Multiphase Polymers: Blends and Ionomers - ACS Publications

Chapter 7

Melt Flow of Polyethylene Blends L. A. Utracki

Downloaded by MONASH UNIV on March 2, 2016 | http://pubs.acs.org Publication Date: July 21, 1989 | doi: 10.1021/bk-1989-0395.ch007

Industrial Materials Research Institute, National Research Council of Canada, Boucherville, Québec J4B 6Y4, Canada

The rheology of polyethylene blends i s discussed with an emphasis on those containing the linear low density polyethylenes, LLDPE. Flow of LLDPE with other types of LLDPE's, with low density polyethylene, LDPE, and with polypropylene, PP, was studied in steady state shear, dynamic shear and uniaxial extensional fields. Interrelations between diverse rheological functions are discussed i n terms of the linear viscoelastic behavior and i t s modification by phase separation into complex morphology. One of the more important observations i s the difference i n elongational flow behavior of LLDPE/PP blends from that of the other blends; the strain hardening (important for e.g. film blowing and wire coating) occurs i n the latter ones but not i n the former. P o l y e t h y l e n e s , PE, c o n s t i t u t e an important p a r t o f t h e p l a s t i c s market (see T a b l e I ) . S i n c e t h e i r d i s c o v e r y i n 1933 t h e y have seen c o n t i n u o u s r i s e i n consumption t o t h e p r e s e n t l e v e l o f 25M tons p e r annum, o r 42% o f a l l p l a s t i c s (1_). T h i s extended p e r i o d o f growth o r i g i n a t e s i n continuous development and m o d i f i c a t i o n o f t h e s e r e s i n s , r e s u l t i n g from a w i d e n i n g range o f p o l y m e r i z a t i o n t e c h n i q u e s . The h i s t o r y o f PE c a n be d i v i d e d i n t o t h r e e p e r i o d s : 1. t h e i n i t i a l , c h a r a c t e r i z e d by predominence o f t h e r a d i c a l p o l y m e r i z a t i o n of e t h y l e n e , C , a t h i g h temperature and p r e s s u r e , 2. development o f c o o r d i n a t i o n c o p o l y m e r i z a t i o n o f C w i t h o t h e r c t - o l e f i n s , and 3. development o f polymer b l e n d i n g t e c h n o l o g y . I t i s interesting that new methods have been developed w i t h o u t t h e o l d e r ones becoming obsolete. Thus i t i s d i f f i c u l t t o p u t f i r m d a t e s on t r a n s i t i o n s between these t h r e e p e r i o d s . Development o f Z i g g l e r - N a t t a c a t a l y s t s r e s u l t e d i n c o m m e r c i a l i z a t i o n o f h i g h d e n s i t y p o l y e t h y l e n e , HDPE, w h i c h had t o be "toughened" by c o p o l y m e r i z a t i o n w i t h butene, C^. Next was development o f t h e l i n e a r l o w d e n s i t y p o l y e t h y l e n e s , LLDPE, by DuPont Canada i n t h e l a t e 1950's. The polymer was prepared by c o o r d i n a t i o n p o l y m e r i z a t i o n i n s o l u t i o n o f C w i t h 10 t o 20 mol% o f C , C o r C . I n 1979 U n i o n C a r b i d e p a t e n t e d the gas phase f l u o d i z e d 2

2

2

4

6

8

0097-6156/89A)395-0153$14.70A) © 1989 American Chemical Society

In Multiphase Polymers: Blends and Ionomers; Utracki, L. A., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.


Low d e n s i t y PE

Very low d e n s i t y PE

U l t r a low d e n s i t y PE

3.

4.

5.

3

low p r e s s u r e ; gas phase, s o l u t i o n o r s u s p e n s i o n

high pressure ; pipe o r autoclave reactor

low p r e s s u r e ; gas phase o r s o l u t i o n

low p r e s s u r e ; gas phase o r s o l u t i o n

LLDPE

LDPE

VLDPE

ULDPE

process

process

low p r e s s u r e ; gas phase, s o l u t i o n o r s u s p e n s i o n

Process

HDPE

Code

( a ) i n kg/m ; (b) i n m i l l i o n t o n s p e r annum.

Linear low d e n s i t y PE

2.

Note:

High d e n s i t y PE

1.

No. Type

Table I . G l o b a l Consumption o f P o l y e t h y l e n e (PE)


-885

900-915

915-930

915-940

940-970

a

0.03

12.3

3.4

8.95

1986

^)

?

0.2

10.0

7.5

9.96

1990

Density^ ^Consumption


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Melt Flow ofPolyethylene Blends

155

bed p o l y m e r i z a t i o n p r o c e s s * I t n o t o n l y made LLDPE more p o p u l a r around the w o r l d but a l s o l e d t o an i n g r e s s o f b l e n d i n g methods a s w e l l a s t o development o f new PE copolymers w i t h v e r y low d e n s i t y , butene based, VLDPE, and u l t r a l o w d e n s i t y , o c t e n e b a s e d , ULDPE. B o t h VLDPE and ULDPE a r e b a s i c a l l y LLDPE copolymers w i t h l o w crystallinity. I t i s e s t i m a t e d t h a t 60 t o 7 0 % LLDPE ( i n c l u d i n g VLDPE and ULDPE) e n t e r s t h e market a s b l e n d s . One may d i s t i n g u i s h s e v e r a l c a t e g o r i e s o f PE-blends. (i) PE blends w i t h a small q u a n t i t y o f " e x t e r n a l l u b r i c a n t " : f l u o r o - p o l y m e r s , s i l o x a n e s , PE-waxes, e t c . These blends a r e p r i m a r i l y f o r m u l a t e d f o r improvement o f p r o c e s s a b i l i t y w i t h o u t a f f e c t i n g the PE performance (2^). ( i i ) PE b l e n d s w i t h h i g h c o n c e n t r a t i o n o f r i g i d polymer. To t h i s category b e l o n g blends o f e n g i n e e r i n g r e s i n s w i t h up t o 10% o f non-compatibilized PE a c t i n g as a toughening agent. Development o f PE-ionomers and m a l e a t e d PE a l l o w s f o r i n c r e a s e o f PE c o n t e n t , g e n e r a t i n g a new c l a s s o f m a t e r i a l s . ( i i i ) PE b l e n d s w i t h up t o 30 wt% o f a r i g i d polymer. The a d d i t i o n a l polymer p l a y s the f i l l e r r o l e i n c r e a s i n g b o t h the modulus a n d t h e heat d e f l e c t i o n temperature. At l o w c o n c e n t r a t i o n , s a y below 5% o f r i g i d polymer, t h e c o m p a t i b i l i z a t i o n i s seldom n e c e s s a r y , but i t i s a must f o r b l e n d s a t h i g h e r l o a d i n g s . ( i v ) LLDPE b l e n d s w i t h o t h e r p o l y o l e f i n s o r e l a s t o m e r s . These blends a r e m a i n l y d e s i g n e d f o r improved p r o c e s s a b i l i t y v i a i n c r e a s e o f the melt s t r e n g t h i n f i l m b l o w i n g o r w i r e c o a t i n g applications. (v) PE b l e n d s w i t h p o l y p r o p y l e n e , PP, and/or w i t h one o f t h e i r copolymers, EPR, EPDM, e t c . c o n s t i t u t e a l a r g e and i m p o r t a n t segment o f the p l a s t i c s market. I n t h i s c h a p t e r o n l y blends ( i v ) and (v) w i l l be d i s c u s s e d . PART I , LITERATURE SURVEY The methods o f PE p o l y m e r i z a t i o n and c h a r a c t e r i z a t i o n o f PE s t r u c t u r e s can be found i n r e c e n t p u b l i c a t i o n s ( 3 - 6 ) . The melt f l o w o f PE's and t h e i r blends has been reviewed by P l o c h o c k i (7-9) and U t r a c k i ( 1 0 , 11). In the f o l l o w i n g t e x t , r e c e n t i n f o r m a t i o n o n PE/PE and PE/PP m e l t r h e o l o g y w i l l be o u t l i n e d . Polyethylene/Polyethylene Blends S i n c e the homologous polymer blends a r e known t o be m i s c i b l e i t i s n o t s u r p r i s i n g t h a t m i x t u r e s o f HDEE w i t h HDPE o r LDPE w i t h LDPE a r e m i s c i b l e a s w e l l (12, 1 3 ) . However, due t o t h e d i v e r s i t y o f p o l y m e r i z a t i o n methods and t h e v a r i e t y o f r e s u l t i n g molecular c h a r a c t e r i s t i c s LLDPE/LLDPE systems a r e n o t always m i s c i b l e ( 1 0 , 14-15). I n our l a b o r a t o r y t h r e e s e r i e s o f blends were prepared by i d e n t i c a l procedure o f m i x i n g the same LLDPE w i t h two o t h e r LLDPE r e s i n s and w i t h LDPE. The z e r o - s h e a r v i s c o s i t y v s . composition dependence, n v s . w , o f t h e s e systems i s p r e s e n t e d i n F i g . 1. Only the LLDPE s prepared w i t h t h e same T i - c a t a l y s t were found t o be m i s c i b l e ( c u r v e 2 ) . N e i t h e r b l e n d o f LLDPE w i t h LDPE ( c u r v e 3) n o r LLDPE prepared w i t h a vanadium c a t a l y s t LLDPE ( c u r v e 1) were miscible. There a r e i n d i c a t i o n s i n t h e l i t e r a t u r e (8) that 0

2

1



156

MULTIPHASE POLYMERS: BLENDS AND IONOMERS

F i g u r e 1. C o m p o s i t i o n a l dependence of the z e r o - s h e a r v i s c o s i t y f o r blends o f a l i n e a r low d e n s i t y p o l y e t h y l e n e (LLDPE) w i t h : (1) and ( 2 ) d i f f e r e n t LLDPE r e s i n s , and ( 3 ) w i t h low d e n s i t y p o l y e t h y l e n e , LDPE.


7.

UTRACKI


157

v a r i a t i o n s o f T)Q w i t h c o m p o s i t i o n such a s shown i n F i g . 1 a r e a r e f l e c t i o n o f s i m i l a r d e n s i t y changes caused by t h e thermodynamic interactions. Dumoulin e t a l . ( 1 6 ) s t u d i e d morphology and p r o p e r t i e s o f HDPE b l e n d e d w i t h a n o t h e r HDPE r e s i n o f n e a r l y i d e n t i c a l d e n s i t y b u t t e n times h i g h e r m o l e c u l a r w e i g h t . The m e l t - b l e n d i n g was c a r r i e d o u t by t h r e e d i f f e r e n t methods. The polymers were found t o be i m m i s c i b l e ; the u l t r a h i g h m o l e c u l a r weight component, UHMWPE, p a r t i a l l y d i s s o l v e d i n t h e normal m o l e c u l a r weight ( M - 280 kg/mole) polymer w i t h t h e r e s t behaving as r e i n f o r c i n g f i l l e r p a r t i c l e s . These o b s e r v a t i o n s were c o n f i r m e d by Vadhar and Kyu (17) who concluded t h a t o n l y by d i s s o l v i n g UHMWPE and LLDPE i n a common s o l v e n t , t h e n c a s t i n g , c o u l d t h e u n i f o r m , m i s c i b l e b l e n d be o b t a i n e d . S i n c e d i s s o l u t i o n o f UHMWPE s t r o n g l y a f f e c t s t h e m o l e c u l a r weight d i s t r i b u t i o n , MWD, o f t h e m a t r i x polymer, any r h e o l o g i c a l f u n c t i o n s e n s i t i v e t o MWD c a n be used t o f o l l o w t h e d i s s o l u t i o n process. The dynamic v i s c o e l a s t i c d a t a p r o v i d e d a s i m p l e and e a s y t o o l ( 1 0 , 1 1 ) . As w i l l be d i s c u s s e d l a t e r , t o a c c o m p l i s h t h i s t h e dynamic d a t a were examined u s i n g e i t h e r : ( i ) Zeichner-Patel cross-point coordinates, ( i i ) Cole-Cole p l o t , o r ( i i i ) the r e l a x a t i o n spectrum. The s t r e s s growth o r r e l a x a t i o n f u n c t i o n s i n s h e a r o r e x t e n s i o n a l s o depend on MWD. These a s w e l l were used i n s t u d i e s o f b l e n d m i s c i b i l i t y by r h e o l o g i c a l means ( 1 1 ) . Use o f r h e o l o g i c a l f u n c t i o n s f o r d e t e c t i n g t h e s t a t e o f PE-blend m i s c i b i l i t y i n t h e melt i s p a r t i c u l a r l y a t t r a c t i v e . The o n l y o t h e r a v a i l a b l e method i s t h e d i r e c t and c o s t l y , Small A n g l e N e u t r o n S c a t t e r i n g , SANS ( 1 8 ) . The l a t t e r method r e q u i r e s d e u t e r a t i o n o f one component w h i c h may a f f e c t miscibility (19). A l l available i n f o r m a t i o n o n m i s c i b i l i t y o f PE b l e n d s i n d i c a t e s t h a t i n t h e absence o f s t r o n g thermodynamic i n t e r a c t i o n s b o t h t h e d i s s o l u t i o n and t h e phase s e p a r a t i o n a r e d i f f u s i o n c o n t r o l l e d . F r e q u e n t l y , one c a n g e n e r a t e homogeneous m e l t v i a d i s s o l u t i o n i n a common s o l v e n t ( 2 0 ) w h i l e t h e melt b l e n d i n g w i l l r e s u l t i n a p h a s e - s e p a r a t e d m a t e r i a l . There i s d i r e c t e v i d e n c e o f t r u e m i s c i b i l i t y i n homologous polymer b l e n d s , w h i l e even a s m a l l change i n p o l y m e r i z a t i o n method, polymer c o m p o s i t i o n o r s t r u c t u r e may l e a d t o apparent i m m i s c i b i l i t y ( 1 4 , 15). Since f o r t h e h i g h m o l e c u l a r w e i g h t , i n d u s t r i a l PE t h e c o n f o r m a t i o n a l e n t r o p y o f m i x i n g i s n e g l i g i b l y s m a l l and t h e r e a r e no specific i n t e r a c t i o n s between two p o l y e t h y l e n e s of different s t r u c t u r e , one c a n a p p r e c i a t e t h a t i n these systems t h e m i s c i b i l i t y i s c o n t r o l l e d by s m a l l d e p a r t u r e s from zero o f t h e f r e e energy o f mixing. B l e n d s o f HDPE with LDPE were s t u d i e d by Dobrescu ( 1 2 ) by means of a c a p i l l a r y viscometer. The c o n s t a n t s t r e s s v i s c o s i t y , l o g n ( a = c o n s t ) v s . w p l o t i n d i c a t e d a s t r o n g p o s i t i v e d e v i a t i o n , PDB, from t h e l o g - a d d i t i v i t y r u l e :


w

1 2

2

log

n - I Wjlog

n i

=

(D

where n n ( c r ) i s t h e c o n s t a n t s t r e s s v i s c o s i t y o f t h e b l e n d and n^, i = 1, 2 t h a t o f t h e components. The blends were r e p o r t e d immiscible. The h i g h e r t h e v i s c o s i t y r a t i o ni/n-j> t h e l a r g e r was t h e PDB d e v i a t i o n . Kammer and Socher ( 2 1 ) s t u d i e d t h e two-phase HDPE/LDPE b l e n d s u s i n g t h e c o n e - a n d - p l a t e , steady s t a t e r o t a t i o n a l 12


