Spin Relaxation and Local Motion in a Dissolved Aromatic Polyformal

5

Downloaded by TUFTS UNIV on June 5, 2018 | https://pubs.acs.org Publication Date: March 28, 1984 | doi: 10.1021/bk-1984-0247.ch005

Spin Relaxation and Local Motion in a Dissolved Aromatic Polyformal M. F. TARPEY, Y.-Y. LIN, and ALAN ANTHONY JONES Jeppson Laboratory, Department of Chemistry, Clark University, Worcester, MA 01610 P. T. INGLEFIELD Department of Chemistry, College of the Holy Cross, Worcester, MA 01610

Carbon-13 and proton spin-lattice relaxation times are reported for 10 wt% solutions of a dissolved aromatic polyformal. The relaxation times for both nuclei were determined at two Larmor frequencies and as a function of temperature from 0 to 120°C. These relaxation times are interpreted i n terms of segmental motion and anisotropic internal rotation. Segmental correlation functions by both Jones and Stockmayer, and Weber and Helfand were used to interpret the data. Internal rotation i s described by the usual Woessner approach, and restricted rotational diffusion, by the Gronski approach. Both segmental correlation functions lead to similar results; but, relative to the analogous polycarbonate, single bond conformational transitions are more frequent i n the polyformal. The phenyl groups i n the backbone undergo segmental rearrangements and internal anisotropic rotation at comparable rates. Motion in the formal linkage i s described by the same segmental correlation times plus restricted rotational diffusion about an axis between the oxygens of the formal group. The interpretation at the formal l i n k based on restricted rotational diffusion is d i s cussed i n terms of the conformations l i k e l y i n the l i n k which are commonly referred to as the anomeric effect. The choice of the axis of restricted rotation i n the formal unit i s only an approximation of the result of anisotropic single bond conformational t r a n s i tions occurring within that unit. 0097 6156/84/0247-0067S06.00/0 © 1984 American Chemical Society Randall; NMR and Macromolecules ACS Symposium Series; American Chemical Society: Washington, DC, 1984.


68

NMR

A N D MACROMOLECULES

S p i n r e l a x a t i o n i n d i l u t e s o l u t i o n has been employed t o c h a r a c t e r i z e l o c a l c h a i n motion i n s e v e r a l polymers w i t h aromatic back bone u n i t s . The two g e n e r a l t y p e s examined so f a r a r e p o l y p h e n y l e n e o x i d e s (1-2) and a r o m a t i c p o l y c a r b o n a t e s ( 3 - 5 ) ; and t h e s e two t y p e s a r e t h e most common h i g h i m p a c t r e s i s t a n t e n g i n e e r i n g plastics. The p o l y m e r c o n s i d e r e d i n t h i s r e p o r t i s an a r o m a t i c p o l y f o r m a l ( s e e F i g u r e 1) where t h e a r o m a t i c u n i t i s i d e n t i c a l t o t h a t o f one o f t h e p o l y c a r b o n a t e s . T h i s p o l y m e r has a s i m i l a r d y namic m e c h a n i c a l s p e c t r u m t o t h e i m p a c t r e s i s t a n t p o l y c a r b o n a t e s ( 6 ) and i s t h e r e f o r e an i n t e r e s t i n g s y s t e m f o r c o m p a r i s o n o f c h a i n dynamics. I n a d d i t i o n , t h e f o r m a l u n i t i t s e l f o f f e r s a new o p p o r t u n i t y for monitoring chain motion r e l a t i v e to the polycarbonates s i n c e t h e c a r b o n a t e u n i t c o n t a i n s no p r o t o n s . The s p i n - l a t t i c e r e l a x a t i o n t i m e s , T j s o f a l l p r o t o n s and a l l c a r b o n s w i t h d i r e c t l y bonded p r o t o n s a r e r e p o r t e d f o r t h e p o l y f o r m a l . A l s o t h e c a r b o n and p r o t o n T j ' s a r e measured a t two d i f f e r e n t Larmor f r e q u e n c i e s t o expand t h e f r e q u e n c y r a n g e c o v e r e d by t h e s t u d y . In a d d i t i o n t o d e t e r m i n i n g the time s c a l e s f o r s e v e r a l l o c a l m o t i o n s i n p o l y f o r m a l , two d i f f e r e n t i n t e r p r e t a t i o n a l models f o r s e g m e n t a l m o t i o n w i l l be e m p l o y e d . An o l d e r model by J o n e s and S t o c k m a y e r (7 ) , based on t h e a c t i o n o f a t h r e e bond jump on a t e t r a h e d r a l l a t t i c e i s compared w i t h a new model by Weber and H e l f a n d ( 8 ) , based on computer s i m u l a t i o n s o f p o l y e t h y l e n e t y p e chains. These two models f o r s e g m e n t a l m o t i o n have been compared b e f o r e ( 5 ) f o r two p o l y c a r b o n a t e s b u t somewhat d i f f e r e n t r e s u l t s are seen i n the p o l y f o r m a l i n t e r p r e t a t i o n . 1

