Recent Developments in Structure Analysis of Fibrous Polymers - ACS

3 Recent Developments in Structure Analysis of Fibrous Polymers Downloaded by UNIV OF CALIFORNIA SAN DIEGO on March 28, 2016 | http://pubs.acs.org Publication Date: November 17, 1980 | doi: 10.1021/bk-1980-0141.ch003

HIROYUKI TADOKORO Department of Polymer Science, Faculty of Science, Osaka University, Toyonaka, Osaka, 560 Japan

As is well known the x-ray diffraction data of polymers are less abundant than in the case of single crystals of low-molecular-weight substances. Therefore the essential process of the x-ray analysis of polymers is still a trial-and-error method (1). To overcome this difficulty, various useful methods have been developed. The Cochran-Crick-Vand equation for helical polymers (2), the molecular transform of nonhelical polymers (3), the calculation of intramolecular interaction energy (4), molecular conformation parameter equations (5-11), the cylindrical Patterson function (12), and information from infrared and Raman spectroscopy (13) are all important for setting up molecular models. The constrained least-squares method (14,15) the packing energy minimization method (16), and the combination of these two methods (17,18) are very useful for the refinement of atomic parameters. A position sensitive proportional counter (PSPC) has found to be useful in wide angle diffraction as well as in small angle scattering (19). A troidal focusing camera (20,21) and a vacuum cylindrical camera with radius 10 cm (22) have been used to obtain well separated, good intensity data. In this paper useful methods and techniques for structure analysis will be discussed using examples from the author's studies. I n t r a m o l e c u l a r I n t e r a c t i o n Energy o f T y p i c a l I s o t a c t i c

Polymers

The i n t r a m o l e c u l a r i n t e r a c t i o n e n e r g y was c a l c u l a t e d f o r f i v e i s o t a c t i c polymers, namely, i s o t a c t i c p o l y p r o p y l e n e , p o l y ( U methyl-l-pentene), poly(3-methy1-1-butene), polyacetaldehyde, and p o l y ( m e t h y l m e t h a c r y l a t e ) (23.). The m o l e c u l a r s t r u c t u r e s o f t h e f i r s t f o u r p o l y m e r s have a l r e a d y b e e n d e t e r m i n e d b y x - r a y a n a l y s e s as (3/1) ( 2 U ) , (7/2) ( l 8 , 2 5 , 2 6 ) , (h/l) ( 2 7 ) , a n d (h/l) h e l i c e s (28), r e s p e c t i v e l y . H e r e (7/2) means s e v e n monomeric u n i t s t u r n twice i n the f i b e r i d e n t i t y p e r i o d . F o ri s o t a c t i c poly(methyl m e t h a c r y l a t e ) (29), a ( 5 / l ) h e l i x was c o n s i d e r e d r e a s o n a b l e a t t h e t i m e o f t h e e n e r g y c a l c u l a t i o n i n 1970, b e f o r e t h e d i s c o v e r i n g o f

0-8412-05 89-2/ 80/47-141-043$05.00/0 © 1980 American Chemical Society French and Gardner; Fiber Diffraction Methods ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on March 28, 2016 | http://pubs.acs.org Publication Date: November 17, 1980 | doi: 10.1021/bk-1980-0141.ch003

44

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METHODS

t h e d o u b l e h e l i x s t r u c t u r e w h i c h w i l l b e d i s c u s s e d l a t e r (30.). The e n e r g y c a l c u l a t i o n s were p e r f o r m e d w i t h o u t f i x i n g t h e f i b e r i d e n t i t y p e r i o d , t h e only assumption being t h a t t h e chain forms a h e l i c a l s t r u c t u r e , t h a t i s , t h e s e t o f i n t e r n a l r o t a t i o n a n g l e s r e p e a t s a l o n g t h e s u b s e q u e n t monomeric u n i t s o f t h e c h a i n . F o r t h e c a l c u l a t i o n t h e i n t e r n a l r o t a t i o n b a r r i e r s , v a n d e r Waals i n t e r a c t i o n s [mainly a f t e r Scheraga ( 3 1 ) ] , and d i p o l e - d i p o l e i n t e r a c t i o n s were t a k e n i n t o a c c o u n t . Polypropylene and polyacetaldehyde a r e t h e s i m p l e s t o f t h e above p o l y m e r s , h a v i n g o n l y t w o i n t e r n a l r o t a t i o n a n g l e s , and T ^ , i n t h e m a i n c h a i n . F i g u r e 1 shows t h e p o t e n c i a l e n e r g y c o n t o u r map f o r p o l y a c e t a l d e h y d e . The c r o s s e s i n d i c a t e t h e p o t e n t i a l minima, and the c l o s e d c i r c l e s t h e x-ray s t r u c t u r e determined by N a t t a e t a l . (28^. The t w o m i n i m a c o r r e s p o n d t o t h e r i g h t - a n d left-hand helices. The o t h e r t h r e e p o l y m e r s have a d d i t i o n a l r o t a t i o n a n g l e s i n the s i d e c h a i n s , T ~ and/or T ^ . Forpoly(3-methyl-l-butene),the minimum was f o u n d i n t h e t h r e e - d i m e n s i o n a l p l o t . F o r poly(dim e t h y l - 1 - p e n t ene) a n d p o l y ( m e t h y l m e t h a c r y l a t e ) , t h e s t a b l e c o n f o r m a t i o n o f t h e s i d e c h a i n was f i r s t c a l c u l a t e d w i t h t h e f i x e d m a i n c h a i n c o n f o r m a t i o n c o r r e s p o n d i n g t o t h e (7/2) a n d ( 5 / 1 ) h e l i ces, respectively. The p o t e n t i a l e n e r g y was c a l c u l a t e d a g a i n s t the main c h a i n r o t a t i o n a n g l e s , x and T ^ , b y f i x i n g T and of the s i d e chain a t t h e values thus obtained. 1