158


rheometer. P l o t s o f the z e r o shear v i s c o s i t y , n , t h e f i r s t normal s t r e s s d i f f e r e n c e c o e f f i c i e n t i|> and t h e p r i n c i p a l r e l a x a t i o n t i m e , T v s . w , a l l i n d i c a t e d PDB. In s p i t e o f i m m i s c i b i l i t y the shear v i s c o s i t y d a t a i n a temperature range from 160 t o 200°C c o u l d be superimposed on a master c u r v e ( 2 2 , 2 3 ) : 0

10

2

n/n

* f(yn /T)

0

(2)

0

a n
1 and f o r those w i t h X < 1; i n t h e f i r s t case t h e d i s p e r s e d phase e x i s t e d i n a form o f f i b r i l l a s , i n t h e second a s s m a l l d r o p l e t s . The d i f f e r e n c e i n s t r u c t u r e o r i g i n a t e d i n t h e k i n e t i c s o f breakage o f f i b r i l l a s c r e a t e d a t t h e e n t r a n c e t o capillary. For systems whose X < 1 t h e f l u i d i t y a d d i t i v i t y e q u a t i o n (34) was found t o be obeyed: 1/n - B i l W i / n i

(6)

w i t h W£ r e p l a c e d by $i and t h e s l i p c o e f f i c i e n t For X > 1 a t concentrations w < 0.5 E q u a t i o n ( 1 ) y i e l d e d good a p p r o x i m a t i o n ; a t h i g h e r PP c o n t e n t , E q u a t i o n 6 was obeyed. The e x t r u d a t e s w e l l , B - B ( a ) , f o r HDPE and h i g h PP-content b l e n d s , w ^ 0.75, was independent o f temperature. The p l o t f o r w - 0.25 and 0.5 was temperature s e n s i t i v e , i n d i c a t i n g T-dependent morphology ( 3 2 , 3 3 ) . At h i g h PP c o n t e n t and l o w s t r a i n s t h e l o w e r v i s c o s i t y HDPE drops became deformed a t t h e c a p i l l a r y e n t r a n c e . R e t r a c t i o n o f these f i b e r s caused l a r g e e x t r u d a t e s w e l l . At h i g h s t r a i n s b o t h phases were s t r a i n e d , y i e l d i n g average, smaller B values. For h i g h HDPE c o n t e n t B d e c r e a s e d w i t h t e m p e r a t u r e , T, p r o b a b l y due t o i n c r e a s e d i n t e r l a y e r s l i p caused by l o w e r i n g t h e viscosity. Blends o f t h r e e PP and two HDPE r e s i n s h a v i n g d i f f e r e n t v a l u e s of n were s t u d i e d i n a c a p i l l a r y v i s c o m e t e r ( 3 5 ) . Independently o f the v i s c o s i t y r a t i o , X, a t 200°C a l l blends showed s m a l l n e g a t i v e d e v i a t i o n from t h e l o g - a d d i t i v i t y r u l e , NDB. The n o n - e q u i l i b r i u m e x t r u d a t e s w e l l a t low s t r e s s (measured a f t e r quenching) showed s m a l l p o s i t i v e d e v i a t i o n from t h e a d d i t i v i t y r u l e w h i l e a t h i g h e r s t r e s s e s t h e a d d i t i v i t y . The NDB tendency f o r t h e v i s c o s i t y combined w i t h t h e c o n s t a n t c r i t i c a l shear s t r e s s f o r melt f r a c t u r e , a^F * 2MPa, i n d i c a t e a b e t t e r e x t r u d a b i l i t y o f t h e PP/HDPE blends t h a n t h a t o f the neat r e s i n s . Blends o f PP with LDPE have been o f i n d u s t r i a l i n t e r e s t f o r y e a r s ( 2 4 , 35-38). P l o t s o f n * r\(o ) v s . w i n v a r i a b l y show NDB ( 3 5 , 36, 38) whose magnitude v a r i e s w i t h t h e method o f b l e n d p r e p a r a t i o n ( 3 7 ) and s t r e s s l e v e l ( 2 4 ) . The n e g a t i v e d e v i a t i o n s i n d i c a t e t h a t t h e mechanism r e s p o n s i b l e f o r NDB i s i n t e r l a y e r s l i p . A c c o r d i n g t o L i n (34) t h e i n t e r l a y e r s l i p f a c t o r i n E q u a t i o n 6: 2

1 2

2

2

0

l2

- 1 + (B

1 2

/a

2

1

1 2

) (w w ) /2 1

2


(7)

160


where 8 i s the c h a r a c t e r i s t i c s l i p f a c t o r of the blend, i . e . the NDB s h o u l d b e , a s o b s e r v e d , more pronounced a t s m a l l a * * e x t r u d a t e s h r i n k a g e was a l s o r e p o r t e d (24, 3 8 ) . Blends w i t h X * l were e x t r u d e d , then p l a c e d i n an o i l b a t h a t 190°C f o r about one h o u r . The s h r i n k a g e was c a l c u l a t e d a s 1 2

T

ie

1 2

e. = I n ( L / L J

(8)

0

where L and L ^ i n d i c a t e t h e i n i t i a l and f i n a l e x t r u d a t e l e n g t h s , respectively. The p l o t o f £«, v s . c o m p o s i t i o n i s p r e s e n t e d i n F i g . 2. I t c a n be shown t h a t w h i l e the a b s o l u t e magnitude o f €«, depends on t h e i n i t i a l a s p e c t r a t i o o f t h e e x t r u d a t e , t h e form o f £«> v s . w does n o t . I t i s apparent t h a t f o r t h e system w i t h X * 1 t h e maximum shrinkage occurs a t w * 0.5 where t h e f i b r i l l a t i o n a f f e c t s b o t h c o - c o n t i n u o u s phases. The f l o w p r o p e r t i e s o f LLDFE/PP b l e n d s were s t u d i e d by Dumoulin et a l . (39-41). T h i s s u b j e c t w i l l be d i s c u s s e d i n the l a s t p a r t o f t h i s chapter. C o n c l u d i n g the l i t e r a t u r e r e v i e w t h e f o l l o w i n g remarks s h o u l d be made: ( i ) the NDB b e h a v i o r o f n • n ( a ) v s . w , a l a r g e e x t r u d a t e s h r i n k a g e near w - 0.5 and a s e n s i t i v i t y o f t h e r h e o l o g i c a l f u n c t i o n s t o methods o f b l e n d p r e p a r a t i o n a l l i n d i c a t e i m m i s c i b i l i t y ( 1 0 , 1 1 , 4 2 , 4 3 ) , ( i i ) t h e s i n g l e phase f l o w o f PE b l e n d s was r e p o r t e d o n l y f o r homologous PE b l e n d s when t h e components' m o l e c u l a r w e i g h t M < 1000 kg/mol; t h e homologous HDPE/UHMWPE b l e n d was found t o form two phases, p r o b a b l y caused by t h e slow r a t e o f UHMWPE d i s s o l u t i o n i n the m e c h a n i c a l l y compounded m i x t u r e s , ( i i i ) b l e n d s o f HDPE w i t h LDPE were found t o be i m m i s c i b l e , although the i m m i s c i b i l i t y may be m a r g i n a l , d i s a p p e a r i n g a t h i g h temperatures f o r low m o l e c u l a r weight components, and ( i v ) blends o f PE w i t h PP show strong, nearly antagonistic immiscibility. 0

2


2

1 2

2

2

w

PART I I ,

LLDPE BLENDS WITH PE

A s t a n d a r d commercial f i l m b l o w i n g LLDPE r e s i n , LPX-30, was blended a t d i f f e r e n t r a t i o s w i t h e i t h e r o t h e r LLDPE's o r a LDPE polymer. The c h a r a c t e r i s t i c p r o p e r t i e s o f these m a t e r i a l s are l i s t e d i n Table I I . The r e s i n s were g e n e r o u s l y donated t o t h e p r o j e c t by Esso Chem., Canada. P r i o r t o b l e n d i n g the polymers were t h o r o u g h l y c h a r a c t e r i z e d by SEC, SEC/LALLS, s o l u t i o n v i s c o s i t y , CNMR, Atomic Absorbance, and t h e i r r h e o l o g i c a l b e h a v i o r was c h a r a c t e r i z e d i n steady s t a t e and dynamic shear f l o w a s w e l l a s i n the u n i a x i a l e x t e n s i o n a l d e f o r m a t i o n (44-46). 13

Experimental B l e n d i n g was done u s i n g a W e r n e r - P f l e i d e r e r c o - r o t a t i n g t w i n screw e x t r u d e r , model ZSK-30 a t 140 rpm. The p e l l e t i z e d r e s i n s were p r e - d r y - b l e n d e d and f e d t o t h e e x t r u d e r u s i n g a v o l u m e t r i c m e t e r i n g f e e d e r , I n c r i s o n model 105-C. The f o l l o w i n g temperature p r o f i l e was used: ( f e e d e r ) 158, 192, 214, 196 and ( d i e ) 196°C. The e x t r u s i o n r a t e was Q - 6 t o 8 kg/hr, i n d i c a t i n g e x t e n s i v e b a c k m i x i n g . The e x t r u d a t e s were g r a n u l a t e d , d r i e d and formed i n t o shapes s u i t a b l e f o r rheological testing. The c o m p o s i t i o n , code and m o l e c u l a r w e i g h t



C a t a l y s t based on:

Branches C

Zero-shear v i s c o s i t y n

6.

7.

8.

n

Comonomer/concentration (wt%)

0

a t 190°C ( k P a s )

10 p e r 1000 C-atoms

n

5.

w

P o l y d i s p e r s i t y i n d e x (-) M /M

4.

n

M o l e c u l a r w e i g h t s (kg/mol)

3. M

M e l t i n d e x (190°C, 2.16 k g , g/10 min)

2.

(kg/m )

Density

3

(units)

34

0

Ti

V7.4

3.4 ± 0.2 6

645

0

V

C /l.l

11 ± 2

9.3

1.2

-

4.1 ± 0.1

16 ± 1 225 ± 8

17 ± 1 593 ± 11

41 ± 2 272 ± 27

6.5

922.5

0.3

955

918

LDPE

[44 t o 46]

1.0

LLDPE-10

LPX-30

C h a r a c t e r i s t i c parameters o f n e a t PE r e s i n s

1.

No. Parameter

Table I I .


8120

0

Ti

C^/4.5

7.6 ± 0.2

28 ± I 719 ± 30

0.3

951

LPX-24


162


averages o f t h e t h r e e t y p e s o f blends a r e l i s t e d i n T a b l e I I I . A n t i o x y d a n t , a m i x t u r e o f I r g a n o x 1010 and Irganox 1029, was used a t a c o n c e n t r a t i o n 0.2 wt %. For d e t e r m i n a t i o n o f t h e s t e a d y s t a t e s h e a r v i s c o s i t y t h e I n s t r o n c a p i l l a r y v i s c o m e t e r model 3211 was used a t 190°C. S i x c a p i l l a r i e s were u s e d , t h r e e each o f d i a m e t e r d • 747 and 1273 um. The l e n g t h t o d i a m e t e r r a t i o i n each s e r i e s v a r i e d from L/d - 0.6 t o 60. The s t a n d a r d Bagley and R a b i n o w i t s c h c o r r e c t i o n s as w e l l a s t h a t f o r the p r e s s u r e e f f e c t s (45) were a p p l i e d . The e x t r u d a t e s w e l l was d e t e r m i n e d on a i r - c o o l e d e x t r u d a t e s , 5 cm i n l e n g t h . Rheometries M e c h a n i c a l Spectrometer, Model 605, RMS, was used i n t h e dynamic mode a t 150°C w i t h t h e p a r a l l e l p l a t e s geometry. To examine t h e t h e r m a l s t a b i l i t y o f the r e s i n s , f i r s t t h e two hours l o n g t i m e sweep a t s t r a i n y • 15% and f r e q u e n c y u> * 10 r a d s / s was c a r r i e d o u t ; t h e t e s t samples were found t o be s t a b l e f o r a t l e a s t 60 min. The f r e q u e n c y sweep a t y - 1 5 % was performed i n two d i r e c t i o n s : f o r two samples from w = 0.1 t o 100 ( r a d s / s ) and f o r two o t h e r s from 1 t o 0.01 ( r a d s / s ) . Two d i a m e t e r s o f p l a t e n s were used: 25 and 50 mm. The r e s u l t s were a c c e p t e d i f t h e maximum d i f f e r e n c e between t h e r e s u l t s o f t h e s e f o u r sweeps i n t h e common range: u » 0.1 t o 1.0 d i d not d i f f e r by more than 5%. A l l t e s t s were done under a b l a n k e t o f dry nitrogen. The measurements were r e c o r d e d u s i n g t h e RMS Columbia t e r m i n a l , Model 964, t h e n t h e d a t a were t r a n s f e r r e d t o a H e w l e t t Packard, HP-85, mini-computer f o r analysis and m a t h e m a t i c a l m a n i p u l a t i o n , v i z . c a l c u l a t i o n o f the z e r o shear v i s c o s i t i e s , n . Rheometrics E x t e n s i o n a l Rheometer, Model 605 (RER) was used a t 150°C i n a c o n s t a n t s t r a i n r a t e (e) mode. To f a c i l i t a t e s t o r a g e and m a n i p u l a t i o n o f d a t a t h e RER was i n t e r f a c e d w i t h a Hewlet-Packard model HP-85 micro-computer. F o r the t e s t , the samples were t r a n s f e r molded under vacuum, a n n e a l e d , and t h e n a f f i x e d w i t h epoxy (24 h o u r s c u r i n g ) t o the aluminum t i e s . Prepared i n t h i s manner, specimens d i d not show any shape change on immersion i n h o t (T * 150°C) s i l i c o n e oil. The specimens were mounted i n t h e i n s t r u m e n t and immersed i n Dow 200 s i l i c o n o i l a t 150°C. The t e s t s t a r t e d a f t e r a 7 t o 10 minute temperature e q u i l i b r a t i o n p e r i o d . D u r i n g t h e measurements t h e maximum temperature d i f f e r e n c e , a s r e a d by t h r e e thermocouples p l a c e d a t d i f f e r e n t h e i g h t s i n t h e sample chamber, d i d n o t exceed 0.5°C. For each sample t h e u n i f o r m i t y o f t h e c y l i n d r i c a l shape was v e r i f i e d a t t h r e e d i f f e r e n t h e i g h t s ; i n a l l cases t h e average d i a m e t e r was found t o be d • 5.55 ± 0.05 mm. The sample l e n g t h used i n t h i s s t u d y was LQ • 22 mm ± 0.1 mm. I t i s c o n v e n i e n t t o d i s c u s s r e s u l t s o f t h i s work under s e p a r a t e s u b - t i t l e s , s t a r t i n g w i t h t h e c a p i l l a r y , t h e n w i t h dynamic and f i n a l l y the e x t e n s i o n a l f l o w behavior. 0