Experimental H i g h m o l e c u l a r w e i g h t samples o f t h e p o l y f o r m a l were k i n d l y s u p p l i e d by G e n e r a l E l e c t r i c . The s t r u c t u r e o f t h e r e p e a t u n i t i s shown i n F i g u r e 1 a s w e l l as t h e s t r u c t u r e o f a p a r t i a l l y d e u t e r a t e d f o r m w h i c h was s y n t h e s i z e d (9) t o r e d u c e p r o t o n c r o s s relaxation. A 10 w e i g h t p e r c e n t s o l u t i o n o f t h e p o l y m e r i n d e u t e r a t e d t e t r a c h l o r o e t h a n e was p r e p a r e d i n an NMR t u b e , s u b j e c t e d t o f i v e f r e e z e , pump, thaw c y c l e s and s e a l e d . S p i n l a t t i c e r e l a x a t i o n measurements were c o n d u c t e d on two s p e c t r o m e t e r s w i t h a s t a n d a r d π-τ-π/2 p u l s e s e q u e n c e . The 30 and 90 MHz p r o t o n measurements as w e l l as t h e 22.6 MHz c a r b o n - 1 3 meas u r e m e n t s were made on a B r u k e r SXP 20-100. The 250 MHz p r o t o n and 62.9 c a r b o n - 1 3 measurements were made on a B r u k e r WM-250. Results S p i n l a t t i c e r e l a x a t i o n times a r e c a l c u l a t e d from the r e t u r n o f t h e m a g n e t i z a t i o n t o e q u i l i b r i u m u s i n g a l i n e a r and n o n - l i n e a r l e a s t s q u a r e s a n a l y s i s o f t h e d a t a . The two a n a l y s e s y i e l d T| v a l u e s w i t h i n 10% o f e a c h o t h e r and a v e r a g e v a l u e s a r e r e p o r t e d . No e v i d e n c e o f c r o s s - r e l a x a t i o n o r c r o s s - c o r r e l a t i o n were o b s e r v e d

Randall; NMR and Macromolecules ACS Symposium Series; American Chemical Society: Washington, DC, 1984.


5.

T A R P E Y ETA L ,

Spin Relaxation

Cl

and Local

Motion

69

Cl

\/ c —c—

Cl

ν

H

H

\ / 0— c — 0 —

Cl

S

D D

O-i--- )] 2

H

(lb)

j The i n t e r n u c l e a r d i s t a n c e s employed a r e 1.095 Â f o r t h e p h e n y l C-H d i s t a n c e , 1.125 Â f o r t h e f o r m a l C-H d i s t a n c e , 2.4 Â f o r t h e 2-3 p h e n y l p r o t o n d i s t a n c e , and 1.75 Â f o r t h e f o r m a l p r o t o n - p r o t o n distance. The 2-3 p h e n y l p r o t o n d i s t a n c e used h e r e i s c o m p a r a b l e t o t h e d i s t a n c e o f 2.41 Â u s e d i n t h e p o l y c a r b o n a t e i n t e r p r e t a tions. The c h o i c e o f 2.4 Â i s based on t h e p h e n y l p r o t o n T| m i n i mum and t h e s l i g h t l y s m a l l e r v a l u e i s c o n f i r m e d by a l a r g e r Pake doublet s p l i t t i n g observed i n the s o l i d s t a t e spectrum o f the phenyl protons i n the p a r t i a l l y deuterated analogue ( 1 0 ) . E x p r e s s i o n s f o r t h e s p e c t r a l d e n s i t y c a n be d e v e l o p e d f r o m m o d e l s f o r l o c a l m o t i o n i n r a n d o m l y c o i l e d c h a i n s . Two g e n e r a l t y p e s o f l o c a l m o t i o n w i l l be c o n s i d e r e d , and t h e y a r e s e g m e n t a l m o t i o n and a n i s o t r o p i c r o t a t i o n . S e g m e n t a l m o t i o n i t s e l f w i l l be



0 20 40 60 80 100 120

T a b l e I:

548 499 522 628 794 1168 1411

90 MHz

Phenyl

30

153 189 274 432 553 763 939

MHz

Protons

(ms)