Table I . S t a b l e Conformations (23) Energy c a l c u l a t i o n Polymer T (°) 2

X-ray a n a l y s i s

N

T (°) 2

N

it-Polypropylene

179

-56

2.91

180

-60

3.0

it-Poly(U-methyl1-pentene)

163

-71

3.52

162

-71

3.5

it-Poly(3-methyl1-butene)

132

-83

It. 17

lk9

-81

lt.0

i t - P o l y a c etaldehyde

131

-80

3.9k

136

-83

lt.0

'

Journal of Polymer Science, Polymer Physics Edition

The r e s u l t s o f t h e f i r s t f o u r p o l y m e r s a r e l i s t e d i n T a b l e I ; t h e i n t e r n a l r o t a t i o n a n g l e s o f t h e m a i n c h a i n , T.. a n d T , t h e number o f monomeric u n i t s p e r t u r n , N, f o r t h e c a l c u l a t e d s t a b l e conformations, and a l s o t h e values f o r t h e s t r u c t u r e determined by x-ray analyses. I n t h e c a s e o f p o l y p r o p y l e n e , t h e number o f monom e r i c u n i t s p e r t u r n i s 2.91, v e r y c l o s e t o t h e x - r a y v a l u e o f 3.0. T h i s r e s u l t f o r p o l y p r o p y l e n e i s e s s e n t i a l l y t h e same as t h o s e o f N a t t a e t a l . (32) a n d L i q u o r i e t a l . (33.). F o r t h e t h r e e o t h e r p o l y m e r s , good a g r e e m e n t s were a l s o o b t a i n e d b e t w e e n t h e p r e d i c t e d models and x - r a y s t r u c t u r e s i n s p i t e o f the s i m p l e assumption o f c o n s i d e r i n g only i n t r a m o l e c u l a r i n t e r a c t i o n s . This p

French and Gardner; Fiber Diffraction Methods ACS Symposium Series; American Chemical Society: Washington, DC, 1980.


3.