Pressure correction I t was observed t h a t B a g l e y p l o t s o f p r e s s u r e drop P v s . L/d were not always l i n e a r ( 4 5 , 47):

P = I C. ( L / d ) i=0

1

1


(9)

In Multiphase Polymers: Blends and Ionomers; Utracki, L. A., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989. 133 114 144 123 151 152 133 112 114 107 66 64 133 141 150 174 199 216

41 33 36 25 25 17 41 36 34 29 19 16 41 39 38 34 30 28

0 0 0 0 0 0 0 0 0 0 0 0 0 10 20 50 80 100

0 10 20 50 80 100 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

100 90 80 50 20 0

100 90 80 50 20 0

11.0 - 1.0 11.10 11.20 11.50 11.80 11.100

I I I . O - 1.0 III.10 I I I . 20 III.50 I I I . 80 III.100

I. 0 I . 10 I . 20 I . 50 I . 80 1.100

0 0 0 0 0 0

w

0 10 20 50 80 100

M

100 90 80 50 20 0

n

LPX-30

M LPX-24

Content (wt%)

( i n kg/mol) o f t h e Three S e r i e s o f LLDPE Blends

LDPE

Polvmer

Composition and M o l e c u l a r Weights

LLDFE-10

Code

Table I I I .


z

272 340 401 548 659 719

272 252 254 242 248 225

272 275 357 397 525 593

M

164


where C^'s a r e parameters! correction), C - 4 a and x

C

• P

Q

( t h e Bagley

e

entrance

and e x i t

1 2

C

2

* c\ a b / 2 P * 1

where: a j i s t h e temperature d e f i n e d by t h e dependence: I n no

88a

o

(10)

1

and p r e s s u r e

+

a

f

i/(

+

a

sensitivity

parameter

2^

w i t h f b e i n g t h e f r e e volume f r a c t i o n computed from t h e SimhaSomcynsky e q u a t i o n o f s t a t e ( 4 8 ) ; b i s t h e f r e e volume p r e s s u r e c o e f f i c i e n t d e f i n e d by t h e r e l a t i o n : x


1/f = b

0

+ bjP/P*;

at

T = T/T*

= const.

(12)

w i t h P* and T* b e i n g t h e c h a r a c t e r i s t i c ( f o r a g i v e n l i q u i d ) p r e s s u r e and temperature r e d u c i n g f a c t o r s , r e s p e c t i v e l y . Note t h a t a c c o r d i n g t o E q u a t i o n 12 b± - b j ( T ^ i s a u n i v e r s a l c o n s t a n t f o r a l l l i q u i d s a t the reduced temperature T, i . e . b o t h b j and P* a r e determined by the thermodynamic p r o p e r t i e s o f a system w i t h o n l y a r e m a i n i n g unknown. F o r HDPE o r LLDPE a t 190°C, E q u a t i o n 10 can be r e a r r a n g e d t o : 1

a

x

* 154 ( C / C i )

(13)

2

w i t h t h e b a r i n d i c a t i n g t h e average v a l u e . The v a l u e s o f a j were computed f o r a s e r i e s o f LLDPE and HDPE samples w i t h a wide range o f m o l e c u l a r w e i g h t s . The d a t a were found t o f o l l o w t h e l i n e a r dependence: a

x

- -0.1065 + 4031

M /M ; w

M /M

n

w

n

< 35

(14)

2

w i t h t h e c o r r e l a t i o n c o e f f i c i e n t squared, r - 0.9945. Computation o f a r e s u l t e d i n t h e v a l u e s p l o t t e d v s . c o m p o s i t i o n i n F i g . 3. A c c o r d i n g t o E q u a t i o n 14, a± depends on p o l y d i s p e r s i t y which f o r a b l e n d can be c a l c u l a t e d from m o l e c u l a r weight averages o f t h e neat polymers assuming t h e i r m i s c i b i l i t y : x

1

Mn "

E»l/M

«w " H

M

/ M

n " I

( w

16

w i

< >

M ^ W i 1^

Mz - 1*1 ^

•'• w

M

(15)

ni

i

/ M

ni>

M

X"i w i

(17)

( 1 8

>

The b r o k e n l i n e i n F i g u r e 3 was computed from E q u a t i o n s 14 and 18 f o r blends o f S e r i e s - I . The agreement between e x p e r i m e n t a l r e s u l t s and the t h e o r e t i c a l p r e d i c t i o n s c o n f i r m s assumed m i s c i b i l i t y . On t h e o t h e r hand, a j v s . LDPE c o n t e n t f o r blends o f S e r i e s I I show


7.

UTRACKI


165

EH 3.0

V


/

J L_ 50 LDPE

100

F i g u r e 2. E x t r u d a t e s h r i n k a g e ( i n Hencky s t r a i n u n i t s ) v s . composition of polypropylene/low density polyethylene blends. (Adapted from r e f . 38.)

0

0.2 0.4 0.6 0.8 1.0

F i g u r e 3. The temperature and p r e s s u r e s e n s i t i v i t y c o e f f i c i e n t f o r LLDPE 1 blended w i t h e i t h e r LLDPE 2 ( t r i a n g l e s ) o r LDPE (circles). The broken l i n e i s t h e o r e t i c a l , computed from v a r i a t i o n of p o l y d i s p e r s i t y i n (assumed) m i s c i b l e b l e n d s .


166


b e h a v i o r incongruous w i t h monotonic E q u a t i o n s 14 t o 18 giving evidence of i m m i s c i b i l i t y . The extrema a t 11.20 and 11.80 may i n d i c a t e l i m i t s of m i s c i b i l i t y . However, i t i s d i f f i c u l t to comprehend why c r o s s i n g s p i n o d a l s from t h e h i g h LLDPE s i d e r e s u l t s i n a system w i t h s t r o n g s e n s i t i v i t y o f r h e o l o g i c a l b e h a v i o r t o T and P w h i l e c r o s s i n g i t from t h e h i g h LDPE s i d e g e n e r a t e s b l e n d s w i t h r h e o l o g y i n s e n s i t i v e t o t h e s e independent v a r i a b l e s . Extrudate Swell The e x t r u d a t e s w e l l , B * D/d, (where D and d a r e the e x t r u d a t e and d i e d i a m e t e r r e s p e c t i v e l y ) i s p l o t t e d as B v s . w i n Fig. 4 for blends o f S e r i e s I and I I . In b o t h cases B f o l l o w s a s i m p l e parabolic equation: 2


B =

+ B

w

2

2

+ B w w 1 2

x

(19)

2

with B - 0.32 ± 0.06 and 0.91 ± 0.05 f o r S e r i e s I and I I respectively. The l a r g e B v a l u e f o r the l a t t e r b l e n d s s u g g e s t s t h a t here s w e l l i n g i s due t o s t r a i n r e c o v e r y o f f i b r i l l a t e d d r o p s r a t h e r than t o e x t r u d a t e s w e l l i n g as i n homologous polymer m e l t s . Note t h a t f o r system I I t h e B v s . w dependence resembles t h e e x t r u d a t e s h r i n k a g e i n F i g . 2. 1 2

1 2

2

Entrance flow The e n t r a n c e t o c a p i l l a r y f l o w was s t u d i e d by a f l o w v i s u a l i z a t i o n method ( 4 9 ) . The f l o w p a t t e r n f o r S e r i e s I I b l e n d s i s p r e s e n t e d i n F i g . 5 ( s i n c e the f l o w i s a x i s y m m e t r i c o n l y the l e f t hand s i d e p a r t of the e n t r a n c e r e g i o n i s shown). There i s a l a r g e d i f f e r e n c e i n f l o w p a t t e r n between t h a t o f LLDPE ( 0 % ) and of LDPE ( 1 0 0 % ) . In the l a t t e r case t h e c l a s s i c a l w i n e - g l a s s shape w i t h l a r g e v o r t i c e s was observed. Upon a d e c r e a s e o f LDPE c o n t e n t b o t h the g l a s s - s t e m and v o r t i c e s slowly decreased. I t was n o t e d t h a t as l i t t l e as 2% o f LDPE was s u f f i c i e n t t o i n t r o d u c e s i g n i f i c a n t changes i n LLDPE f l o w pattern. The m a t h e m a t i c a l modeling o f the e n t r a n c e f l o w a l l o w s c o r r e l a t i o n between the v o r t e x s i z e and the s t r a i n h a r d e n i n g i n extensional flow. The frequency dependence The dynamic f l o w d a t a can r e a d i l y be e v a l u a t e d i n a t h r e e s t e p process: ( i ) e x a m i n a t i o n o f t h e d a t a f o r presence o f an a p p a r e n t y i e l d s t r e s s , a , and s u b s e q u e n t l y i t s s u b t r a c t i o n , ( i i ) f i t t i n g t h e d a t a t o e i t h e r the g e n e r a l i z e d C a r r e a u model ( 4 2 ) : v

n or

f

- G"(o))/(0 - n

111

0

U+UX!) !]"™

2

(20)

t o the H a v r i l i a k - f l a g a m i dependence ( 5 0 ) : 1

a

n* = G*/u> - Ti [l-Kia>T2> ~ ]'"

B

0

(21)

and ( i i i ) g e n e r a l i z a t i o n o f the r e s u l t s by d e r i v i n g o t h e r l i n e a r v i s c o e l a s t i c dependencies by means o f t h e i n t e r m e d i a t i o n o f t h e Gross* f r e q u e n c y r e l a x a t i o n spectrum:



7.

UTRACKI


167

F i g u r e 4. E x t r u d a t e s w e l l a t 190°C v e r s u s weight f r a c t i o n of t h e second component i n S e r i e s - I and I I ; curves - E q u a t i o n 19.

F i g u r e 5. Flow p a t t e r n a t the e n t r a n c e t o c a p i l l a r y f o r l i n e a r low d e n s i t y / l o w d e n s i t y p o l y e t h l e n e b l e n d (LLDPE/LDPE) a t 190°C and y - 125 ( s " ) . From the l e f t hand s i d e : 0, 20, 50 and 100% of LDPE. (Reproduced from r e f . 49.) 1


168

MULTIPHASE POLYMERS: BLENDS AND IONOMERS ±i7r

H (a)) - ± (l/a>ir)ImG(a)e ) « (2/aiir) ReG"(u>e

±l7r/2

G

)

(22)

1

f

In E q u a t i o n s 20 t o 22: n , n* a r e dynamic and complex v i s c o s i t y ; G , G", G* a r e t h e s t o r a g e , l o s s and complex s h e a r modulus; a) i s t h e frequency; the primary r e l a x a t i o n time; n i j , m , a, 3 a r e parameters: i - / - l ; and Im, Re i n d i c a t e t h e i m a g i n a r y and r e a l p a r t s o f t h e complex f u n c t i o n , r e s p e c t i v e l y . The c o n v e n i e n t way o f d a t a e x a m i n a t i o n f o r presence o f t h e apparent y i e l d s t r e s s i s by means o f t h e m o d i f i e d Casson p l o t ( 5 1 ) : 2

F* = F

* + a F * — m

(23)

where F, F and F are r h e o l o g i c a l f u n c t i o n s of the blend, the m a t r i x phase and i t s y i e l d v a l u e , r e s p e c t i v e l y ; a, i s a parameter r e p r e s e n t i n g t h e square r o o t o f t h e r e l a t i v e F - f u n c t i o n . Note t h a t E q u a t i o n 23 l o o s e s i t s sense i n systems where i d e n t i f i c a t i o n o f t h e d i s p e r s e d and m a t r i x l i q u i d i s becoming ambiguous. For F any r h e o l o g i c a l f u n c t i o n s , e.g. o , G , G", can be used. The y i e l d phenomenon o r i g i n a t e s i n a s t a b l e t h r e e - d i m e n s i o n a l s t r u c t u r e . when t h e s t r e s s exceeds i t s y i e l d v a l u e , a > a , the structure i s d e s t r o y e d and t h e m a t e r i a l b e h a v i o r changes from s o l i d - l i k e t o liquid-like. In t h i s c l a s s i c a l d e s c r i p t i o n the rate i s not considered. I n b l e n d s a t h i g h c o n c e n t r a t i o n o f d i s p e r s e d phase the d r o p l e t s e i t h e r form i n t e r a c t i v e c l u s t e r s o r t h e y c o a l e s c e i n t o a c o - c o n t i n u o u s network. The r e l a x a t i o n time o f t h e s e i n t e r a c t i v e e n t i t i e s , T , i s rather long. When an experiment i s c a r r i e d out s l o w l y enough, a l l o w i n g t h e c l u s t e r t o r e f o r m , F + 0 can be found. On t h e o t h e r hand, when t h e experiment i s conducted on a time s c a l e comparable t o T , t h e n t h e network response i s analogous t o t h a t i n t h e c l a s s i c a l concept and F * 0 i s observed. F o r m a l l y one may e x p r e s s t h i s i d e a i n t h e form o f t h e f o l l o w i n g r e l a t i o n : m


y

y

f

1 2

1 2

y

v

y

v

y

F

y

=F~

[1-exp { - } ]

U

(24)

V

where x i s t h e r e l a x a t i o n time o f i n t e r a c t i v e c l u s t e r and u * 0.2 t o 1.0 i s an exponent. At a g i v e n frequency u> and when x > 0 and » t h e apparent y i e l d s t r e s s F • 0 and F • F , respectively. Similarly f o r x - c o n s t , ( s p e c i f i c polymer blend) Fy reaches t h e s e l i m i t s f o r u> 0 and o> «. Experimental v e r i f i c a t i o n of dependencies 23 and 24 was r e c e n t l y p u b l i s h e d ( 5 2 , 5 3 ) . A f t e r t h e apparent y i e l d s t r e s s i s c a l c u l a t e d , t h e e x p e r i m e n t a l v a l u e s , F , s h o u l d be c o r r e c t e d by s u b t r a c t i n g F : y

y

00

y

y

y

a

y

F(o)) - F (u>) - F (u>) a y

(25)

Once t h e v a l u e s o f F(u>) a r e known e i t h e r E q u a t i o n 20 o r 2 1 c a n be used. The advantage o f E q u a t i o n 20 i s t h a t o n l y F • G needs t o be c o r r e c t e d f o r t h e apparent y i e l d s t r e s s . I f E q u a t i o n 21 i s t o be used b o t h G and G must be c o r r e c t e d i n d e p e n d e n t l y and then: |4

a

a

a


a

7.