137 174 243 377 543 798 1113

62.9 MHz 72 106 156 349 448 679 936

MHz

Carbons

22.6

Protonated Phenyl

S p i n - L a t t i c e R e l a x a t i o n times

MHz

335 282 268 295 350 467 628

250

Formal 90 129 114 133 198 258 320 433

MHz

Protons


81 91 115 158 229 339 403

62.9

MHz

Formal

36 52 82 123 193 275 377

22.6

Carbons MHz


72

NMR

A N D

MACROMOLECULES

d e s c r i b e d i n two ways. The f i r s t d e s c r i p t i o n i s d e r i v e d f r o m t h e a c t i o n o f a t h r e e bond jump on a t e t r a h e d r a l l a t t i c e (7_) and t h e s e c o n d i s d e v e l o p e d f r o m c o n s i d e r a t i o n o f computer s i m u l a t i o n s o f backbone t r a n s i t i o n s i n p o l y e t h y l e n e c h a i n s 0 8 ) . A n i s o t r o p i c r o t a t i o n c a n a l s o be c h a r a c t e r i z e d i n s e v e r a l ways. I t can be d e s c r i b e d as jumps between two minima ( 1 1 ) , jumps between t h r e e m i n ima ( 1 2 ) o r s t o c h a s t i c d i f f u s i o n ( 1 2 ) . I n t h e t h r e e bond jump model f o r s e g m e n t a l m o t i o n t h e r e a r e two p a r a m e t e r s . The t i m e s c a l e i s s e t by t h e h a r m o n i c a v e r a g e c o r r e l a t i o n time, and t h e e f f e c t i v e d i s t r i b u t i o n o f c o r r e l a t i o n t i m e s i s s e t by t h e number o f c o u p l e d bonds m. The s h a r p c u t o f f o f c o u p l i n g s o l u t i o n o f t h e t h r e e bond jump model i s employed here. The c o m p o s i t e s p e c t r a l d e n s i t y f o r i n t e r n a l r o t a t i o n by jumps o r s t o c h a s t i c d i f f u s i o n p l u s s e g m e n t a l m o t i o n by t h r e e bond jump i s J.(ω.) = 2ZG

Α τ k

k-1

1

+

^0

T

A

= WÀ

k

1

2

^ k O

x

B T

+

k0

+

_ 1

w

bkO i

2 T

= tk"

C T

+

bko

2

1

+

W

i

ckQ 2 T

ck0

2

1

s = (m + l ) / 2

k

2

k

= 4 s i n [ ( 2 k - 1)π/2(πι + 1 ) ] x -l

=

h

2W

s-1 G

k

= 1/s + ( 2 / s ) E e x p ( - y q ) cos [ ( 2 k - 1)πς/2β] q-i γ = In 9 2

A = (3 c o s

Δ -l ) / 4 2

Β = 3(sin

2

2Δ)/4

C = 3(sin

4

Δ)/4

for stochastic diffusion T

T

for a threefold

bk(f

τ

1

= \Γ

1

τ

1

c k O = \Γ

+

îr""

1

+ (Tir/4)-

1

jump


(2)

5.

Spin Relaxation and Local

TARPEY ET AL.

73

Motion

The a n g l e Δ i s between t h e i n t e r n u c l e a r v e c t o r and t h e a x i s o f internal rotation. The t h r e e bond jump s e g m e n t a l m o t i o n d e s c r i p t i o n c a n a l s o be combined w i t h a d e s c r i p t i o n o f r e s t r i c t e d a n i s o t r o p i c r o t a t i o n a l diffusion (13-14). I n t h i s case, the composite s p e c t r a l d e n s i t y equation i s s J.(u).) = 2ZG, ι ι k τ~ k=l 2

{ [ ( 1 - c o s I)

+ sin

A T k

Q

5

ι 2

r

1}


l

2

n=l

(1 - Ξ Ι ) s i n ( £ + rm)} ,}2

T

Ί

(1+21)

{ I [(1 - cos 2 J 0

2

2

1

+ sin

2

+

ω .

z

+

(3)

+

2

^

k

k

o

2

τ, ku

Q

1 + ω. ι

+ 2

[ ( [ 1 - c o s ( 2 i - η π ) ] + [1 - c o s ( 2 £ + η π ) ] > (2 - Ξ 1 ) (2 + Β ! )

2 +

I 2

(2 - TL> I

2

J 2

T

21]

2

(sin(2Jt - η π ) + s i n ( 2 £ + η π ) } ]

r

kO

nkO

ι

T

T

(1 + Ξ 1 )

2

+

(1 -f)

JL 2l

2

[ f [ l ~ cos(J6 - η π ) ] + [1 - c o s U + η π ) ] }

| s i n ( £ - ηπ)

where

k0

1 + ω.