TADOKORO

45

Structure Analysis Developments

suggests t h a t the h e l i c a l s t r u c t u r e o f these four polymers a r e determined p r i m a r i l y by the i n t r a m o l e c u l a r i n t e r a c t i o n s , e s p e c i a l l y the s t e r i c hindrance o f the side chains. F i g u r e 2 shows t h e e n e r g y c o n t o u r map f o r i s o t a c t i c p o l y ( methyl methacrylate). The l o w e s t e n e r g y minimum was f o u n d a t t h e p o s i t i o n c o r r e s p o n d i n g t o a (12/1) h e l i x c o n t r a r y t o t h e e x p e c t a t i o n o f t h e (5/1) h e l i x . The minimum c o r r e s p o n d i n g t o t h e ( 5 / l ) h e l i x i s h i g h e r t h a n t h e (12/1) h e l i x b y 3 k c a l / m o l e o f monomer u n i t . This r e s u l t l e d t o the p o s t u l a t i o n o f the double stranded h e l i x f o r t h i s polymer. These energy c a l c u l a t i o n s c a n p r o v i d e s u i t a b l e and s t a b l e m o l e c u l a r m o d e l s , a n d have b e e n s u c c e s s f u l l y u t i l i z e d f o r t h e s t r u c t u r e a n a l y s e s o f many o t h e r p o l y m e r s , s u c h a s p o l y ( t e r t b u t y l e t h y l e n e o x i d e ) (3^0 a n d p o l y i s o b u t y l e n e (35)« Polyisobutylene The x - r a y a n a l y s i s o f p o l y i s o b u t y l e n e was a c h i e v e d b y t h e a u t h o r a n d h i s c o w o r k e r s (35.) a s shown i n F i g u r e 3 b y s t a r t i n g w i t h t h e (8/3) m o l e c u l a r m o d e l p r o p o s e d b y A l l e g r a e t a l . f r o m e n e r g y c a l c u l a t i o n s (36.). The p o l y i s o b u t y l e n e m o l e c u l e h a s o n l y a t w o f o l d screw-symmetry i n t h e c r y s t a l l a t t i c e , and d e v i a t e s a p p r e c i a b l y f r o m t h e (8/3) u n i f o r m h e l i x a s shown i n F i g u r e 3 ( b ) . The h e l i c a l molecule has a f i b e r p e r i o d c o n s i s t i n g o f two asymmetric u n i t s e a c h c o n t a i n i n g f o u r monomeric u n i t s . The h e l i x a x i s c o i n c i d e s w i t h t h e 2 s c r e w a x i s i n t h e l a t t i c e ^ i x~ 2 ^* a v e r a g e d b o n d a n g l e C-C(CH ) «C i s a b o u t 1 1 0 ° , but the a n g l e C-CI^-C i s much l a r g e r , a b o u t 1 2 8 ° . The c o n f o r m a t i o n i s t h e a l t e r n a t e s e q u e n c e o f n e a r l y gauche (-5^°) a n d n e a r l y t r a n s (-l6U° ). The o v e r a l l s t r u c t u r e i s s t i l l s i m i l a r t o t h e (8/3) h e l i x p r o posed by A l l e g r a e t a l . (36). 2 2

1

2

I)

T

h

e

1

2

P o l y ( e t h y l e n e o x y b e n z o a t e ) : q-Form The x - r a y d i a g r a m s u g g e s t e d t h a t t w o h e l i c a l c h a i n s , e a c h f i b e r p e r i o d c o n s i s t i n g o f t w o monomeric u n i t s , p a s s t h r o u g h a n o r t h o r h o m b i c u n i t c e l l (k). A s shown i n T a b l e I I , t h e number o f i n t e r n a l r o t a t i o n a n g l e s i s l a r g e ; x f o r t h e v i r t u a l b o n d 0-Ph-C, 0) f o r t h e d i h e d r a l a n g l e b e t w e e n t h e p l a n e s o f t h e b e n z e n e r i n g , and t h e e s t e r g r o u p a n g l e s , x ^ , x ~ , x ^ , a n d x . F i r s t , t h e i n t e r n a l r o t a t i o n a n g l e s e x c e p t f o r co were e x a m i n e d b y a s s u m i n g t h a t t h e a n g l e 1 o f t h e e s t e r g r o u p i s e s s e n t i a l l y l80° a n d t h a t t h e f i b e r p e r i o d i s 15.60 A. The p o s s i b l e c o n f o r m a t i o n s a r e l i m i t e d on t h e c l o s e d s u r f a c e i n t h e cube d e f i n e d b y t h e t h r e e - d i m e n s i o n a l C a r t e s i a n c o o r d i n a t e s x ^ , x» , a n d x ^ , e a c h c o v e r i n g f r o m 0° t o 360° ( F i g u r e U ) . I f x and x^ a r e g i v e n , x s h o u l d t a k e two v a l ues, upper and lower i n t e r s e c t i n g p o i n t s , r e s u l t i n g i n a p a i r o f v a l u e s o f x « The i n t r a m o l e c u l a r p o t e n t i a l e n e r g i e s f o r a b o u t 5,000 m o d e l s were c a l c u l a t e d , a n d s e v e n s t a b l e m o l e c u l a r m o d e l s were o b t a i n e d . Among t h e s e , o n l y m o d e l 3 was f o u n d t o g i v e a 1


FIBER

DIFFRACTION

METHODS

55)


> 5kcol.

1 / /i / / \\\t

/

!\

\ \*— \

v—

tf

I2CT

^—Lj 24CT

T

36Cf

2


Figure 1.

Potential energy map of isotactic polyacetaldehyde. The energy values are given in units of kilocalories per mole of monomer unit (23).


Figure 2.

Potential energy map of isotactic poly (methyl methacrylate) (23)



3.

TADOKORO


47

(a)

(b) Journal of Polymer Science, Polymer Physics Edition

Figure 3.