UTRACKI

2

169

2

G* = (G» + G " ) *

(26)

calculated. (Note: s i n c e Gy * Gy a n attempt t o u s e F - G* u s u a l l y leads t o nonsensical r e s u l t s ) . F i g . 6 shows t h e c u r v e - f i t o f n v s . to dependence f o r S e r i e s I and I I blends by means o f E q u a t i o n 20. The f i t t i n g procedure generated t h e n u m e r i c a l v a l u e s o f t h e f o u r parameters o f t h e e q u a t i o n : TIQ, T, m and m . I t was found t h a t t h e z e r o shear v i s c o s i t y o f homopolymers and b l e n d s f o l l o w e d t h e r e l a t i o n : 1

1

2


n

« M

0

a

(27)

where a * 3.5. The m o l e c u l a r weight M^, f o r polymers w i t h l o g - n o r m a l d i s t r i b u t i o n o f m o l e c u l a r w e i g h t s , c a n be e x p r e s s e d a s (45): M

0

- M (M /M ) -

n

2

W

2

(28)

n

The dependence i s shown i n F i g . 7. From E q u a t i o n 20 a t u> » 1 the power law exponent n • 1 - m m i . e . 0 £ m m ^ 1 a r e p r e d i c t e d and e x p e r i m e n t a l l y v e r i f i e d . The l a s t parameter o f E q u a t i o n 19, t h e p r i n c i p a l r e l a x a t i o n t i m e T j , i s a complex f u n c t i o n dependent o n sample p o l y d i s p e r s i t y which can not be r e a d i l y c o r r e l a t e d w i t h a s i n g l e m o l e c u l a r o r T h e o l o g i c a l f u n c t i o n ( 4 5 ) . However, the c o r r e l a t i o n can be o b t a i n e d through HQ as intermediary. U s i n g p r i n c i p l e s o f complex a l g e b r a HQ c a n be e x p r e s s e d i n terms o f e i t h e r E q u a t i o n 20 o r E q u a t i o n 21 parameters: 1

1

2

2

H U)

- (2

G

n o

/Tr)r "

i n 2

1

sin m 8 2

1

- (n /7r)r 0

e

sin

2

38

2

(29)

where: r

m

x

= [ l + 2 ( a ) T ) l cos (mnx/2) +

6! = a r c s i n {(o)T) r 6

((AT )

1

1

{[l-CaiTa) "

mi

0

X

"M*

1

r^" sin

= a r c t a n {[ (WT ) " cos ( i r a / 2 ) ] / [ l - ( a ) T ) ]

2

"

a )

2

1

+ (a)T )

2 ( 1

s

2

s i n (ira/2)]

2

2

a

2

cos

2

1 - 0 1

s i n (ira/2)}

(ia/2)}*

F u r t h e r m o r e , from E q u a t i o n 21 t h e r e a l and i m a g i n a r y p a r t s o f n* c a n be e x p r e s s e d as: n

f

- (n /r

0

) cos 8 6

2

(30a)

« (n /r ) sin 36

2

(30b)

o

0

2

2




170


7.

UTRACKI


171

Comparing E q u a t i o n s 29 and 30 i t i s e v i d e n t t h a t f o r systems whose n* v s . a) dependence can be d e s c r i b e d by E q u a t i o n 21 t h e r e i s a s i m p l e e q u i v a l e n c e : n"(u>) • TTHQ(U)). The m o l e c u l a r weight dependence e n t e r s E q u a t i o n 29 t h r o u g h nQ• For t h i s r e a s o n i t i s c o n v e n i e n t t o d e f i n e t h e reduced frequency r e l a x a t i o n spectrum as: H (o>) = H ( u ) ) / n G

An example integral:

of this

G

(31)

0

f u n c t i o n i s presented

i n F i g . 8.

Since t h e

J ^ H ^ s ) dins = 1

(32)


—CO

H

the coordinates of H (u)) maximum (^max* G max^ should c o r r e l a t e w i t h t h e m o l e c u l a r parameters o f the m e l t . indeed, i t can be shown t h a t i n s i n g l e phase systems ( % depends o n n * H o n sample p o l y d i s p e r s i t y (11, 14, 54). These dependencies a r e p r e s e n t e d i n F i g . 9. I t i s evident that f o r S e r i e s I blends t h e r e i s a l i n e a r c o r r e l a t i o n between l o g o ) and l o g np ell a s between l o g HQ and \ / % b u t f o r LLDPE/LDPE, S e r i e s I I , t h e l i n e a r i t y i s n o t observed. The l i n e a r i t y o f dependencies i n F i g . 9 c a n be p r e d i c t e d assuming m i s c i b i l i t y i n a b l e n d composed o f polymers w i t h s i m i l a r molecular weights. For s u c h systems t h e g e n e r a l , t h i r d o r d e r m i x i n g r u l e f o r r e l a x a t i o n spectrum (55, 56): G

a n (

a x

G

m

a

0

x

a

s

w

m a x

m

a

x

H ( T

c a n be reduced

t o simple

>-j

k

W

(

T

/

V>

(

3

3

)

additivity: H(T)

« JW^CT)

(34)

I n E q u a t i o n 33 P ^ ^ i s t h e t h i r d o r d e r i n t e n s i t y f u n c t i o n ( r e p l a c e d i n E q u a t i o n 33 by t h e weight f r a c t i o n w^) and A j j k i s t h e t h i r d o r d e r i n t e r a c t i v e r e l a x a t i o n time f a c t o r , w h i c h o r i g i n a t e s i n t h e intermolecular interactions between d i s s i m i l a r molecules. In homologous polymer b l e n d s where the m o l e c u l a r weight o f one polymer i s l o w e r than t h e entanglement m o l e c u l a r w e i g h t , and t h a t o f t h e second i s h i g h e r than Mg, E q u a t i o n 34 must be extended t o accommodate a second o r d e r term (57). The proposed method o f d a t a t r e a t m e n t has two advantages: ( i ) i t a l l o w s assessment o f t h e s t a t u s o f b l e n d m i s c i b i l i t y i n the m e l t , and ( i i ) i t p e r m i t s c o m p u t a t i o n o f any l i n e a r v i s c o e l a s t i c f u n c t i o n from a s i n g l e f r e q u e n c y scan. Once t h e n u m e r i c a l v a l u e s o f E q u a t i o n 20 o r E q u a t i o n 21 parameters a r e e s t a b l i s h e d t h e r e l a x a t i o n spectrum a s w e l l a s a l l l i n e a r v i s c o e l a s t i c f u n c t i o n s o f the m a t e r i a l a r e known. Since t h e r e i s a d i r e c t r e l a t i o n between t h e r e l a x a t i o n and t h e r e t a r d a t i o n time s p e c t r a , one c a n compute from HQ(U>) t h e s t r e s s g r o w t h f u n c t i o n , c r e e p c o m p l i a n c e , complex dynamic c o m p l i a n c e s , e t c .


172


1000 (kPa.s) 100


10

1 100

KA

1000

Figure 7. M o l e c u l a r weight dependence o f t h e z e r o - s h e a r viscosity f o r Series-I and I I . The l i n e represents the dependence f o r neat LLDPE r e s i n s . (Reproduced w i t h p e r m i s s i o n from r e f . 45. C o p y r i g h t 1987 SPE.)

'ogHgfGO)

Series-II.

logo)

F i g u r e 8. Reduced Gross f r e q u e n c y r e l a x a t i o n spectrum f o r S e r i e s - I and I I . The arrows i n d i c a t e computed c o o r d i n a t e s of t h e maximum ( H maxj^max)G



UTRACKI


173

F i g u r e 9. (a) C o r r e l a t i o n between the a b s c i s s a s o f r e l a x a t i o n spectrum maximum and t h e z e r o - s h e a r v i s c o s i t y f o r S e r i e s - I and I I ; (b) C o r r e l a t i o n between the o r d i n a t e o f r e l a x a t i o n spectrum maximum and the p o l y d i s p e r s i t y f a c t o r M /M . n

w


174


(58). However, one must keep i n mind t h a t v a l i d i t y o f the computed f u n c t i o n s i s o n l y a s s u r e d w i t h i n t h e range o f independent v a r i a b l e s (u>,T,P,t,...) used i n d e t e r m i n i n g HQ. F o r example: +00

G (u>) - J {s calc -» f

2

H (s)/[l+(s/u>) ]} dins

(35a)

G"(aO - J {» H ( s ) / [ l + ( a ) / s ) ] } d i n s calc -»

(35b)

G

2

G

+00 +

n ( t ) - J H (s)[l-exp{st}] dins calc -°°

(36)


G

+

where n i s the s t r e s s growth shear v i s c o s i t y . In F i g . 10 t h e e x p e r i m e n t a l v a l u e s o f G' f o r blends S e r i e s I and I I ( p o i n t s ) a r e compared w i t h G j , i ( l i n e s ) computed from HQ w h i c h i n t u r n was determined u s i n g the n'-data. The agreement i s q u i t e s a t i s f a c t o r y with residuals |G - G | < 5% f o r b o t h s e r i e s . The concluded immiscibility f o r LLDPE/LDPE blends of S e r i e s I I make this observation p a r t i c u l a r l y interesting. a

c

f

c a l c

Cole-Cole plot The n" v s . n dependence i s o f t e n used w h i l e d i s c u s s i n g the dynamic d a t a o f polymer b l e n d s . Since f o r s i m p l e l i q u i d s the p l o t has t h e form of a s e m i - c i r c u l a r a r c , d e v i a t i o n from a s e m i - c i r c l e i s sometimes i d e n t i f i e d w i t h i m m i s c i b i l i t y . However, as f r e q u e n t l y demonstrated f o r homopolymers (16) and homologous polymer b l e n d s (59) the form o f the n" v s . n' p l o t i s determined by t h e shape o f t h e r e l a x a t i o n spectrum; t h e m o l e c u l a r p o l y d i s p e r s i t y can modify the C o l e - C o l e p l o t as much as t h e presence o f t h e i n t e r p h a s e . As a r u l e , t h e presence o f ( u n s u b t r a c t e d ) y i e l d s t r e s s appears i n the p l o t as a sudden d e p a r t u r e from a s e m i - c i r c u l a r p a t t e r n a t h i g h e r n* l e v e l . From E q u a t i o n s 29 and 30 i t i s e v i d e n t t h a t b o t h H (aO and the C o l e - C o l e p l o t c o n t a i n the same i n f o r m a t i o n ; i n p r i n c i p l e t h e s e d a t a treatments are equivalent. The advantage of HQ is the straight-forward interpretation and access to other linear v i s c o e l a s t i c f u n c t i o n s . The advantage o f the C o l e - C o l e p l o t i s i t s simplicity i t can be constructed simply by plotting one experimental f u n c t i o n versus another. In accordance w i t h E q u a t i o n 30 n and n" can be n o r m a l i z e d by d i v i d i n g by , i.e. n V ^ and TI"/T^. Such a n o r m a l i z e d C o l e - C o l e p l o t has f r e q u e n t l y been used f o r polymer blends (60, 6 1 ) . In F i g . 11 the n o r m a l i z e d C o l e - C o l e p l o t i s shown f o r b l e n d s o f S e r i e s I and II. The d a t a used f o r c o n s t r u c t i n g the F i g u r e a r e the same as those used f o r c o m p u t a t i o n o f HQ i n F i g . 8. f

G

1

Cross-point coordinates The c o o r d i n a t e s d e f i n e d as G = G * G" a t o> • u>x were r e p o r t e d ( 6 2 , 63) t o be r e l a t e d t o the m o l e c u l a r parameters of melts: Gx « (M^/M^ and « w i t h a and 0 negative. From E q u a t i o n s 34 and 35 i t f o l l o w s t h a t G = G" a t ui » s 1/x, i . e . when f

x

01

1

a


UTRACKI


175


7.

Figure 10, Storage modulus v s . f r e q u e n c y f o r Series I LLDPE/LLDPE ( t o p ) and f o r S e r i e s I I LLDPE/LDPE b l e n d s (bottom) a t 190°C. P o i n t s - e x p e r i m e n t a l , s o l i d l i n e s computed from HQ( w), broken l i n e s connect the c o n s t a n t - u> d a t a p o i n t s . C o n c e n t r a t i o n of the second component i s g i v e n i n wt%. The r e s u l t s f o r each b l e n d i s d i s p l a c e d h o r i z o n t a l l y by one decade.