Σ

00 Σ n=l

+

kO

l

1

τ

(2 +

ÏÏDL) I

T

nkO

1 + ω. ι

| 2

τ

, nkO

+

2

Λ

1 = _J_ kO k T

1 = JL + λ nkO

λ n

- (Bl) I

2

and

% r


74

N M R

A N D

MACROMOLECULES

The new parameters f o r r e s t r i c t e d a n i s o t r o p i c r o t a t i o n a l d i f f u s i o n are the angular amplitude over which r o t a t i o n d i f f u s i o n occurs, i, and the r o t a t i o n a l d i f f u s i o n constant f o r r e s t r i c t e d a n i s o t r o p i c r o t a t i o n a l d i f f u s i o n , D-^. A second d e s c r i p t i o n of segmental motion can be combined with the various types of i n t e r n a l a n i s o t r o p i c i n t e r n a l r o t a t i o n , Weber and Helfand (8^) c h a r a c t e r i z e segmental motion i n terms of a c o r r e l a t i o n time f o r s i n g l e conformational t r a n s i t i o n s , T Q , and a c o r r e l a t i o n time f o r cooperative conformational t r a n s i t i o n s , τ^. This model has been a p p l i e d to nuclear spin r e l a x a t i o n before ( 5 ) and the form of the s p e c t r a l density f o r a composite segmental motion and a n i s o t r o p i c i n t e r n a l r o t a t i o n i s w r i t t e n


r

J

w

i( i)

= AîaÔ»

τ

ω

B J

1» ί> +

T

τ

ib( bO>

Α = (3 cos

2

ω

CJ

T

τ

1> ί ) + ie( eO»

ω

1> ί>

2

Δ - 1) /4

Β = 3 (sin

2

2Δ)/4

(4)

4

C = 3 ( s i n Δ)/4 for

stochastic diffusion T

b0"

TcO" for

1

1

1+

= το""

= το"

1 +

Tir""

1

4

(τ^/ )"

1

a three bond jump T

b0~

1

= TcO"

1

= TO"

1

+ Tir""

1

The form of J± , J-j^ and J-^ i s the same as J ^ j given below with T Q replaced by T Q , T ^ Q and T Q r e s p e c t i v e l y . a

c

C

+ 21^)

J i j ( ^ i ) = 2{[(τ -1)(τ -1 0

0

χ cos [1/2 a r c t a n ( 2 ( x " 0

1

-

2 ω

ι

2 2 - I / ] +[2(τ ""1 + τ Γ ^ ) ] } 0

+ τj" )ω /το"" (TQ" 1

1

1

1

2

+ 2 τ ~ ) - ω± ] 1

1

This d e s c r i p t i o n of segmental motion can also be combined restricted anisotropic rotational diffusion


with

4

5.

Spin Relaxation and Local Motion

T A R P E Y E TA L .

Ji(o)i) JL 2

= AJ

2

{ [ ( 1 - c o s I)

0 1

(

i

+ sin

W l

) +

1} J .

2

0

1

(ω.) +

t

Α

Σ

- cos(£ - ηπ)] + [1 - cos(Z + η π ) ] >

2

n=l

(1 - EL)

I

λ n ( . ) |+ sin(£ + η π ) } 2, ] j / 2

{ s i n U - ηπ)

τ

φ

τ

ω

( 1 + IHL)ι

(1 - IE.) Downloaded by TUFTS UNIV on June 5, 2018 | https://pubs.acs.org Publication Date: March 28, 1984 | doi: 10.1021/bk-1984-0247.ch005

+

(1 + EL)

ι

{ I [(1 - cos 2JO

JL 2i

2

2

1

+ sin

1

01 21} J , (ω.) +

2

2

Σ

[ { [ 1 - c o s ( 2 £ - ηπ)] + [1 - c o s ( 2 £ + η π ) ] > (2 - EL)

n=l

+

(2 + EL)

I f s i n ( 2 £ - ηπ)

ζ

I s i n ( 2 £ + ηπ)> ] j ^ n ( . ) } ] 2

+

ω

(2 - EL> ι

1

(2 + EL) I

1

where Ji

(2

0

1

(on) = { [ τ - 1 ( τ 0

2 ~ UK)}

1

/

0 1

-1 +

-

W i

2]2 +

_

2x 9J_

4

χ cosfi. arctan V ^ o f

1

+

i

τ

••Γ

1

}

2

χ cos[I arctan 2

(τ,, 0 τοΓ

1

0 1

+

+ λ Κ τ " η 01 /

= 0 τ

λ

AH

1

2(τ - 1

1

χ

τ

+ 1

λ ) ω η

1

±

+ λ ) - ω. η' ι

ω

ι

2

-1/4

} 2

1

= ( £ 1 ) D. 2

o f t h e terms have been d e f i n e d i n e q s . 2-4.