(a) Crystal packing and (b) enlarged view of a single chain in crystal of polyisobutylene (35)

I

V

/

» /

** i

/f

/y

Y

(

T4(degree)

180

360

T3 (degree)

Figure 4. Three-dimensional closed surface for possible conformations of the skeletal chain of polyfethylene oxybenzoate) with the (2/1) helical symmetry and afiberperiod of 15.60 A (4)

American Chemical Society Library 1155 16th St. N. w. Washington. D. Diffraction C. 20036 French and Gardner; Fiber Methods ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

48

FIBER

DIFFRACTION

Table I I . I n t e r n a l Rotation Angles o f Poly(ethylene a-Form o n t h e P r o c e s s o f A n a l y s i s (k)

- 0 - U

0

A

P

\=/

u -

CH

T (°)

V°>

3

Oxybenzoate)

n g

2

T (°) 2


CH

T (°) 5

Initial

-kl

10

180

-75

-60

-16U

Final

-13

-15

-172

-102

-59

-186

28

25

8

27

1

22

Difference

METHODS

f a i r l y good agreement b e t w e e n t h e o b s e r v e d a n d c a l c u l a t e d d i f f r a c tion intensities. M o d e l 3 was r e f i n e d w i t h t h e c o n s t r a i n e d l e a s t s q u a r e s method ( l U , 1 5 ) , u s i n g a v a r i e t y o f s t a r t i n g p o i n t s . This model 3, however, d i d n o t converge t o t h e f i n a l s t r u c t u r e . S i n c e t h e i n t e r m o l e c u l a r i n t e r a c t i o n was c o n s i d e r e d t o b e i m p o r t a n t , a n e w l y d e r i v e d p a c k i n g e n e r g y m i n i m i z a t i o n method (l6_) was a p p l i e d , and e v e n t u a l l y t h e f i n a l s t r u c t u r e was o b t a i n e d . The i n t e r n a l r o t a t i o n a n g l e s o f t h e i n i t i a l model and t h e f i n a l s t r u c t u r e a r e g i v e n i n t h e t a b l e t o g e t h e r w i t h t h e i r d i f f e r e n c e s . The d i f f e r e n c e s i n T . . , a), a n d T ~ a r e e s p e c i a l l y l a r g e , 25-28°. The r o t a t i o n a n g l e o f t h e b e n z e n e r i n g a) c h a n g e d f r o m 10° t o - 1 5 ° , a r e m a r k a b l e c h a n g e . T h i s example shows b o t h t h e u t i l i t y a n d t h e l i m i t a t i o n o f t h e i n t r a m o l e c u l a r i n t e r a c t i o n e n e r g y c a l c u l a t i o n a s t h e method t o assume t h e m o l e c u l a r m o d e l s f o r s t r u c t u r e a n a l y s i s . As shown i n F i g u r e 5, t h e m o l e c u l a r c h a i n has a z i g z a g conformation o f l a r g e s c a l e , one monomeric u n i t b e i n g a z i g z a g u n i t . This structurei s r e s p o n s i b l e f o r t h e u n u s u a l l y l o w c r y s t a l l i t e modulus o f t h i s p o l y m e r , 6 GPa (1+3). Poly (ethylene

Oxide)

I n 1 9 6 l a m o l e c u l a r m o d e l o f a (7/2) h e l i x [ F i g u r e 6 ( a ) ] was p r o p o s e d b y t h e a u t h o r a n d h i s c o w o r k e r s (13.) b a s e d o n t h e i n f o r m a t i o n f r o m x - r a y , i n f r a r e d , a n d Raman s p e c t r o s c o p y , b u t t h e c r y s t a l s t r u c t u r e c o u l d not be determined a t t h a t time. Afterten y e a r s , o w i n g t o t h e d e v e l o p m e n t o f methods' a n d a p p a r a t u s , e s p e c i a l l y t h e c o n s t r a i n e d l e a s t - s q u a r e s method a n d a vacuum c y l i n d r i c a l camera w i t h a r a d i u s o f 10 cm, t h e c r y s t a l s t r u c t u r e h a s b e e n d e t e r m i n e d a s shown i n F i g u r e 6 ( c ) ( 2 2 ) . The i n t e r n a l r o t a t i o n angles a r e c o n s i d e r a b l y d i s t o r t e d from t h e uniform h e l i x , although t h e m o l e c u l a r c o n f o r m a t i o n i s e s s e n t i a l l y t h e (7/2) h e l i x a n d c l o s e t o t h e TTG s e q u e n c e s . The r e a s o n f o r t h e d i s t o r t i o n was c l a r i f i e d b y u s i n g a p a c k i n g e n e r g y m i n i m i z a t i o n method (16). S t a r t i n g from a c r y s t a l s t r u c t u r e m o d e l c o n s i s t i n g o f t h e u n i f o r m (7/2) h e l i c e s [ F i g u r e 6 ( a ) ] , t h e p a c k i n g e n e r g y m i n i m i z a t i o n method w i t h o u t t h e c o n d i t i o n o f a u n i f o r m h e l i x symmetry r e s u l t e d i n t h e m o d e l shown i n




49

Figure 5. Crystal structure of the a-form of polyfethylene oxybenzoate) (4)

(7/2) uniform helix

Stable crystal structure model

Polymer Journal

Figure 6. Application of packing energy minimization method to polyfethylene oxide) (16). (a) Starting model of uniform helix; (b) stable crystal structure model obtained by energy minimization calculations; and (c) the structure determined by x-ray analysis.