176


the t e s t frequency e q u a l s t h e I n v e r s e d r e l a x a t i o n time system. S u b s t i t u t i n g t h i s c o n d i t i o n i n t o t h e r e l a t i o n :

of the

G'(u)) - A n a > T / U + ( a ) T ) ] 2

0

(37)

2

d e r i v e d f o r s i m p l e l i q u i d s w i t h a s i n g l e r e l a x a t i o n time (A«l) and by Rouse ( A - 6/TT ), one g e t s :

by Maxwell

2

n

- 2G /Ao>

0 M

x

(38)

x

f

o

r

L

D

P

E

In F i g . 12 n , c a l c u l a t e d w i t h A - 1, i s p l o t t e d v s . n and LLDPE r e s i n s and f o r t h e i r b l e n d s . F o r n ^ 60 kPas t h e t o t a l l y unexpected agreement noM no obtained. Above t h i s l i m i t t h e v a l u e s d i v e r g e d i n t o no - o M HQ > kPas, where E q u a t i o n 38 r e q u i r e s t h a t A * 1/7. From t h e g e n e r a l Rouse t h e o r y ( 6 4 ) A d e c r e a s e s w i t h an i n c r e a s e o f p o l y d i s p e r s i t y o f t h e r e l a x a t i o n t i m e s but t h e i n f l u e n c e i s n o t l a r g e enough t o a l l o w such a low A - v a l u e . As w i l l be shown i n p a r t 4 t h e dependence p r e s e n t e d i n F i g . 12 was d u p l i c a t e d by t h e r e s u l t s o f LLDPE/PP blends i n d i c a t i n g a broad a p p l i c a b i l i t y o f E q u a t i o n 38 ( 4 1 , 65). For LLDPE blends t h e r e l a t i o n s r e p o r t e d by Z e i c h n e r e t a l . ( 6 2 , 63) were n o t obeyed. F o r example t h e p l o t o f G v s . w showed an o p p o s i t e t r e n d from t h e p r e d i c t e d n e g a t i v e d e v i a t i o n from t h e additivity rule. For these systems t h e a c t i v a t i o n energy o f f l o w E = R ( 3 l n n/3 1/T) . - E^/n « 30 ± 2 kJ/mol was found ( 4 5 ) . 0 M

0

0

w

38

7n


a

F

s

O

R

x

2

a

a

c

o

n

s

t

The uniaxial extensional flow The b e h a v i o r o f LLDPE blends a t c o n s t a n t r a t e o f s t r e t c h i n g , e, was examined a t 150°C. Hie r e s u l t s a r e shown i n F i g . 13 f o r S e r i e s I and I I a s w e l l as i n F i g . 14 f o r S e r i e s I I I . The s o l i d l i n e s i n F i g . 13 r e p r e s e n t 3 n i v a l u e s computed from t h e frequency r e l a x a t i o n spectrum by means o f E q u a t i o n ( 3 6 ) , w h i l e t r i a n g l e s i n d i c a t e t h e measured i n s t e a d y s t a t e 3 n v a l u e s a t y • 1 0 " ( s ) , i . e . the s o l i d l i n e s and t h e p o i n t s r e p r e s e n t t h e p r e d i c t e d and measured l i n e a r v i s c o e l a s t i c behavior r e s p e c t i v e l y . The agreement i s s a t i s f a c t o r y . The b r o k e n l i n e s i n F i g . 13 r e p r e s e n t the e x p e r i m e n t a l v a l u e s o f t h e s t r e s s growth f u n c t i o n i n u n i a x i a l e x t e n s i o n , nE * ^ h distance between t h e s o l i d and broken l i n e s i s a measure o f n o n l i n e a r i t y o f the system caused by s t r a i n h a r d e n i n g , SH. +

c a

c

+

2

- 1

+

e

The SH p l a y s a p o s i t i v e r o l e i n f i l m b l o w i n g ( 1 5 , 4 4 ) o r i n w i r e coating (66). LPX-30 does n o t show t h i s effect and i t s p r o c e s s a b i l i t y i n d e x i s low. On the o t h e r hand, SH o f LDPE i s q u i t e h i g h and so i s t h e p r o c e s s a b i l i t y i n d e x . The a c c e p t e d mechanism f o r improvement o f f i l m bubble s t a b i l i t y i s s e l f h e a l i n g o f a p o t e n t i a l l y weak spot by a l o c a l i n c r e a s e o f e x t e n s i o n a l v i s c o s i t y caused by SH. I t i s i m p o r t a n t t o note t h a t adding t o LPX-30 e i t h e r 10 wt% LDPE, 20% LLDPE-10 o r 10% LPX-24 was s u f f i c i e n t f o r g e n e r a t i o n o f SH. The subsequent t r i a l on a p r o d u c t i o n l i n e c o n f i r m e d these results; i n c r e a s e d bubble s t a b i l i t y a l l o w e d f o r h i g h e r p r o d u c t i o n r a t e s o f t h e blends.


177

Melt Flow of Polyethylene Blends

UTRACKI

n'Vri

S e r i e s II.

S e r i e s I. LLDPE-10 LLDPE- 30 o 80% LLDPE -30 A 50% LLDPE -30 • 20% LLDPE-30

• o A •

LDPE LLDPE-30 90% LLDPE-30 80% LLDPE-30 50% LLDPE-30 20% LLDPE-30


0.2

0.2

S e r i e s II. (Immiscible) i

0.2

I

I

I

0.4

,,

0.6

TIM

4

10

n

0 M

(

k P a s

0.8

1.0

0

F i g u r e 11. C o l e - C o l e p l o t f o r m i s c i b l e ( S e r i e s - I I ) polyethylene blends.

10

L

( S e r i e s - I ) and i m m i s c i b l e

)

3

•

LLDPE's

A

Series -1, o Series - II. 10

2

LPX-30

ffi

LDPE

10' 10°

1

10

10

2

10

3

10

4

rj (kPa.s) 0

Figure 12. Maxwellian zero-shear viscosity computed from c r o s s - p o i n t c o o r d i n a t e s v e r s u s n f o r S e r i e s - I and I I as w e l l a s f o r neat LLDPE r e s i n s . 0



1

F i g u r e 13. S t r e s s growth f u n c t i o n f o r b l e n d s o f l i n e a r low d e n s i t y p o l y e t h y l e n e , LLDPE, w i t h ( l e f t ) a n o t h e r type o f LLDPE ( m i s c i b l e , S e r i e s - I ) and ( r i g h t ) w i t h low d e n s i t y p o l y e t h y l e n e ( i m m i s c i b l e , S e r i e s I I ) . Broken l i n e s : experimental data i n e l o n g a t i o n ; t r i a n g l e s : experimental data i n steady s t a t e shearing a t y - 0.01s" . S o l i d l i n e s were computed from t h e f r e q u e n c y r e l a x a t i o n spectrum. (Adapted from r e f . 14.)


i

° O § 2

7.

UTRACKI


179

F i g s . 13 and 14 a l s o p r o v i d e i n f o r m a t i o n o n sample p o l y dispersity. The i n i t i a l s l o p e o f the s t r e s s growth f u n c t i o n can b e e x p r e s s e d as: S-dlnr£/dlnt|

(39)

l o w t

1

F o r a s e r i e s o f LLDPE s t h e r e l a t i o n p r e s e n t e d i n F i g . 15 was found. An e x p l a n a t i o n f o r t h i s e m p i r i c a l c o r r e l a t i o n c a n be found i n G l e i s s l e ' s m i r r o r image p r i n c i p l e ( 6 7 ) : n(Y)

- n (t); +

t oc 1/}

(40)


Accordingly, S i s equivalent to: S * d i n n / d l n y\.. - n-1 1 high y 1

u

where n i s t h e power l a w i n d e x . Both (n-1) and S a r e r e l a t e d t o p o l y d i s p e r s i t y (68) Since f o r m i s c i b l e b l e n d s the p o l y d i s p e r s i t y c a n be c a l c u l a t e d from E q u a t i o n s 15 t o 18, t h e dependence i n F i g . 15 p r o v i d e s a means f o r d e t e c t i n g m i s c i b i l i t y i n samples under u n i a x i a l e x t e n s i o n a l f l o w . The d a t a i n F i g . 16 show the e x p e r i m e n t a l S v s . w dependence ( p o i n t s ) a s w e l l a s t h a t p r e d i c t e d from v a r i a t i o n o f t h e p o l y d i s p e r s i t y w i t h c o m p o s i t i o n (broken l i n e s ) f o r blends o f S e r i e s I and I I . The d a t a i n F i g . 16 c o n f i r m the p r e v i o u s r e s u l t s s u g g e s t i n g t h a t w h i l e LLDPE/LLDPE S e r i e s I b l e n d s a r e m i s c i b l e , those o f LLDPE w i t h LDPE, S e r i e s I I b l e n d s , a r e n o t . The S v s . w dependence f o r S e r i e s I I I shown i n F i g . 17 i s particularly interesting. A p p a r e n t l y , upon a d d i t i o n o f a s m a l l q u a n t i t y o f LPX-24, w ^ 20%, t h e p o l y d i s p e r s i t y i n c r e a s e s , a s i t s h o u l d i n a m i s c i b l e system. However, f o r w > 20% t h e p o l y d i s p e r s i t y seems t o d e c r e a s e . Phase s e p a r a t i o n i n the v i c i n i t y o f 20 wt% o f LPX-24 c o u l d p r o v i d e a mechanism f o r such b e h a v i o r . Curve No. 1 i n F i g . 1 shows t h e TIE " HE^c • 0.1 s " ) dependence o n w f o r S e r i e s I I I b l e n d s . The p o i n t s a r e e x p e r i m e n t a l , the curve i s a t h i r d o r d e r p o l y n o m i a l . S i m i l a r i t y o f the shape o f t h i s dependence and t h a t shown i n F i g . 17 a l l o w s p o s t u l a t i n g t h a t b o t h a r e caused by the phase b e h a v i o r . I t i s worth p o i n t i n g out t h a t the extrema o n the ng v s . w p l o t r e p r e s e n t c o m p o s i t i o n s w h i c h may be o f p a r t i c u l a r i n t e r e s t f o r p r o c e s s o r s : a t the maximum the e f f e c t of LPX-24 o n t h e s t r e s s h a r d e n i n g i s most pronounced and t h e c o m p o s i t i o n i s most s u i t a b l e f o r f i l m b l o w i n g . At the minimum the Tig, p a r a l l e l w i t h i t the shear v i s c o s i t y , i s the l o w e s t . The e x t r u d a b i l i t y o f LPX-24 w i t h about 10 t o 20 wt% LPX-30 i s most e f f i c i e n t and s t a b l e . The u s e f u l n e s s o f b l e n d s w i t h c o m p o s i t i o n s c o r r e s p o n d i n g t o extrema i n the p r o p e r t y - c o n c e n t r a t i o n dependence was r e c o g n i z e d by P l o c h o c k i , who l a b e l e d t h e s e a s t h e " r h e o l o g i c a l l y p a r t i c u l a r c o m p o s i t i o n s " , o r RPC (8)* A c c o r d i n g t o t h a t a u t h o r the shape o f a r h e o l o g i c a l f u n c t i o n v s . c o m p o s i t i o n dependence i s paralleled by a s i m i l a r relation between t h e d e n s i t y and concentration. J u d g i n g by i n f o r m a t i o n i n F i g . 17 i t i s the phase s e p a r a t i o n w h i c h p r o v i d e s t h e mechanism r e s p o n s i b l e f o r v a r i a t i o n o f d e n s i t y of Series I I I blends. 2

2

2

2

1

2

2

a

n

d




180

F i g u r e 15. I n i t i a l s l o p e s of t h e s t r e s s growth f u n c t i o n s o f LLDPE*s ( c o n t a i n i n g butene, hexene o r octene comonomer) as f u n c t i o n of r e s i n p o l y d i s p e r s i t y .



7.

UTRACKI

181


F i g u r e 16. C o m p o s i t i o n a l dependence o f the i n i t i a l s l o p e o f the e l o n g a t i o n a l s t r e s s growth f u n c t i o n f o r LPX-30/LLDPE 10 ( t o p ) and LPX-30/LDPE ( b o t t o m ) . The broken l i n e s were computed assuming miscibility.

F i g u r e 17. I n i t i a l s l o p e o f t h e s t r e s s LPX-30/LPX-24 b l e n d s v s . c o m p o s i t i o n .

growth

function for


182


From the dependence: • ( e , t ) i n F i g . 13 t h e v a l u e s o f t h e e q u i l i b r i u m e x t e n s i o n a l v i s c o s i t y , n g , were determined and p l o t t e d i n F i g . 18. O p e r a t i o n a l l y , ng was t a k e n as t h e maximum v a l u e o f rig a t a g i v e n e. F o r specimens w i t h maximum s t r a i n a t b r e a k l a r g e r than t h e rheometer l i m i t , - 3.2, t h e arrow on a s i d e o f the d a t a p o i n t was p l a c e d . The TIE * e dependences f o r S e r i e s I a r e s i m p l e , r e s e m b l i n g the c l a s s i c a l shear f l o w c u r v e s , n v s . y. The few arrows i n d i c a t e t h a t f o r most o f these blends ^ 3.2. By c o n t r a s t , t h e p l o t f o r S e r i e s I I i s q u i t e complex. Note t h a t f o r s e v e r a l blends rig a s w e l l as eg > 3.2 a r e l a r g e r than those f o r neat polymers. The complex shape o f TIE * s dependence f o r 11.50 b l e n d i s p a r t i c u l a r l y n o t i c e a b l e . A p p a r e n t l y the c o - c o n t i n u o u s b l e n d morphology, expected a t t h i s concentration, resulted i n selfr e i n f o r c i n g b e h a v i o r , more s e n s i t i v e t o the r a t e o f d e f o r m a t i o n than t h a t observed f o r 11.10 (LPX-30 w i t h 10% LDPE) where t h e d i s p e r s e d LDPE d r o p s were t r a n s f o r m e d by u n i a x i a l s t r e s s i n t o r e i n f o r c i n g s h o r t fibers. In F i g . 19 t h e steady s t a t e u n i a x i a l e l o n g a t i o n a l v i s c o s i t y , ng/3, i s compared w i t h t h e steady s t a t e shear, n, a s w e l l as dynamic, n , and complex, r\* v i s c o s i t i e s . I t i s e v i d e n t t h a t some s t r a i n h a r d e n i n g , e v i d e n t i n 1.100 (LLDPE-10) i s s y s t e m a t i c a l l y d i l u t e d by t h e i n c r e a s i n g amount o f LPX-30. Thus, S e r i e s I behaves as a t r u l y m i s c i b l e system. By c o n t r a s t , a d d i t i o n o f LDPE (11.100) to LPX-30 (1.0) i s g e n e r a t i n g more a complex v a r i a t i o n o f properties. The s t r a i n h a r d e n i n g , a l r e a d y v i s i b l e a t 10% o f LDPE, reaches i t s maximum not a t 100% LDPE b u t r a t h e r a t 50:50 c o m p o s i t i o n . Note t h a t a t e £ 0.1 ( s " ) t h e maximum s t r a i n a t b r e a k f o r 11.50 i s e > e * 3.2. The blends behave as i m m i s c i b l e . The s t r a i n h a r d e n i n g , SH, causes t h e polymer t o show a d u a l n a t u r e ; a t l o w s t r a i n s i t behaves a s a l i n e a r v i s c o e l a s t i c l i q u i d , whereas a t h i g h ones t h e n o n - l i n e a r i t y suggests a n e t w o r k - l i k e behavior. F o r t h i s reason t h e TIE 2 dependence may be m i s l e a d i n g - i t i s n o t known where t h e l i n e a r b e h a v i o r ends and SH begins. T h i s i s why i n F i g . 20 o n l y t h e l i n e a r v i s c o e l a s t i c p a r t o f TIE i s shown, t h e p a r t computed from HQ by means o f E q u a t i o n 36. A s i g n i f i c a n t d i f f e r e n c e i n b e h a v i o r between S e r i e s I and S e r i e s I I i s again v i s i b l e a t a l l deformation r a t e s . For S e r i e s I t h e values of 3ncalc s i m p l e a d d i t i v i t y , whereas f o r S e r i e s I I , t h e r e i s a p o s i t i v e d e v i a t i o n from t h e l o g - a d d i t i v i t y r u l e , PDB. While t h e PDB b e h a v i o r per s e i s i n s u f f i c i e n t t o c a l l i m m i s c i b i l i t y , it i s c o n s i s t e n t w i t h t h e expected behavior of emulsion-like i m m i s c i b l e polymer b l e n d s . v s


v s

f

9

1

b

L

V

s

h

o

8

#

w

w

Conclusions ( i ) Blends o f LLDPE w i t h o t h e r LLDPE• s o r LDPE may show w i d e l y v a r y i n g b e h a v i o r , dependent on s m a l l changes i n m o l e c u l a r s t r u c t u r e engendered by e.g. d i f f e r e n t c a t a l y s t , p o l y m e r i z a t i o n method o r c o m p o s i t i o n . The LLDPE/LLDPE m i x t u r e may be m i s c i b l e , as a l l r h e o l o g i c a l t e s t s i n d i c a t e d f o r S e r i e s I , o r p a r t i a l l y miscible as f o r Series I I I blends. LLDPE w i t h LDPE i s immiscible ( v i z . Series I I ) . ( i i ) B l e n d i n g two d i f f e r e n t t y p e s o f LLDPE r e s u l t e d i n improved s t r a i n h a r d e n i n g a t about 20 wt% o f l o a d i n g . However, i t was more e f f i c i e n t t o b l e n d LLDPE w i t h l o w m o l e c u l a r w e i g h t , MW,


UTRACKI


183


7.