76

NMR A N D

MACROMOLECULES

To a p p l y t h e models t o t h e i n t e r p r e t a t i o n o f t h e d a t a , t h e a p p r o a c h d e v e l o p e d f o r t h e p o l y c a r b o n a t e s w i l l be f o l l o w e d . The p h e n y l p r o t o n T j s a r e i n t e r p r e t e d f i r s t i n terms o f s e g m e n t a l motion. For these protons, the d i p o l e - d i p o l e i n t e r a c t i o n i s p a r a l l e l t o t h e c h a i n backbone and t h e r e f o r e r e l a x e d o n l y by s e g mental motion. I n t h e t h r e e bond jump model t h e p a r a m e t e r s τ and m a r e a d j u s t e d t o a c c o u n t f o r p h e n y l p r o t o n d a t a , and i n t h e W e b e r - H e l f a n d model t h e p a r a m e t e r s T Q and T J a r e a d j u s t e d . T a b l e I I c o n t a i n s t h e t h r e e bond jump p a r a m e t e r s , and T a b l e I I I , t h e W e b e r - H e l f a n d model p a r a m e t e r s . Both models can s i m u l a t e t h e d a t a w i t h i n 10% w h i c h i s e q u i v a l e n t t o t h e e x p e r i m e n t a l e r r o r . P h e n y l g r o u p r o t a t i o n c a n be c h a r a c t e r i z e d f r o m t h e p h e n y l c a r b o n T j s by a s s u m i n g t h e s e g m e n t a l d e s c r i p t i o n d e v e l o p e d f r o m the p r o t o n d a t a ( 5 ) . E i t h e r s e g m e n t a l model c a n be u s e d , and t h e c o r r e s p o n d i n g c o r r e l a t i o n t i m e s f o r i n t e r n a l r o t a t i o n o f t h e phe n y l g r o u p by s t o c h a s t i c d i f f u s i o n , T - j ^ p ' s , a r e d i s p l a y e d i n T a b l e I I and T a b l e I I I . A g a i n b o t h a p p r o a c h e s match t h e o b s e r v e d c a r b o n - 1 3 d a t a w i t h i n t h e 10% u n c e r t a i n t y . T

η


1

Table I I :

P h e n y l Group M o t i o n S i m u l a t i o n P a r a m e t e r s U s i n g t h e T h r e e Bond Jump M o d e l

°C

m

0 20 40 60 80 100 120

1 1 1 1 3 5 7

E (

kj/mole) x 10 (s) Correlation Coefficient a

Too

1 4

τ

η

(ns)

T

2.69 1.30 0.79 0.49 0.180 0.080 0.049 30 0.59 0.99


i

r

p

(ns)

1.85 1.19 0.73 0.299 0.247 0.192 0.145 20 30 0.99

5.

TARPEY ET AL.


Table I I I :

Spin Relaxation

τι ( n s )

0 20 40 60 80 100 120

3.80 1.89 1.09 0.49 0.259 0.142 0.070

kj/mole) x 10 (s) Correlation Coefficient a

Too

1 4

11

Motion

P h e n y l Group M o t i o n S i m u l a t i o n P a r a m e t e r s U s i n g t h e W e b e r - H e l f a n d Model

°c

E (

and Local

30 1.04 0.99

TQ

(ns)

T

2.15 1.15 0.72 0.280 0.240 0.170 0.150

6.01 3.7 2.34 2.00 1.99 1.86 1.70 9 97 χ 1 0

i r p (ns)