50

FIBER DIFFRACTION METHODS

F i g u r e 6 ( b ) . T h i s s t r u c t u r e i s i n a f a i r l y good agreement w i t h the s t r u c t u r e determined b y x-ray a n a l y s i s [Figure 6 ( c ) ] . This r e s u l t suggests t h a t the deformation i n the c r y s t a l o f the poly( e t h y l e n e o x i d e ) c h a i n f r o m t h e u n i f o r m h e l i x i s due p r i n c i p a l l y t o intermolecular interaction.


Isotactic Poly(methyl Methacrylate) The s t r u c t u r e o f t h i s p o l y m e r h a s n o t l o n g b e e n d e t e r m i n e d , and m o d e l s o f (5/2) (37) a n d (5/1) (29,38) h a v e b e e n p r o p o s e d . The a u t h o r a n d h i s c o w o r k e r s s t a r t e d t h e a n a l y s i s i n 1966, a n d a f t e r a l o n g roundabout q u e s t , they determined the c r y s t a l s t r u c t u r e w h i c h c o n s i s t s o f d o u b l e s t r a n d e d h e l i c e s ( 3 0 ) . I n 1970, t h e y h a d c o n s i d e r e d a ( 5 / l ) h e l i x t o b e t h e most r e a s o n a b l e (29)> However, no r e a s o n a b l e p a c k i n g was f o u n d f o r t h e ( 5 / l ) h e l i c e s i n the orthorhombic l a t t i c e . On t h e o t h e r h a n d , t h e c a l c u l a t i o n o f the i n t r a m o l e c u l a r i n t e r a c t i o n energy suggested t h a t the h e l i c e s w i t h l a r g e r r a d i i s u c h a s a (12/1) h e l i x s h o u l d b e more s t a b l e t h a n t h e (5/1) h e l i x ( 2 3 ) . The a u t h o r a n d h i s c o w o r k e r s t h e n r e examined t h e s t r u c t u r a l models w i t h l a r g e r r a d i i h e l i c e s , a n d found t h a t the x - r a y d a t a can be e x p l a i n e d r e a s o n a b l y i f the c r y s t a l s t r u c t u r e c o n s i s t s o f (10/1) d o u b l e h e l i c e s , t h e f i r s t s u c h case f o r s y n t h e t i c polymers ( F i g u r e 7 ) . I n r i g h t - h a n d h e l i c e s , the e s t e r group p o i n t i n g upward and t h e m o l e c u l a r parameters a r e as f o l l o w s . The m a i n c h a i n t o r s i o n a l a n g l e s a r e : x, = - 1 7 9 ° a n d T p = - l U 8 ° , s i d e c h a i n t o r s i o n a l a n g l e s : x [MCC(0)0J = -2**° a n d T. [CC(0)0M] = 1TU°. E n e r g y c a l c u l a t i o n s a l s o i n d i c a t e d t h a t t h e d o u b l e h e l i x i s k.k k c a l / m o l e o f monomer u n i t more s t a b l e t h a n t w o i s o l a t e d (10/1) h e l i c e s . T h i s r e s u l t s u g g e s t s t h e s t a b l i l i z a t i o n i s due t o good f i t t i n g o f t h e i n t e r t w i n e d c h a i n s , a l t h o u g h t h e r e i s no h y d r o g e n - b o n d b e t w e e n them a s i n t h e c a s e o f DNA. Further refinement o f the c r y s t a l s t r u c t u r e c o n s i s t i n g o f double h e l i c e s i s d i f f i c u l t , because the x-ray photograph i s n o t w e l l - d e f i n e d , a n d t h e p o s s i b i l i t y o f a d i s o r d e r e d s t r u c t u r e must be c o n s i d e r e d , e . g . , r i g h t a n d l e f t - h a n d h e l i c e s , a n d u p a n d down c h a i n s . A l t h o u g h t h e r e a r e some u n e x p l a i n e d f e a t u r e o f t h e d o u b l e h e l i c a l m o d e l , s u c h a s t h e mode o f r a p i d d o u b l e h e l i x f o r m a t i o n d u r i n g c r y s t a l l i z a t i o n , the author and h i s coworkers b e l i e v e t h e r e s u l t t o be e s s e n t i a l l y c o r r e c t . Syndiotactic Poly(methyl Methacrylate) T h e r e h a s b e e n no r e p o r t o f o r i e n t e d c r y s t a l l i n e s y n d i o t a c t i c PMMA s o f a r a s t h e a u t h o r knows. The a u t h o r a n d h i s c o w o r k e r s (39) f o u n d t h a t o r i e n t e d c r y s t a l l i n e s a m p l e s o f s y n d i o t a c t i c PMMA can be o b t a i n e d b y a d s o r p t i o n o f v a r i o u s s o l v e n t s such as c h l o r o acetone and d i e t h y l ketone. F i g u r e 8 shows t h e x - r a y d i a g r a m s . When t h e p o l y m e r i s c a s t f r o m c h l o r o f o r m s o l u t i o n a n d i s s t r e t c h e d i n h o t w a t e r a t 80°C, t h e sample i s n o n c r y s t a l l i n e a s shown i n F i g u r e 8. By a d s o r p t i o n o f the s o l v e n t t h e f i b e r diagram can be