F i g u r e 18. The e l o n g a t i o n a l v i s c o s i t y i n s t e a d y s t a t e f l o w a t T = 150°C v s . s t r a i n r a t e f o r S e r i e s - I LPX-30/LLDPE-10 b l e n d s ( t o p ) and S e r i e s - I I , LLDPE/LDPE b l e n d s ( b o t t o m ) . The d a t a p o i n t s marked w i t h arrow on a s i d e i n d i c a t e t h a t e q u i l i b r i u m v a l u e has not been reached.



184


10-

2

10-

10"

10 "

2

1

1

1

10°

10

1

10

2

1

£(s- );0)(rad/sec); y(s~ ) F i g u r e 19. Comparison of r a t e of d e f o r m a t i o n dependence o f t h e s t e a d y s t a t e ( c a p i l l a r y ) v i s c o s i t y , n, ( p o i n t s ) w i t h the complex, rf*, ( s o l i d l i n e ) dynamic, n , ( b r o k e n l i n e ) and e x t e n s i o n a l v i s c o s i t y , ng/3 (open c i r c l e s ) . The d a t a a r e reduced t o common temperature 150°C. L e f t , S e r i e s - I , LLDPE/LLDPE, r i g h t , S e r i e s - I I LLDPE/LDPE b l e n d s . F o r c l a r i t y , t h e d a t a o f each b l e n d i s v e r t i c a l l y d i s p l a c e d by one decade. f



7.

UTRACKI

185


0

I 0.5 w

120 1.0

2

F i g u r e 20. C o m p o s i t i o n a l dependence o f 3 ^ 3 ; ^ = 10 and 100(s) f o r S e r i e s - I ( t o p ) and S e r i e s - I I

= r% n (bottom). n


at t


186


LDPE. High MW LLDPE and low MW LDPE have s i m i l a r v a l u e s o f TIE w h i c h g u a r a n t e e s f i n e d r o p l e t d i s p e r s i o n . A d d i t i o n o f 10% LDPE was s u f f i c i e n t f o r e n g e n d e r i n g SH i n LLDPE and i n c r e a s i n g i t s maximum s t r a i n a t b r e a k . ( i i i ) There i s a d i r e c t correspondence between SH and p r o c e s s a b i l i t y on a f i l m b l o w i n g l i n e . The SH c a n be g e n e r a t e d by l o n g c h a i n b r a n c h i n g , b l e n d i n g , i n c r e a s e i n MW o r MW d i s t r i b u t i o n . ( i v ) The T h e o l o g i c a l s t u d i e s o f LLDPE and i t s b l e n d s l e d t o development o f s e v e r a l new T h e o l o g i c a l dependencies, v i z . E q u a t i o n 10 w h i c h a l l o w s c a l c u l a t i o n o f t h e p r e s s u r e c o r r e c t i o n i n s h e a r v i s c o s i t y ; E q u a t i o n 24 e x p r e s s i n g t h e r a t e dependence o f t h e a p p a r e n t y i e l d s t r e s s ; E q u a t i o n 28 a new e x p r e s s i o n f o r m e l t - v i s c o s i t y average m o l e c u l a r w e i g h t ; E q u a t i o n 29 a l l o w i n g c o m p u t a t i o n o f t h e f r e q u e n c y r e l a x a t i o n spectrum from w h i c h a l l o t h e r l i n e a r v i s c o e l a s t i c f u n c t i o n s c a n be d e r i v e d ; E q u a t i o n 38 a l l o w i n g e s t i m a t i o n o f no from t h e c r o s s - p o i n t coordinates; E q u a t i o n 39 d e f i n i n g t h e i n i t i a l s l o p e o f t h e s t r e s s g r o w t h f u n c t i o n , w h i c h depends m a i n l y on MW d i s t r i b u t i o n . PART I I I , LLDPE BLENDS WITH PP Commercial PP and LLDPE r e s i n s were used. Their properties are l i s t e d i n Table I V . For t h e f i r s t s t a g e o f t h e program PP/LLDPE = 50:50 b l e n d s were examined w i t h o r w i t h o u t 10 w t % o f c o m p a t i b i l i z i n g e t h y l e n e - p r o p y l e n e b l o c k copolymer EP-1 o r EP-2 (3»9). S u r p r i s i n g l y , even a t -40°C, t h e m e c h a n i c a l p r o p e r t i e s o f t h e two-component b l e n d s were found t o be e i t h e r a d d i t i v e o r s y n e r g i s t i c . A d d i t i o n o f EP d i d n o t s i g n i f i c a n t l y a f f e c t them. F o r t h i s reason, i n t h e more e x t e n s i v e s t u d i e s w h i c h f o l l o w e d o n l y two component LLDPE/PP b l e n d s were i n v e s t i g a t e d ( 4 0 , 4 1 , 6 9 ) . The m i x t u r e s were p r e p a r e d i n a Werner and P f l e i d e r e r c o r o t a t i n g t w i n - s c r e e w e x t r u d e r , ZSK-30, a t 350 RPM and T - 170°C i n t h e f e e d zone i n c r e a s i n g l i n e a r l y t o 240°C a t t h e d i e . To p r e v e n t o x i d a t i o n 0.1 wt% o f I r g a n o x 1010/1024 b l e n d was added. The e x t r u d e r screws were o p t i m i z e d f o r maximum m i x i n g e f f i c i e n c y a t l o w o u t p u t r a t e , Q = 4 kg/hr. The g r a n u l a t e d and d r i e d e x t r u d a t e s were c o m p r e s s i o n o r t r a n s f e r molded i n t o specimens f o r T h e o l o g i c a l t e s t i n g . The T h e o l o g i c a l t e s t i n g was c a r r i e d o u t i n RMS and ICR a t 190°C and i n RER a t 150°C. The i n s t r u m e n t s and p r o c e d u r e s were d e s c r i b e d i n the preceeding p a r t . Preliminary tests B o t h t h e t h e o r e t i c a l and e x p e r i m e n t a l studies indicated that the h i g h e s t degree o f d i s p e r s i o n c a n be o b t a i n e d b l e n d i n g two l i q u i d s w i t h s i m i l a r v i s c o s i t i e s a t t h e same s t r e s s l e v e l as t h a t e x p e c t e d during mixing: x

opt = ni/n

38 2

0.3 t o 1.0

where s u b s c r i p t 1 i n d i c a t e s t h e d i s p e r s e d polymer and 2 i n d i c a t e s t h e m a t r i x ( 1 1 , 4 2 , 4 3 ) . F o r t h i s r e a s o n PP-1 and LLDPE-A were chosen as the most s u i t a b l e p a i r ( 3 9 ) . The samples c o n t a i n i n g 0, 50 and 100



Note:

1.32

108

36

25

917

5.2/6.3

-

5/0.5

901/897

—

Hercules

EP-l/EP-2

w i t h 11 and 14% o f e t h y l e n e , r e s p e c t i v e l y

8120

13

13

8.5

( a ) E t h y l e n e - p r o p y l e n e - e t h y l e n e copolymers

0

Zero shear v i s c o s i t y , 190°C, n (k Pas)

6.

216

261

28.4

97.5

106 392

0.3

1.0

250

Molecular weights: M n (kg/mol) M w

5.

951

Dowlex 2517

LPX-24

918

Dow Chem.

LLDPE-C

resins

Exxon

LLDPE-B

325

0.8

4.0

M e l t i n d e x (g/10 min)

4.

900

D e n s i t y (kg/m )

3.

6701

6704

LLDPE-1

Esso

Hercules

Hercules

PF-1

LLDPE-A

o f PP/PE neat

PP-2

C h a r a c t e r i s t i c parameters

904

Designation

2.

3

Manufacturer

Parameter

1.

No.

Table IV.


( a )

188


wt% LLDPE-A were studied. The 50:50 blends containing 0 or 10% EP-1 or EP-2 were labeled: BL, BL-1 and BL-2, respectively. The capillary flow. The interlayer slip, apparent in uncompatibilized blend, BL, disappeared upon addition of EP-1 or EP-2. As shown i n F i g . 21 the s l i p affected the entrance-exit pressure drop, P , ("Bagley correction") more than v i s c o s i t y . The second interesting observation based on ICR and RMS r e s u l t s i s related to the need for pressure correction i n c a p i l l a r y flow. Already i n F i g . 19 an agreement between the dynamic v i s c o s i t y , n , and corrected for pressure e f f e c t c a p i l l a r y shear v i s c o s i t y , n, was shown. In F i g . 22 f i v e d i f f e r e n t measures of v i s c o s i t y are shown for LLDPE-A (four for the other samples): steady state elongational v i s c o s i t y , TIE/3, complex and dynamic v i s c o s i t y , n* and n , as well as the steady state c a p i l l a r y v i s c o s i t y corrected and uncorrected for the pressure e f f e c t s , n and n(ICR), r e s p e c t i v e l y . There i s a double equivalence of data points: n o r r " ' n( ) - n*» The latter equivalence has a form of an apparent Cox-Mertz r u l e . Evidently the true steady state v i s c o s i t y for LLDPE with the narrow molecular weight d i s t r i b u t i o n requires the pressure correction. When the data are properly corrected the equivalence between the steady state shear v i s c o s i t y and the loss-part of complex v i s c o s i t y is found. On the other hand, neglecting the pressure corrections results i n coincidental equivalence between n(ICR) and n*» In agreement with the polydispersity data i n Table IV for PP the pressure correction was s i g n i f i c a n t l y smaller than that determined for LLDPE-A. For the blends the correction was reduced even f u r t h e r , suggesting that molecular weight d i s t r i b u t i o n i n the phase adjacent to the c a p i l l a r y wall i s broader than that of either polymeric component, i n d i c a t i n g that LLDPE-A and PP may be p a r t i a l l y miscible. e

1


f

c o r r

n

a

n

d

I C R

C

The Dynamic flow. The flow curves, n vs. u> i n F i g . 22, were not corrected for the apparent y i e l d s t r e s s . For PP and LLDPE-A the curves nearly reached the Newtonian plateau and the Cole-Cole plots were found to be semi-circular i n d i c a t i n g that a * 0. However, for blends the s i t u a t i o n i s less c l e a r . Judging by the flow curves for BL, BL-1 and BL-2 at low deformation r a t e s , the Newtonian plateau seems to be far away. This may indicate the i n c i p i e n t y i e l d s t r e s s . To c l a r i f y this point n" vs. n* was plotted i n F i g . 23. An onset of the second relaxation mechanism i s v i s i b l e . The long relaxation times i n BL may only originate i n the interphase i n t e r a c t i o n s . These usually lead to the presence of the apparent y i e l d s t r e s s . The high frequency cross point coordinates ( G , u> ) were used for c a l c u l a t i o n of the Maxwellian zero-shear v i s c o s i t y , n oM> from Equation 38. For the neat polymers n M was i n agreement with no calculated from the shear and extensional responses. For BL, BL-1 and especially BL-2 TIQM ^ 0* presence of an apparent y i e l d s t r e s s i s the most l i k e l y explanation for the discrepancy. 1

y

x

x

0

n

T

n

e

The extensional flow* The stress growth functions i n shear (n > l a b e l l e d RMS) and extension, TIE* are shown i n F i g . 24. The dependencies for a l l five materials are s i m i l a r . There i s an excellent agreement between ng and 3TI . Note the absence of s t r a i n hardening, SH, c l e a r l y v i s i b l e (see F i g s . 13 and 14) i n blends of +

+



7.

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189

F i g u r e 21· Bagley p r e s s u r e c o r r e c t i o n term, Pe, v e r s u s shear s t r e s s , σ , f o r BL, BL-1, and BL-2. Data f o r BL-1 and BL-2 have been d i s p l a c e d h o r i z o n t a l l y by a f a c t o r o f 5 and 10 r e s p e c t i v e l y . 1 2


190



n(Pa.s)

F i g u r e 22. Elongational, T £ , complex, Tf*, dynamic, η , and s h e a r , η, v i s c o s i t i e s v e r s u s s t r a i n r a t e , έ, f r e q u e n c y , ω, o r shear r a t e , γ, f o r (from the t o p ) : LLDPE, BL, BL-1, BL-2 and PP a t 190°C. The d a t a c o r r e c t e d f o r p r e s s u r e e f f e c t s a r e shown as f u l l squares. F o r c l a r i t y the t r a c e s a r e d i s p l a c e d v e r t i c a l l y each by one decade. 1



7.

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191


F i g u r e 23. Imaginary p a r t , η", v e r s u s r e a l complex v i s c o s i t y f o r BL, BL-1, and BL-2.

part,

1

η , of


the



192

+

+

F i g u r e 24. Comparison of s h e a r , 3 η , and e l o n g a t i o n a l , T £ time dependent v i s c o s i t i e s f o r (from t o p ) PP, BL-2, BL-1, and LLDPE a t 190°C.