2

0.94

21 20 0.99

Now t h e i n t e r p r e t a t i o n d i v e r g e s f r o m t h e p o l y c a r b o n a t e p a t t e r n as t h e f o r m a l g r o u p i s considered· As m e n t i o n e d , t h e s t r u c t u r a l analogue t o t h e f o r m a l group i n t h e p o l y c a r b o n a t e i s the c a r b o n a t e g r o u p , and t h e l a t t e r c a n n o t be d i r e c t l y s t u d i e d by s o l u t i o n s p i n r e l a x a t i o n s t u d i e s s i n c e i t has no d i r e c t l y bonded protons. I f t h e f o r m a l i s f i r s t viewed i n d e p e n d e n t l y from the p h e n y l g r o u p d a t a , one m i g h t a t t e m p t t o employ s e g m e n t a l m o t i o n d e s c r i p t i o n s a l o n e s i n c e t h e f o r m a l g r o u p l i e s i n t h e backbone. P u r s u i n g t h i s a p p r o a c h , b o t h t h e t h r e e bond jump and t h e WeberH e l f and models were a p p l i e d t o s i m u l a t e t h e p r o t o n and c a r b o n - 1 3 d a t a i n T a b l e I . N e i t h e r model i s a b l e t o a c c o u n t f o r t h e d a t a , w i t h s y s t e m a t i c d i s c r e p a n c i e s up t o 70% i n b o t h attempts· The l a r g e s t d i s c r e p a n c i e s o c c u r a t l o w t e m p e r a t u r e s w i t h o n l y somewhat b e t t e r simulations p o s s i b l e at higher temperatures. I n one s e n s e i t i s r e a s s u r i n g t o d e t e r m i n e t h a t models f o r segmental motion cannot account f o r a l l d a t a s e t s . On t h e o t h e r h a n d , i t i s s t i l l d e s i r a b l e t o d e v e l o p some d e s c r i p t i o n o f m o t i o n w h i c h w i l l a c c o u n t f o r t h e d a t a a t hand, s i n c e t h e f a i l u r e t o s i m u l a t e i m p l i e s some p o t e n t i a l l y i n t e r e s t i n g i n f o r m a t i o n a l content· The s u c c e s s f u l p h e n y l g r o u p i n t e r p r e t a t i o n c a n a s s i s t t h e e f f o r t to a c c o u n t f o r t h e f o r m a l d a t a . The s e g m e n t a l m o t i o n d e s c r i p t i o n s a p p l i e d t o t h e p h e n y l p r o t o n d a t a a r e based on i s o t r o p i c a v e r a g i n g of t h e d i p o l e - d i p o l e i n t e r a c t i o n s by t h e s e g m e n t a l m o t i o n . One c o u l d assume t h a t t h e same s e g m e n t a l m o t i o n d e s c r i p t i o n o c c u r r i n g at t h e p h e n y l groups a l s o o c c u r s a t t h e f o r m a l group s i n c e b o t h g r o u p s a r e a d j a c e n t i n t h e backbone. I f t h i s a s s u m p t i o n i s made, some a d d i t i o n a l m o t i o n must be c o n s i d e r e d t o match t h e o b s e r v e d f o r m a l r e l a x a t i o n t i m e s . I n t h e c o n t e x t o f t h e models b e i n g a p p l i e d , t h e added m o t i o n c o u l d be a a n i s o t r o p i c r o t a t i o n o r r e stricted rotation. F o r t h e f o r m a l group, t h e f i r s t guess i s r o t a -


78

NMR

A N D MACROMOLECULES

t i o n or r e s t r i c t e d r o t a t i o n about the C-0 a x i s . This would be a s i n g l e backbone conformational t r a n s i t i o n o c c u r r i n g as an anisot r o p i c motion on top of the segmental motion of say the WeberHelf and model determined from the phenyl proton data. Complete a n i s o t r o p i c r o t a t i o n about the C-0 bond adequately accounts f o r the higher temperature data, but f a i l s to simulate the lower temperature data by about 40%. A r e s t r i c t e d r o t a t i o n model at lower temperatures i s also not able to simulate the observed T| s though i t comes c l o s e r . Adding a r o t a t i o n or r e s t r i c t e d r o t a t i o n about the C-0 axis to the three bond jump model i s e q u a l l y unsuccessful as might be expected since so f a r the three bond jump and WeberHelf and model have p a r a l l e d each other. The next motion considered i s r o t a t i o n or r e s t r i c t e d r o t a t i o n of the 0CH 0 u n i t about the 0-0 axis of the u n i t . The i n i t i a l l o g i c here was that the l a r g e r aromatic groups were slower moving anchors and the formal group was a n i s o t r o p i c a l l y r o t a t i n g r e l a t i v e to the two oxygens which were the connections to the more s l u g g i s h phenyl groups. At higher temperatures, complete a n i s o t r o p i c r o t a t i o n about the 0-0 axis i n a d d i t i o n to a segmental motion d e s c r i p t i o n using the Weber-Helfand model developed from the phenyl proton data accounted f o r the formal data but d i s c r e p a n c i e s of 30% s t i l l remained at lower temperatures. The lower temperature data could be accounted f o r by allowing f o r incomplete a n i s o t r o p i c r o t a t i o n a l d i f f u s i o n about the 0-0 axis i n a d d i t i o n to segmental mot i o n . With complete r o t a t i o n at higher temperatures and r e s t r i c t ed r o t a t i o n at lower temperatures, a l l formal proton and carbon-13 data can be simulated w i t h i n the experimental u n c e r t a i n t y of the T | s . The a n i s o t r o p i c r o t a t i o n simulation parameters are reported i n Table IV f o r the case where segmental motion i s c h a r a c t e r i z e d with the Weber-Helfand model on the basis of the phenyl proton data. A s u b s t i t u t i o n of the three bond jump model f o r the WeberHelf and model leads to nearly the same results·


f

2

f

Table IV:

°c 0 20 40 60 80 100 120 (a)

Formal Group Simulation Parameters Using the WeberHelfand M o d e l a )

JL 86 119 164 360 360 360 360

D

i r

x

10~

1 0

0.100 0.110 0.130 0.100 0.160 0.210 0.230

The values of T j and T Q reported i n Table I I I are used here as w e l l as the parameters l i s t e d .


1

(s""" )

5.