3.

TADOKORO


51

Figure 7. Double-stranded helix of isotactic poly (methyl methacrylate) (30)

Figure 8. X-ray diagrams of syndiotactic polyfmethyl methacrylate)(39)



52

FIBER

DIFFRACTION

METHODS

o b t a i n e d . B y h e a t i n g a t a b o u t 9 0 ° C , t h e c r y s t a l l i n e sample b e comes n o n c r y s t a l l i n e b u t o r i e n t e d , a n d t h e p r o c e s s i s r e v e r s i b l e . In the f i b e r diagram, spots corresponding t o a l o n g f i b e r p e r i o d (35 A ) were o b s e r v e d , i n a d d i t i o n t o t h e l i n e s c o r r e s p o n d i n g t o 8 . 8 A. The s t r u c t u r e a n a l y s i s i s i n p r o g r e s s b u t a v e r y complicated molecular and a c r y s t a l s t r u c t u r e i s a n t i c i p a t e d . F i g u r e 9 shows t h e change o f t h e p o l a r i z e d i n f r a r e d s p e c t r a by a d s o r p t i o n o f d i e t h y l k e t o n e . S e v e r a l bands a p p e a r b y c r y s t a l l i z a t i o n e s p e c i a l l y a t 858 cm" . The b a n d s due t o d i e t h y l k e t o n e i t s e l f are not observed. The e s s e n t i a l f e a t u r e s o f t h e x - r a y d i a g r a m s a n d i n f r a r e d s p e c t r a a r e t h e same i r r e s p e c t i v e o f t h e k i n d s o f s o l v e n t s . From t h e s e r e s u l t s i t may b e c o n s i d e r e d t h a t f o r m a t i o n o f a c o m p l e x o f s y n d i o t a c t i c PMMA a n d s o l v e n t m o l e c u l e s i s n o t reasonable, and the adsorbed molecules c o n t r i b u t e t o t h e s t a b i l i z a t i o n o f c r y s t a l l i t e s o f s y n d i o t a c t i c PMMA. Polyethylene R e c e n t l y t h e a u t h o r a n d h i s c o w o r k e r s made d e t a i l e d s t r u c t u r e a n a l y s e s f o r h i g h d e n s i t y p o l y e t h y l e n e samples w i t h v a r i o u s h i s t o r i e s u s i n g a PSPC (ho). The PSPC h a s b e e n a p p l i e d t o s m a l l angle s c a t t e r i n g , and f u r t h e r a p p l i c a t i o n s t o the wide-angle d i f f r a c t i o n o f h i g h polymers have a l s o been found. The PSPC h a s been v e r y u s e f u l i n e x p e r i m e n t s w i t h p o l y e t h y l e n e . T h i s may b e t h e f i r s t c a s e o f s t r u c t u r e a n a l y s i s b y u s i n g a PSPC. Deformation e f f e c t s o n r e f l e c t i o n p r o f i l e s f r o m o b l i q u e i n c i d e n c e was c o n s i d ered f i r s t . F i g u r e 10 shows r e f l e c t i o n s f r o m a s i l i c o n s i n g l e c r y s t a l t a k e n a t v a r i o u s p o s i t i o n s o n t h e l i n e a r - a n o d e o f t h e PSPC p r o b e . The i n t e g r a t e d i n t e n s i t i e s a r e c o n s t a n t i n d e p e n d e n t o f t h e positions. F i g u r e 11 shows t h e s i m i l a r f i g u r e s f o r a p o l y e t h y l e n e sample. The p o l y e t h y l e n e s a m p l e s e x a m i n e d a r e shown i n T a b l e I I I ; s l o w l y c o o l e d o r quenched from m e l t , o r i g i n a l m o n o f i l a m e n t , a n n e a l e d , over drawn, c o l d drawn, s i n g l e c r y s t a l , c a s t f i l m , e x t e n d e d c h a i n c r y s t a l , e t c . The s a m p l e - p r o b e d i s t a n c e c a n b e c h o s e n f r o m 70 t o 260 mm. The s e t t i n g a n g l e c|> i s d e f i n e d a s t h e a n g l e b e t w e e n t h e m o l e c u l a r p l a n e a n d t h e b e p l a n e a c c o r d i n g t o Bunn (hi) a s shown i n F i g u r e 12. A summary o f t h e c e l l c o n s t a n t s a n d s e t t i n g a n g l e s o f t h e s a m p l e s a r e g i v e n i n T a b l e I V . The a a x i s d i m e n s i o n a n d t h e s e t t i n g a n g l e a r e s m a l l e s t i n t h e sample s l o w l y c r y s t a l l i z e d f r o m m e l t ; 1A. The a a x i s d i m e n s i o n i s 7.399 A a n d $ i s l+l+.l+°. T h e s e two v a l u e s i n c r e a s e b y s t r e t c h i n g , f r o m 1A t o 3A, t o 7.1+32 A a n d 1+6.2°, a n d d e c r e a s e b y a n n e a l i n g , f r o m 3A t o 1+A, t o 7.1+27 A a n d 1+5.8°. These v a l u e s f o r a s i n g l e c r y s t a l mat a r e r a t h e r l a r g e , 9A, 7.1+16 A a n d 1+7.1°, a n d d e c r e a s e b y a n n e a l i n g , 11a, 7-389 A a n d 1+6.3°. The e x t e n d e d c h a i n c r y s t a l , ECC, g i v e s r a t h e r l a r g e v a l u e s 7.1+12 A a n d 1+7.2°. The b a n d c a x i s d i m e n s i o n s show no s i g n i f i cant change. I n F i g u r e 13 c e l l d i m e n s i o n s a r e p l o t t e d a g a i n s t t h e l a t t i c e o

