss compliance as a function of frequency and temperature for poly(styrene-b-butadiene-styrene).


MULTIPHASE POLYMERS

200

taneously h o w a g i v e n viscoelastic p a r a m e t e r , i n this case t h e d y n a m i c loss c o m p l i a n c e , d e p e n d s o n b o t h t h e f r e q u e n c y

(or time)

a n d tem

perature ( 7 0 ) . T h e effect o f m o r p h o l o g y o n t h e v i s c o e l a s t i c i t y of b l o c k c o p o l y m e r s has b e e n i n v e s t i g a t e d (71, 72).

T h e most i m p o r t a n t factor appears to b e

the c o n n e c t i v i t y of d o m a i n s .

If t h e s a m p l e w a s cast f r o m a solvent,

w h i c h results i n extensive i n t e r c o n n e c t i o n s a m o n g t h e h a r d d o m a i n s ( for instance t h e glassy P S d o m a i n s i n S B S ) , t h e n the m o d u l u s i n t h e r e g i o n ( above the T

g

of P S ) w i l l b e relatively high.

O n t h e other h a n d , i f t h e

h a r d d o m a i n s are d i s p e r s e d i n a soft m a t r i x ( t h e r u b b e r y P B d o m a i n s ) ,

then the m o d u l i (71).

shear

i n t h e same r e g i o n w i l l b e l o w e r f o r t h e same

In a d d i t i o n , t h e r a t i o of storage m o d u l i ( E ' / G ' )

sample

i n tensile a n d

m o d e s w a s f o u n d t o b e n e a r l y three f o r t h e P B - c o n t i n u o u s S B S ,

w h i c h is as e x p e c t e d f o r elastomers.

H o w e v e r , t h e ratio f o r t h e same

s a m p l e w h i c h w a s cast f r o m solvents that r e n d e r t h e m P S c o n t i n u o u s is n o w greater b y a n o r d e r o f m a g n i t u d e (72).

T h e anomalously high value

is a t t r i b u t e d t o t h e a n i s o t r o p i c P S - d o m a i n c o n n e c t i v i t y i n t h e f o r m o f l o n g fibrils o r l a m e l l a e . Rheology

of

Heterogeneous

Block

Copolymer

Melts

B e c a u s e t h e existence o f d o m a i n structure i n heterogeneous

block

c o p o l y m e r s persists e v e n i n t h e m o l t e n state, t h i e r r h e o l o g i c a l b e h a v i o r is

rather

unique when compared with

ι

I

1

I

1er

2

icr

1

1

polymer melts.

1

I

I

I

ι

ίο

ίο

Shear Rate

Figure 10.

homogeneous

Γ

I 2

ιο

1 3

(sec ) - 1

Shear viscosity as a function steady-state shear rate for poly(styrene-b-butadiene-b-styrene) at 150°C (after Ref. 47)


9.

201


SHEN

H o l d e n et a l . (47) first n o t e d t h e p e c u l i a r characteristics i n t h e steady shear b e h a v i o r o f t h e S B S b l o c k c o p o l y m e r m e l t s . F o r a c e r t a i n c o m p o s i t i o n of styrene a n d b u t a d i e n e , n o l i m i t i n g N e w t o n i a n v i s c o s i t y w a s f o u n d at l o w shear rates.

F o r some of t h e others, there exist t w o d i s t i n c t v i s

cosity v s . shear rate r e l a t i o n s h i p s ( F i g u r e 10). A r n o l d a n d M e i e r c a r r i e d o u t t h e experiments

(73)

i n o s c i l l a t o r y shear a n d f o u n d t h e same

7S-43B-7S

ω

(RAD/ÊC) 0.148

CO

ο Q. t ω Ο CO

5

10

14.87

-ο 2 < Ζ

46.9

ο

Ι * — :

10

10*

100

110

120 130 140 150 T E M P E R A T U R E , Γ(°0)

160

170

Journal of Polymer Science, Polymer Physics Edition

Figure 11. Dynamic shear viscosity as a function of temperature for poly(styrene-b-butadiene-b-styrene) at various angular frequencies (77)


202

MULTIPHASE POLYMERS

anomaly.

I n a d d i t i o n , these authors f o u n d that t h e viscosities

w e r e m u c h h i g h e r t h a n that o f e i t h e r h o m o p o l y m e r

obtained

o f the same m o l e c

u l a r w e i g h t as the b l o c k c o p o l y m e r . T h e absence of a N e w t o n i a n v i s c o s i t y w a s e x p l a i n e d i n terms of a fluid d o m a i n s t r u c t u r e i n t h e m e l t that w a s p r o g r e s s i v e l y d i s r u p t e d , c a u s i n g t h e v i s c o s i t y to decrease m a r k e d l y w i t h i n c r e a s i n g shear rate.

T h e h i g h v i s c o s i t y is a t t r i b u t e d t o t h e a d d i t i o n a l

w o r k n e e d e d t o o v e r c o m e t h e t h e r m o d y n a m i c resistance t o t h e m i x i n g process f o r the different b l o c k species to flow past e a c h other. K r a u s et a l . (74, 75) s t u d i e d t h e steady

flow

a n d oscillatory

flow

behavior of linear triblocks of S - B - S a n d B - S - B a n d r a d i a l block copoly mers o f the t y p e ( B - S - ) , ( S - B - ) , a n d ( S - B - ) . 3

3

4

F o r block copolymers

of t h e s a m e m o l e c u l a r w e i g h t a n d c o m p o s i t i o n , those w i t h e n d b l o c k s o f P S a l w a y s h a v e h i g h e r viscosities. H o w e v e r , w h e n c o m p a r e d w i t h corre sponding linear block

c o p o l y m e r s , t h e viscosities

of the r a d i a l block

c o p o l y m e r s are g e n e r a l l y l o w e r . M o r e r e c e n t l y , i t has b e e n d e m o n s t r a t e d that m a n y o f t h e u n u s u a l r h e o l o g i c a l b e h a v i o r o f b l o c k c o p o l y m e r s w i l l d i s a p p e a r w h e n the meas u r e m e n t s w e r e c a r r i e d o u t at temperatures

higher than the separation

t e m p e r a t u r e p r o p o s e d b y L e a r y a n d W i l l i a m s (43).

F i g u r e 11 s h o w s that

for b u l k S B S block copolymers w i t h a composition of 7 - 4 3 - 7

(xlO ), 3

the t r a n s i t i o n occurs a r o u n d 1 4 5 ° C ( e s p e c i a l l y clear at l o w f r e q u e n c i e s ) ( 76, 77 ). T h e s e d a t a a r e consistent w i t h those o f P i c o a n d W i l l i a m s o n plasticized block copolymers

(78).

Acknowledgment T h i s w o r k w a s s u p p o r t e d b y the Office o f N a v a l R e s e a r c h .

W e wish

to t h a n k M . H o f f m a n , R . E . C o h e n , E . H e l f a n d , a n d C . I. C h u n g f o r t h e use o f t h e i r

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figures.

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RECEIVED April 14, 1978.


Properties and Morphology of Amorphous Hydrocarbon Block

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