T A R P E Y ET A L .

Spin Relaxation and Local

Motion

79


Discussion As the f i r s t p o i n t , the dynamics of the phenyl group i n the poly formal can be considered. Motional d e s c r i p t i o n s from the two seg mental models can be compared as they have been before f o r the polycarbonates ( 5 ) . In the three bond jump model the primary parameter i s the harmonic mean c o r r e l a t i o n time, τ^; and i n the Weber-Helfand model the primary parameter i s the c o r r e l a t i o n time f o r cooperative backbone t r a n s i t i o n s , τ ι. At the lower tempera tures s t u d i e d , T Q plays an i n c r e a s i n g r o l e i n the Weber-Helfand model but T J i s s t i l l the major f a c t o r . This i s an i n t e r e s t i n g point i n i t s e l f since cooperative t r a n s i t i o n s were also found to predominate when the Weber-Helfand model was a p p l i e d to the p o l y carbonates . Here i n the polyformal, s i n g l e bond conformational t r a n s i t i o n s do play a l a r g e r r o l e ; and t h i s can be seen i n the three bond jump model as w e l l by the drop of m to 1 at lower tem peratures. Since T J and τ are both measures of the time s c a l e f o r cooperative motions, i t i s i n t e r e s t i n g to note that the Arrhenius summaries of the two c o r r e l a t i o n times i n Tables II and I I I are very s i m i l a r . This s i m i l a r i t y , taken together with the domination of cooperative t r a n s i t i o n s i n the i n t e r p r e t a t i o n s , sup ports the u t i l i t y of both models though the Weber-Helfand model i s developed from a more d e t a i l e d a n a l y s i s of chain motion. One i n t e r e s t i n g d i f f e r e n c e between the Weber-Helfand i n t e r p r e t a t i o n of the polyformal and the polycarbonates i s the r e l a t i v e apparent a c t i v a t i o n energies f o r τ ι and T Q . For the polycarbo nates , the a c t i v a t i o n energies f o r T Q and τ ι were about the same ( 5 ) as would be expected i f the cooperative t r a n s i t i o n s occurred s e q u e n t i a l l y as opposed to simultaneously (15-17)· For the polyformal, the a c t i v a t i o n energy f o r the cooperative process i s much higher than f o r the s i n g l e t r a n s i t i o n s which i s more i n d i c a t i v e of simultaneous cooperative t r a n s i t i o n s such as a crank shaft · Since the s i n g l e t r a n s i t i o n s are minor processes i n both the polycarbonates and to a l e s s e r extent i n the polyformal, dwelling on the a c t i v a t i o n energy d i f f e r e n c e s may be r i s k y . It i s worth noting that the d e s c r i p t i o n of phenyl group r o t a t i o n i s not s i g n i f i c a n t l y i n f l u e n c e d by changing d e s c r i p t i o n s of segmental motion. This too supports the u t i l i t y of both models and the v a l i d i t y of the general a n a l y s i s of l o c a l motion f o r phe n y l groups as being d i v i d e d between segmental motion and i n t e r n a l rotation. Segmental motion and phenyl group r o t a t i o n i n the polyformal can be compared to that of the polycarbonates. R e l a t i v e to the analogous C h l o r a l polycarbonate Ç5), the cooperative segmental mot i o n i n the polyformal i s s i m i l a r i n general time s c a l e but has a s i g n i f i c a n t l y higher a c t i v a t i o n energy. Phenyl group r o t a t i o n i n the polyformal and the polycarbonate are n e a r l y i d e n t i c a l . This suggests phenyl group r o t a t i o n i s a very l o c a l i z e d process not g r e a t l y i n f l u e n c e d by r e p l a c i n g the carbonate l i n k with a formal link. On the other hand, i t i s hard to imagine phenyl group r o t a η