0


3.

TADOKORO

53



Adsorption-Time Dependence (DEK)

Figure 9. The change of the polarized IR spectra of syndiotactic poly (methyl methacrylate) by adsorption of diethyl ketone (39)

1000 8 0 0 Wavenumber (cm ') -

4 20(deg.) 8000r

S g

12

12

8 6 4 2 0 2 4 6

£

J 1 6000JT c

400Q **

300a •fg 3

200O 1000

50

100

150

200

channel number Figure 10. Oblique effect on profile and integrated intensity of reflection of silicon single crystal (40)


FIBER

DIFFRACTION

4

8

METHODS

4 29(deg.) 12

8

4

0

12


c 22000 •2 — § 18000

| 8 ioooo 6000-

f

JO 6 0 0 0 H 4000 3 ° 2000 200 channel number

Figure 11.

Figure 12.

(a) Oblique effect on profile and (b) integrated intensity of reflections of polyethylene (40)

The setting angle of polyethylene molecule in the unit cell (41)



Under h i g h pressure

lUC

No

No No No No Yes

From s o l u t i o n

9A 10A 11A 12A 13A

Drawing No No Yes Yes Yes Yes No Yes

Crystallization

Extended chain c r y s t a l ( s u p p l i e d by P r o f e s s o r o f Kyushu U n i v e r s i t y )

T. Takemura

S i n g l e c r y s t a l grown f r o m 0.01$ p - x y l e n e s o l u t i o n a t 80°C As No. 9A, a n n e a l e d a t 110°C As No. 9A, a n n e a l e d a t 120°C C a s t f r o m 5% t e t r a c h l o r o e t h y l e n e s o l u t i o n a t 110°C As No. 12A, c o l d - d r a w n ( x 13)

S l o w l y c o o l e d f r o m l60°C a n d a n n e a l e d a t 110°C Quenched f r o m l60°C i n d r y - i c e / m e t h a n o l O r i g i n a l m o n o f i l a m e n t (X 11) As No. 3A, a n n e a l e d a t 120°C u n d e r f r e e t e n s i o n As No. 3A, o v e r - d r a w n a t 70°C (X 23) As No. 2A, c o l d - d r a w n a t room t e m p e r a t u r e (x 7) S l o w l y c o o l e d f r o m l60°C a n d a n n e a l e d a t 110°C C o l d - d r a w n a n d a n n e a l e d a t 110°C f r o m 7B (x 10)

Treatment

Sample Number a n d T r e a t m e n t (kO)

From m e l t

1A 2A 3A UA 5A 6A 7B 8B

Sample No.

Table I I I .