7.

UTRACKI

MeU Flow ofPolyethylene Blends

193

LLDPE s i m i l a r t o LLDPE-A polymer, the LPX-30. For PP a s t r a i n t h i n n i n g e f f e c t may be s u s p e c t e d . I n F i g . 22 the s t e a d y s t a t e v i s c o s i t i e s f o r PP and BL n g d ) « 3η(ω) were r e p o r t e d . F o r t h e o t h e r samples Tig * o b s e r v e d , but the d e p a r t u r e from e q u a l i t y was s m a l l . The i n i t i a l s l o p e S o f t h e r e l a t i o n shown i n F i g . 24 was c a l c u l a t e d a c c o r d i n g t o E q u a t i o n 39. For t h e two homopolymers S i n c r e a s e d w i t h M^Mn i n a c c o r d w i t h d a t a p r e s e n t e d i n F i g . 15. F o r b l e n d s , S was above average i n d i c a t i n g p a r t i a l m i s c i b i l i t y .


w

a

s

Sumary. The f o l l o w i n g o b s e r v a t i o n s a r e w o r t h n o t i n g : ( i ) The b l e n d s were p r e p a r e d from r e l a t i v e l y low m o l e c u l a r w e i g h t , n e a r l y i s o v i s c o u s polymers. They were i m m i s c i b l e , a l t h o u g h t h e T h e o l o g i c a l d a t a i n d i c a t e d b r o a d e n i n g o f the r e l a x a t i o n time spectrum, c o n s i s t e n t w i t h p a r t i a l m i s c i b i l i t y o f the l o w e s t m o l e c u l a r weight f r a c t i o n s . ( i i ) The p a r t i a l m i s c i b i l i t y was not s u f f i c i e n t t o p r e v e n t the i n t e r l a y e r s l i p i n c a p i l l a r y f l o w ; f o r t h i s purpose a c o m p a t i b i l i z i n g b l o c k copolymer had t o be added. ( i i i ) The c a p i l l a r y f l o w d a t a f o r polymers w i t h narrow molecular weight distribution s h o u l d be c o r r e c t e d f o r the p r e s s u r e e f f e c t s ; a f t e r c o r r e c t i o n the e q u i v a l e n c e η * η' was found, ( i v ) For t h e d e f o r m a t i o n r a t e s ω, γ > 10"" sec t h e apparent y i e l d s t r e s s was u n i m p o r t a n t . (v) The s t r a i n h a r d e n i n g i n e x t e n s i o n was absent f o r PP-1, LLDPE-A and t h e i r b l e n d s . 2

Detailed Studies o f LLDPE/PP Blend Flow (40, 41, 69) P o l y p r o p y l e n e PP-2 was blended e i t h e r w i t h LLDPE-B (System-1) o r LLDPE-C (System-2). The homopolymer c h a r a c t e r i s t i c s a r e g i v e n i n T a b l e IV. I n each system seven blends c o n t a i n i n g 0, 5, 25, 50, 75, 95 and 100 wt% PP was p r e p a r e d . Neat polymers and t h e i r blends were s t u d i e d i n dynamic shear f i e l d ( u s i n g RMS) and i n c o n s t a n t s h e a r s t r e s s f i e l d u s i n g Rheometric S t r e s s Rheometer, RSR. The m o l e c u l a r parameters o f polymers and b l e n d s were determined by S i z e E x c l u s i o n Chromatography i n t r i c h l o r o b e n z e n e a t 140°C. The morphology o f f r e e z e - f r a c t u r e d specimens was c h a r a c t e r i z e d i n Scanning E l e c t r o n M i c r o s c o p e , SEM, J e o l JSM-35CF. Molecular weights* The number, weight and average m o l e c u l a r w e i g h t s , M, M and M , r e s p e c t i v e l y a r e shown i n F i g . 25. The broken l i n e s r e p r e s e n t t h e dependencies p r e d i c t e d by E q u a t i o n s 15 t o 17. There i s good agreement between the experiment and p r e d i c t i o n s f o r samples c o n t i n u i n g l e s s t h a n 75% PP; f o r P P - r i c h samples t h e e x p e r i m e n t a l data i n d i c a t e d e g r a d a t i o n . I t i s worth p o i n t i n g o u t t h a t w i t h i n the e x p e r i m e n t a l e r r o r ( i n d i c a t e d by a b a r i n F i g . 25) the m o l e c u l a r w e i g h t s o f neat PP b e f o r e and a f t e r compounding/ e x t r u s i o n were t h e same. Thus PP degraded o n l y i n the presence o f LLDPE. The e x t e n t o f t h i s e f f e c t was l a r g e r f o r h i g h e r m o l e c u l a r weight LLDPE-B t h a n LLDPE-C. I t primarily affected the highest m o l e c u l a r weight f r a c t i o n s , r e d u c i n g M^^ and M but leaving M virtually intact. The r e s p o n s i b l e mechanism seems t o be s h e a r d e g r a d a t i o n o f PP c a t a l y z e d by LLDPE o r r a t h e r by same i t s impurities. n

w

z

z

n

Morphology. The SEM o f f r e e z e - f r a c t u r e d System-1 specimens i n d i c a t e s d i s p e r s e d d r o p l e t morphology i n blends c o n t a i n i n g 5, 75 and 95% PP



F i g u r e 25. C o m p o s i t i o n a l v a r i a t i o n of average m o l e c u l a r weights f o r System 2 ( l e f t ) and \ · P o i n t s - e x p e r i m e n t a l , broken l i n e s c a l c u l a t e d from E q u a t i o n s 15 t o 17.


7.

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195

and c o - c o n t i n u o u s s t r u c t u r e f o r t h e r e m a i n i n g blends c o n t a i n i n g 2 5 and 50% PP. I n System-2 c o - c o n t i n u o u s morphology f o r 50% PP b l e n d s was observed. The apparent y i e l d stress» The complex v i s c o s i t y η* v s . ω f o r PP b l e n d s w i t h LLDPE-B and LLDPE-C i s shown i n F i g . 2 6 . The p l o t c l e a r l y i n d i c a t e s p o s s i b l e y i e l d s t r e s s behavior e s p e c i a l l y f o r b l e n d s c o n t a i n i n g 5 0 % PP. The apparent y i e l d s t r e s s i n dynamic f l o w d a t a was c a l c u l a t e d u s i n g E q u a t i o n 2 3 , w i t h F - G* o r F * G". The y i e l d s t r e s s v a l u e s a s w e l l a s t h e assumed m a t r i x m a t e r i a l f o r c a l c u l a t i n g F a r e l i s t e d i n T a b l e V. F o r b o t h systems t h e maximum v a l u e o f t h e apparent y i e l d s t r e s s o c c u r r e d a t 5 0 % PP. I n f a c t , t h e r e i s a d i r e c t c o r r e l a t i o n - i n a g i v e n system t h e y i e l d i n g i s p r i m a r i l y observed i n b l e n d s h a v i n g a c o - c o n t i n u o u s s t r u c t u r e . As b e f o r e ( 5 3 0 Gy > ( Ç I n t h e l a s t column o f T a b l e V t h e d i r e c t l y measured shear s t r e s s values a t y i e l d are l i s t e d . These measurements were c a r r i e d o u t i n RSR, s e t t i n g t h e d e s i r e d l e v e l o f s t r e s s and r e c o r d i n g t h e s t r a i n a f t e r 2 0 0 s. The r e s u l t s a r e shown i n F i g . 2 7 . There i s good agreement between Gy and σ f o r System-1 b u t n o t f o r s y s t e m - 2 . The two s e t s o f e x p e r i m e n t s a r e c a r r i e d o u t on a d i f f e r e n t time scale. S i n c e , a c c o r d i n g t o E q u a t i o n 2 4 , t h e apparent y i e l d s t r e s s i n b l e n d s depends o n time one s h o u l d n o t expect t h e same r e s u l t s from the dynamic and c r e e p measurements. F u r t h e r m o r e , t h e differences i n l e s s viscous System-2 a r e expected t o be l a r g e r than those f o r System-1.


m

ν

The frequency dependence o f d a t a [ c o r r e c t e d f o r t h e y i e l d s t r e s s by means o f E q u a t i o n 2 5 ] was found t o f o l l o w E q u a t i o n 1 9 . Having e s t a b l i s h e d v a l u e s o f t h e f o u r parameters: i j , mj and m t h e r e l a x a t i o n s p e c t r a were computed from E q u a t i o n 2 9 . These a r e shown in Fig. 28. F o r v e r i f i c a t i o n o f t h e procedure G'calc^) computed from E q u a t i o n 3 5 . I n F i g . 2 9 i t s v a l u e s a r e compared w i t h experimental G (ω) data uncorrected f o r the y i e l d stress. Furthermore, knowing η , t h e l o s s modulus, G^ ^ , a s w e l l as t h e y i e l d v a l u e s f o r G and G" i t was p o s s i b l e t o compute η* = η*(ω) dependence. These v a l u e s a r e shown a s l i n e s i n t e r s e c t i n g t h e experimental data p o i n t s i n F i g . 2 6 . 2

w

a

s

1

1

a

c

1

The concentration dependence o f η computed from E q u a t i o n 2 0 i s shown i n F i g . 3 0 , where t h e s o l i d p o i n t s r e p r e s e n t t h e e x p e r i m e n t a l d a t a and t h e open p o i n t s t h e i r v a l u e s c o r r e c t e d f o r t h e e f f e c t s o f PP degradation. F o r System-1 t h e r e i s s t r o n g n e g a t i v e d e v i a t i o n (NDB) from t h e l o g a d d i t i v i t y r u l e , v i z . E q u a t i o n 1 , but f o r System-2 NDB i s v i s i b l e a t low PP c o n t e n t , c o n v e r t i n g t o p o s i t i v e d e v i a t i o n (PDB) at high. I t i s worth r e c a l l i n g t h a t η was computed from c o r r e c t e d f o r t h e y i e l d s t r e s s v a l u e s o f η'. The NDB b e h a v i o r , i n d i c a t i v e o f i n t e r l a y e r s l i p , r e f l e c t s poor m i s c i b i l i t y i n System-1 and t h a t a t low c o n c e n t r a t i o n o f PP i n S y s t e m - 2 . The e m u l s i o n - l i k e b e h a v i o r o f System-2 a t h i g h PP c o n t e n t r e f l e c t s a b e t t e r i n t e r p h a s e i n t e r a c t i o n . 0

0

The Cole-Cole plot f o r System-2 i s p r e s e n t e d i n Fig. 31. A "classical" semi-circular dependence was o b t a i n e d f o r blends c o n t a i n i n g 0 , 5 , 2 5 , 9 5 and 1 0 0 % PP. F o r t h e r e m a i n i n g two b l e n d s



196


F i g u r e 26. Complex v i s c o s i t y v s . f r e q u e n c y , τ|* v s . ω, f o r System 1 ( t o p ) and 2. P o i n t s a r e e x p e r i m e n t a l , l i n e s computed from t h e f r e q u e n c y r e l a x a t i o n spectrum.


7.

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197

Met Flow ofPolyethylene Blends

Table V. Apparent y i e l d s t r e s s f o r PP blended LLDPE-B o r LLDPE-C

G» (Pa)

5

PE

0

0

2.

25

PE

40

0

3.

50

PP

58

1.0

4.

75

PP

0.8

0

5.

95

PP

0

0

5

PE

0

0

7.

25

PE

0.5

0.2

8.

50

PP

5

0

9.

75

PP

2

1.4

10.

95

PP

0

0

1.


G" (Pa) y

Material

No. B l e n d

PP ( w t % )

System-1

6.

System-2

y

with

o (Pa) y

36

52

-

0.1 Ύ 0.05

0

100 a (Pa)

200

12

F i g u r e 27. Shear s t r a i n , γ, as a f u n c t i o n o f shear s t r e s s , σχ2> f o r b l e n d s c o n t a i n i n g 50% o f each polymer. Curve 1: PP/LLDPE-1, c u r v e 2: PP/LLDPE-2




198

F i g u r e 28. Reduced f r e q u e n c y r e l a x a t i o n System 1 ( t o p ) and System 2.

spectrum f o r LLDPE/PP


UTRACKI


199


7.

F i g u r e 29. Storage shear modulus v s . f r e q u e n c y f o r System 1. The p o i n t s are e x p e r i m e n t a l , u n c o r r e c t e d f o r the apparent y i e l d s t r e s s , the l i n e s computed from the r e l a x a t i o n spectrum.



200


F i g u r e 30. Zero shear v i s c o s i t y , η , v s . PP c o n t e n t i n Systems 1 and 2; open p o i n t s - d a t a c o r r e c t e d f o r P P - d e g r a d a t i o n . 0

η F i g u r e 31. 190°C.

Cole-Cole p l o t ,

1

3

(X10" Pa.s) n" v s . η', f o r LLDPE/PP System 2 a t


7.