0.2

0.4

0.6

0.8

LATTICE DISTORTION, e (*) Figure 13. Cell dimensions plotted against the lattice distortion parameter of polyethylene (40) ((O) melt crystallized, A; (%) melt crystallized, B; (A) single crystal; (±) castfilm;( Q ) high pressure crystallized, C)



3.

TADOKORO


48

0.2

0.4

0.6

0.8

LATTICE DISTORTION, e (%) Figure 14. Setting angle plotted against the lattice distortion parameter (AO) ((O) melt crystallized; (%) melt crystallized; (A) single crystal from p-xylene; (A) castfilmfrom tetrachloroethylene; ([J) pressure crystallized)


FIBER

58

Table IV.

Crystallograpic


a

1A C o o l e d f r o m m e l t 2A Quenched f r o m m e l t 3A O r i g i n a l - d r a w n 1*A Annealed 5A Over-drawn 6A C o l d - d r a w n TB C o o l e d f r o m m e l t 8B Drawn a n d a n n e a l e d 9A S i n g l e c r y s t a l 10A A n n e a l e d (110°C) 11A A n n e a l e d (120°C) 12A C a s t f i l m 13A C a s t a n d drawn l U C ECC

METHODS

D a t a o f P o l y e t h y l e n e Samples (1*0) Cell

Sample

DIFFRACTION

c o n s t a n t s (A) b

7.399 7.^03

7.^32 7.1*27 7.1*1*0 7.1*1*8 7.389 7.1*10 l.kl6 l.hOO 7.398 7.1*00 7.1*1*7 7.1*12

k.936 k.932 U.9U6 ^.959 k.9h0 1*.935 U.955 U.935 U.950 k.9h0 J+.955 4.937

c

Setting a n g l e (°)

2.5^3 2.5^2 2.5^3 2.5^3 2.5kk 2.5k5 2.5k2 2.5^3 2.5^2 2.5^3 2.5kk 2.$k2 2.5U6 2.5kh

1*1*.1* U5.3 1*6.2 1*5.8 46.6

1*6.9 45.3 1*6.1* 1*7.1 1*6.7 1*6.3 1*6.6 1*6.6 1*7.2

d i s t o r t i o n p a r a m e t e r o b t a i n e d b y t h e B u c h a n a n - M i l l e r method (1*2). The a a x i s d i m e n s i o n shows a l i n e a r r e l a t i o n s h i p . This suggests t h a t t h e i n c r e a s e o f l a t t i c e d i s t o r t i o n i s one r e a s o n f o r t h e e x pansion o f the unit c e l l e s p e c i a l l y the a a x i s . F i g u r e ik shows t h e s e t t i n g a n g l e p l o t t e d a g a i n s t t h e l a t t i c e distortion. Open a n d f i l l e d c i r c l e s a r e f o r m e l t c r y s t a l l i z e d samples w i t h v a r i o u s e x t e n t s o f s t r e t c h i n g a n d a n n e a l i n g . These p l o t s h a v e a good l i n e a r r e l a t i o n s h i p . Open t r i a n g l e s a r e f o r s i n g l e c r y s t a l mats w i t h a n d w i t h o u t a n n e a l i n g , f i l l e d t r i a n g l e s are c a s t f i l m s , and squares represent extended c h a i n c r y s t a l s . The l a t t e r s a m p l e s show l a r g e s e t t i n g a n g l e s a n d t h e e x p l a n a t i o n t h e r e o f i s an i n t e r e s t i n g f u t u r e problem. The d e t a i l e d a n a l y s e s o f p o l y e t h y l e n e s a m p l e s w i t h v a r i o u s h i s t o r i e s , show a p p r e c i a b l e v a r i a t i o n o f t h e s e t t i n g a n g l e , t h e a a x i s d i m e n s i o n , a n d l a t t i c e d i s t o r t i o n . These changes a r e s m a l l b u t a p p r e c i a b l e , a n d some o f them a r e i n a l i n e a r r e l a t i o n , b u t some a r e n o t . S i m i l a r phenomena w i l l b e f o u n d i n o t h e r p o l y m e r s , and t h e r e a s o n may b e i n t e r e s t i n g . F u r t h e r Remarks In the future, complicated s t r u c t u r e s which are d i f f i c u l t t o be a n a l y s e d w i l l r e m a i n . F u r t h e r development o f t h i s f i e l d w i l l r e q u i r e more a c c u r a t e measurements o f d i f f r a c t i o n d a t a , c o n s i d e r a t i o n o f d i s o r d e r s , s p e c i a l s a m p l i n g t e c h n i q u e s , new d e v i c e s a n d ideas f o r a n a l y s i s o f i n d i v i d u a l samples.


3.

TADOKORO


59


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February 19, 1980.


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