UTRACKI

Mdt Flow ofPolyethylene Blends

201

w i t h 50 t o 7 5 % PP t h e r e i s a n i n d i c a t i o n o f a bimodal r e l a x a t i o n spectrum. F o r t h i s system t h e b i m o d a l i t y cannot be g e n e r a t e d a p p l y i n g a m i x i n g r u l e t o t h e homopolymer s p e c t r a . C l e a r l y an i n f l u e n c e o f the i n t e r p h a s e i s r e s p o n s i b l e f o r the a p p a r e n t y i e l d stress. The dependence f o r System-1 shows a d e p a r t u r e from s e m i - c i r c u l a r b e h a v i o r f o r b l e n d s c o n t a i n i n g 5, 25 and 5 0 % PP b u t none f o r those w i t h 0, 75, 95 and 100% PP. I f the appearance o f b i m o d a l i t y o f the r e l a x a t i o n s i n C o l e - C o l e p l o t i s equated w i t h f o r m a t i o n o f co-continuous s t r u c t u r e , t h e n i n System-1 t h e s e o c c u r a t 5 t o 40 wt% PP whereas i n System-2 a t 50 and 75 wt% PP. P a u l and Barlow proposed the f o l l o w i n g dependence ( 7 0 ) ; Φ /(1-Φ ) - n i / n


ί

1

42

< >

2

where i s the volume f r a c t i o n o f the d i s p e r s e d phase i n v e r t i n g i n t o the c o n t i n u o u s and η , η a r e v i s c o s i t i e s o f the d i s p e r s e d and c o n t i n u o u s phases. Assuming t h a t the s h e a r s t r e s s i n t h e compounding e x t r u d e r was about 10 kPa, t h e n E q u a t i o n 42 p r e d i c t s i n v e r s i o n a t 8 t o 79% o f PP i n System-1 and -2, r e s p e c t i v e l y . The d i r e c t SEM o b s e r v a t i o n s i n d i c a t e d i s p e r s e d s t r u c t u r e s a t 5% but co-continuous ones a t 25 and 50% PP i n System-1 a s w e l l a s a t 50 and 75% PP i n System-2. I t i s a p p a r e n t t h a t phase i n v e r s i o n , t a k e s p l a c e v i a c o - c o n t i n u o u s s t r u c t u r e . E q u a t i o n 42 seems t o p r e d i c t t h e i n v e r s i o n concentration f a i r l y well. However, the c o - c o n t i n u o u s s t r u c t u r e i s observed not o n l y near the p r e d i c t e d but a l s o a t 50:50 l o a d i n g where the volume f r a c t i o n s o f t h e two polymers a r e n e a r l y e q u a l . The b r o a d e n i n g o f the i n v e r s i o n r e g i o n from a s i n g l e t o a wide range o f c o m p o s i t i o n ( i n c l u d i n g e q u i - v o l u m e t r i c ) most l i k e l y i s due t o a n o n - e q u i l i b r i u m n a t u r e o f morphology. 1

2

The cross-point coordinates G = G' G" a t ω * ωχ were d e t e r m i n e d f o r a l l c o m p o s i t i o n s t h e n the M a x w e l l i a n v i s c o s i t y η ^ was c a l c u l a t e d from E q u a t i o n 38. The r e s u l t s a r e shown i n F i g . 32 a s 0M · ο· !n agreement w i t h the p r e v i o u s l y d i s c u s s e d d a t a f o r LLDPE blends (see F i g . 12) i n i t i a l l y η « η ; only f o r higher v a l u e s : η > 1 0 0 k P a s , t h e r e i s a d e v i a t i o n from e q u a l i t y . x

n

ν δ

η

0

0 Μ

0

In summary, the PP/LLDPE b l e n d s a r e i m m i s c i b l e and the degree o f i n c o m p a t i b i l i t y i n c r e a s e s w i t h m o l e c u l a r w e i g h t o f the homopolymers. An i n c r e a s e o f m o l e c u l a r weight a l s o s h i f t s t h e appearance o f t h e apparent y i e l d s t r e s s t o higher frequencies a c c e s s i b l e i n standard t e s t equipment. The y i e l d s t r e s s seems t o be a s s o c i a t e d w i t h f l o w and deformability o f co-continuous blend structure. The c o - c o n t i n u o u s morphology extended from the c o n c e n t r a t i o n p r e d i c t e d by P a u l and Barlow's e m p i r i c a l e q u a t i o n up t o equi-volume polymer content. The f l o w c u r v e s , c o r r e c t e d f o r the y i e l d s t r e s s , c o u l d be d e s c r i b e d by the f o u r - p a r a m e t e r e q u a t i o n , w h i c h i n t u r n l e a d t o the spectrum o f r e l a x a t i o n times and d e r i v a t i o n o f o t h e r linear v i s c o e l a s t i c f u n c t i o n s i n good agreement w i t h d i r e c t l y measured values. There a r e s e v e r a l o t h e r observations important f o r those i n t e r e s t e d i n PP/LLDPE r h e o l o g y , but t h e i r g e n e r a l i t y i s u n c e r t a i n .



202


Tlo(k Pa.s) F i g u r e 32. Maxwellian v i s c o s i t y v s . zero-shear v i s c o s i t y f o r LLDPE/PP Systems 1 and 2. L a r g e r symbols i n d i c a t e homopolymer values.



Interlayer

Presence o f apparent yield stress, σ

5.

6.

Concentration dependence o f n

Cole-Cole p l o t

8.

9.

0

Frequency dependence

yes

no

yes

yes

large

yes

depends on LLDPE-Y t y p e

depending on t y p e o f LLDPE-Y: a d d i t i v e o r sigmoidal

s e m i c i r c u l a r f o r low MW; t h e n bimodal bimodal

( C o n t i n u e d on n e x t page.)

s i g m o i d a l o r goes through a minimum

miscible

goes t h r o u g h a maximum

a f t e r c o r r e c t i n g f o r σ i t c a n be d e s c r i b e d by a f o u r parameter e q u a t i o n , t h e n f r e q u e n c y r e l a x a t i o n s p e c t r u m and l i n e a r v i s c o e l a s t i c f u n c t i o n s can be c a l c u l a t e d

no

no

γ

very large


Extrudate swell

4.

slip

yes

yes

n ( c a p i l l a r y ) » η'

3.

partially

PP

depends on p o l y d i s p e r s i t y

yes

Need f o r p r e s s u r e correction i n capil l a r y flow

2.

immiscible


M i s c i b i l i t y with LLDPE-X i n t h e m e l t

1.

LDPE

PROPERTY

LLDPE-Y

Summary o f T h e o l o g i c a l b e a v i o r o f LLDPE-X b l e n d s w i t h LLDPE-Y, LDPE and PP

No.

Table V I .


δ

ι


I n i t i a l s l o p e o f ng, S

Maximum s t r a i n a t break, ε

The r a t i o η,,(ε)/3η(ω)

12.

13.

14.

Shear d e g r a d a t i o n

The a c t i v a t i o n energy o f f l o w η (kJ/mole) at constant s t r e s s

15.

16.

Ci

S t r a i n hardening i n extensional flow

11.

at ε * ω

Cross-point coordinates

PROPERTY

^ 3.2

30 ± 2

yes

>1

n

0 " 0j4

present

n

LLDPE-Y

f

r

n

0

strong

*00 kPas; above t h i s l i m i t η

1

42 ± 2

»

>3.2

0

Μ

absent

ης

PP

45 ± 3

yes o f PP

* 1

$ 3 . 2 depending o n I and c o n c e n t r a t i o n

t h e v a l u e depends on p o l y d i s p e r s i t y

o

LDPE

Summary o f T h e o l o g i c a l b e a v i o r o f LLDPE-X b l e n d s w i t h LLDPE-Y, LDPE and PP ( c o n t . )

10.

No.

Table V I .


ι

Ο

Ο

i

7.

UTRACKI

205


An example o f t h e s e i s t h e s t r a i n s o f t e n i n g f o r PP o r LLDPE-induced d e g r a d a t i o n o f PP. The b e h a v i o r i s complex but s e l f - e v i d e n t .


PART IV.

GENERAL CONCLUSIONS

The s i m i l a r i t i e s and d i f f e r e n c e s between LLDPE blends w i t h LLDPE, LDPE and PP a r e summarized i n Table V I . The LLDPE was found t o b e : i m m i s c i b l e w i t h LDPE (even o f low MW), m i s c i b l e o r not w i t h a n o t h e r LLDPE r e s i n (miscibility seems t o be l i m i t e d t o t h e same p o l y m e r i z a t i o n p r o d u c t s ) and c o m p a t i b l e w i t h PP. Miscibility broadens MWD what a f f e c t s t h e r h e o l o g i c a l b e h a v i o r i n a p r e d i c t a b l e way. On the o t h e r hand the i m m i s c i b i l i t y e s p e c i a l l y a t l o w e r l o a d i n g l e a d s t o d i s p e r s e d morphology; upon imposed s t r a i n t h i s may t u r n i n t o a co-continuous s t r u c t u r e . I n most blends t h e l o g - a d d i t i v i t y r u l e i s d i s o b e y e d ; when t h e i n t e r f a c i a l interactions are attractive a p o s i t i v e d e v i a t i o n from the r u l e i s o b s e r v e d , when they a r e r e p u l s i v e an i n t e r l a y e r s l i p l e a d s t o n e g a t i v e d e v i a t i o n . Immiscibility i s a l s o r e s p o n s i b l e f o r t h e apparent y i e l d s t r e s s and u s u a l l y l a r g e extrudate length reduction. There i s little difference i n e x t e n s i o n a l b e h a v i o r between m i s c i b l e and i m m i s c i b l e blends a l t h o u g h t h e l a t t e r system show r e d u c t i o n o f t h e maximum s t r a i n a t b r e a k and a s l o w e r i n c r e a s e o f t h e t r a n s i e n t v i s c o s i t y , TIE> w i t h s t r a i n i n g time (MWD e f f e c t ) . Working f o r y e a r s w i t h t h e s e " s i m p l e " polymers one i s c o n t i n u o u s l y s u r p r i s e d how d i v e r s e t h e i r b e h a v i o r can be. NOTATION » c o e f f i c i e n t i n E q u a t i o n 23

V i

• c o e f f i c i e n t s i n E q u a t i o n s 11 and 12

Β

• extrudate swell

b

β

polynomial c o e f f i c i e n t s i n Equation 9

β

η-paraffins

C,

d

• capillary

D

» extrudate diameter

ΕPR,

EPDM

diameter

• b i n a r y and t e r n a r y copolymers propylene

o f ethylene and

Ε , Ε.

• a c t i v a t i o n energy o f f l o w e i t h e r a t c o n s t a n t s t r e s s o r constant r a t e of shear

F, F , F , F a* y* m

m

r h e o l o g i c a l f u n c t i o n , i t s a p p a r e n t , y i e l d and i n the m a t r i x v a l u e ; E q u a t i o n s 23 and 24

β

h i g h frequency y i e l d s t r e s s i n E q u a t i o n 24

β

s t o r a g e , l o s s and complex shear modulus (Pa)

F

00 y

G», G", G*


206


G = G» » G" χ

• c r o s s - p o i n t shear modulus (Pa) - h i g h d e n s i t y PE

HDPE

β

V

H

G

and Η^/η ; 0

• maximum v a l u e o f

G, max i

» /-I

Im

• i m a g i n a r y p a r t o f a complex f u n c t i o n

J

• steady s t a t e e


f r e q u e n c y r e l a x a t i o n spectrum E q u a t i o n 29

compliance

* c a p i l l a r y length

L * long chain branching LCB • low d e n s i t y p o l y e t h y l e n e LDPE « l i n e a r LDPE LLDPE ^0 »

L

* specimen l e n g t h a t t

oo

= parameters M , M , M , M η w ζ n

β

s

0 and t • »

of E q u a t i o n 2 0

number, w e i g h t , z- and η-average

= molecular

MW

weight

MW • m o l e c u l a r weight

distribution

MWD - power-law exponent η Ni

• f i r s t normal s t r e s s d i f f e r e n c e

NDB

- negative d e v i a t i n g blends

Ρ

β

t o t a l p r e s s u r e l o s s i n c a p i l l a r y f l o w (Pa)

PDB, PNDB

β

p o s i t i v e , p o s i t i v e - n e g a t i v e d e v i a t i n g blends

P*

β

pressure

Ρ

• c a p i l l a r y e n d - e f f e c t s p r e s s u r e l o s s (Pa) e

PE PP Q

β

a

reducing

factor

in

Equation

polyethylene polypropylene

• e x t r u d e r output • correlation coefficient

squared


10

7.

UTRACKI


i\

= f u n c t i o n d e f i n e d i n E q u a t i o n 29 s

Re R

R

T> T 0

r e a l p a r t o f a complex f u n c t i o n

~ Trouton

ratio

deformation,


207

at f i n i t e

and z e r o

respectively

s

- v a r i a b l e i n E q u a t i o n 32

S

= i n i t i a l s l o p e d e f i n e d i n E q u a t i o n 39

SCB

- short chain branching

SEC

= s i z e e x c l u s i o n chromatography

SH

- strain

t

= time

Τ

- temperature (°C)

T*

= temperature

u

« exponent i n E q u a t i o n 24

ULDPE

= u l t r a low d e n s i t y PE

VLDPE

= v e r y low d e n s i t y PE

w^

= weight

a,0

= parameters =

01, 0 i 2 γ

s l i

P

rate of

hardening

reducing f a c t o r (K)

f r a c t i o n of polymer i n E q u a t i o n 21

coefficient

and i t s i n t r i n s i c v a l u e

= shear s t r a i n i n dynamic

tests

•

γ / ε,

= shear r a t e ( 1 / s ) = Hencky s t r a i n , s t r a i n at break

ε

= s t r a i n rate i n extension (1/s)

η

= steady s t a t e shear v i s c o s i t y

η'

= dynamic shear

no, noM

ΤΪ+

Λ 1 Λ

=

zero-shear liquid = compted

viscosity

viscosity

from

(Pa»s)

Η

and no f o r M a x e w e l l i a n

stress

growth

function i n


208 n


E> ^ , 0

* u n i a x i a l extensional v i s c o s i t y zero deformation rate ( P a « s )

Tig ^ '


finite

* l i n e a r v i s c o e l a s t i c component of the growth function i n uniaxial extension

n^, n

- stress growth function i n uniaxial and i n shear

+

η*

- complex v i s c o s i t y

λ

« viscosity ratio

0

at

and

stress

extension

» functions defined i n Equation 29

i

• volume f r a c t i o n 3

Ρ

- density

o*k

« extensional stress at break (Pa)

an

- extensional

σ

- shear stress (Pa)

τ

1 2

γ

ω ω

(kg/m )

stress (Pa)

• primary relaxation time

(s)

* relaxation

network;

time

• angular frequency • cross-point

χ

ω

of

a

Equation 24

(rad/s)

frequency

• frequency for maximum of Η

LITERATURE CITED 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Anon., Chem. Market Reporter 1987, pg 3, 23. Ruof, M.; Fritz, H.-G.; Geiger, K. Kunststoffe, 1987, 77, 480. Romanini, D. Polym.-Plast. Technol. Eng. 1982, 19, 201. Nowlin, T.E. Prog. Polym. Sci. 1985, 11, 29. Keii, T.; Soga, Κ., Eds. Catalytic Polymerization of Olefins, Kodansha, Tokyo, 1986. "Modern Plastics Encyclopaedia - 1988", McGraw-Hill, New York, 1987. Plochocki, A.P. Trans. Soc. Rheology 1976, 20, 287. Plochocki, A.P. In Polymer Blends; Paul, D.R; Newman, S., Eds.; Academic Press, New York, 1978. Plochocki, A.P. Polym. Eng. Sci. 1982, 22, 1153. Utracki, L.A. Adv. Plast. Technol. 1985, 5, 41: J. Elastom. Plast. 1986, 18, 177.


7. UTRACKI Melt Flow of Polyethylene Blends 11. 12. 13. 14. 15. 16. 17. 18.


19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43.

209

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RECEIVED April 27,

1989


Multiphase Polymers: Blends and Ionomers - ACS Publications

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