80

NMR

AND

MACROMOLECULES

t i o n as a s i m p l e p r o c e s s w i t h i n the b i s p h e n o l u n i t s i n c e MNDO c a l c u l a t i o n s (18) i n d i c a t e a h i g h b a r r i e r w i t h i n t h i s u n i t . A n o t h e r i n t e r e s t i n g p o i n t about p h e n y l g r o u p r o t a t i o n i n t h e p o l y f o r m a l and p o l y c a r b o n a t e s i s t h a t i t i s b e s t modeled i n s o l u t i o n as s t o c h a s t i c d i f f u s i o n r a t h e r t h a n two f o l d jump (π f l i p s ) . I n s o l i d BPA p o l y c a r b o n a t e , b o t h d e u t e r i u m ( 1 9 ) and c a r b o n - 1 3 ( 2 0 ) l i n e s h a p e a n a l y s i s p o i n t t o two f o l d jumps o r π f l i p s as t h e p r i mary p r o c e s s . C a l c u l a t i o n s by T o n e l l i ( 2 1 - 2 2 ) a l s o p o i n t t o l o w b a r r i e r s t o p h e n y l g r o u p r o t a t i o n f o r i s o l a t e d BPA c h a i n s . I f t h e i n t r a m o l e c u l a r b a r r i e r f o r p h e n y l g r o u p r o t a t i o n i s i n d e e d l o w as i n d i c a t e d by t h e s o l u t i o n s t u d i e s and t h e c a l c u l a t i o n s , t h e change t o a h i g h e r b a r r i e r ( 6 , 1 8 ) and π f l i p s i n t h e s o l i d must r e f l e c t intermolecular interactions. T h i s i s indeed p l a u s i b l e s i n c e the new c o n f o r m a t i o n f o l l o w i n g a π f l i p i n t h e s o l i d r e q u i r e s no change i n t h e s u r r o u n d i n g s (no change i n f r e e v o l u m e ) y e t t h e s u r r o u n d i n g s c o u l d p r o v i d e an a p p r e c i a b l e b a r r i e r t o t h e t r a n s i t i o n . As m e n t i o n e d , t h e f o r m a l l i n k p r o v i d e s new d y n a m i c i n f o r m a t i o n r e l a t i v e t o the p o l y c a r b o n a t e s where no d e t a i l e d a n a l y s i s o f the carbonate u n i t i s p o s s i b l e . In the i n t e r p r e t a t i o n , a r a t h e r complex d e s c r i p t i o n i s r e q u i r e d to account f o r the f o r m a l r e l a x a t i o n d a t a . A c c o r d i n g t o t h e i n t e r p r e t a t i o n , t h e f o r m a l g r o u p un d e r g o e s s e g m e n t a l m o t i o n as d e t e r m i n e d a t t h e p h e n y l g r o u p p l u s a n i s o t r o p i c r o t a t i o n about t h e o x y g e n - o x y g e n a x i s o f t h e f o r m a l group. At low temperatures t h i s a n i s o t r o p i c r o t a t i o n i s d e s c r i b e d as r e s t r i c t e d r o t a t i o n a l d i f f u s i o n . The m a i n q u e s t i o n i s w h e t h e r t h e r e i s any p h y s i c a l s e n s e t o s u c h a p i c t u r e . S i n c e t h e segment a l m o t i o n i s somewhat c o o p e r a t i v e and t h e p h e n y l g r o u p i s a d j a c e n t , i t seems r e a s o n a b l e t o assume t h a t t h i s m o t i o n e x t e n d s o v e r b o t h t h e p h e n y l and f o r m a l g r o u p s . The r e a l q u e s t i o n i s t h e a n isotropic restricted rotation. To p u r s u e t h i s a s p e c t , c o n f o r m a t i o n a l e n e r g y maps o f d i m e t h o x y m e t h a n e were r e v i e w e d ( 2 3 - 2 4 ) . The lowest conformations are gg and g g and t h i s u n u s u a l s i t u a t i o n r e l a t i v e t o p o l y e t h y l e n e c h a i n s i s commonly c a l l e d t h e a n o m e r i c effect. E a c h o f t h e s e c o n f o r m a t i o n s has two c o n f o r m a t i o n s w h i c h a r e o n l y 4 k J h i g h e r i n e n e r g y . The t g and g t c o n f o r m a t i o n s a r e e n e r g e t i c a l l y near the g g c o n f o r m a t i o n and t h e t g and g ' t c o n f o r m a t i o n s a r e e n e r g e t i c a l l y n e a r t h e g'g c o n f o r m a t i o n . The g ' g , gg and t t s t a t e s a r e c o n s i d e r a b l y h i g h e r i n e n e r g y . The most f a c i l e c o n f o r m a t i o n a l changes f r o m t h e l o w e s t s t a t e s c o u l d be r e p r e s e n t e d by T

f

f

f

1

t g

t

β

g

t

=

g

g

t

s

g t

g =

t g

(6) g

t

t

A t l o w e r t e m p e r a t u r e s where a g i v e n f o r m a l u n i t i s l i k e l y t o be e i t h e r gg or g'g, t h e t r a n s i t i o n s r e p r e s e n t e d by eq. 6 w o u l d r e s u l t i n r e s t r i c t e d r o t a t i o n a l averaging. T h i s would g e n e r a l l y agree w i t h the r e s u l t s o b t a i n e d from the s i m u l a t i o n of the f o r m a l r e l a x a t i o n d a t a f r o m 0 t o 40 d e g r e e s where t h e a n g u l a r a m p l i t u d e f


5.

TARPEY ET AL.

Spin Relaxation

and Local

81

Motion

o f r e s t r i c t e d r o t a t i o n , I, r a n g e s f r o m 86 t o 164 d e g r e e s . A t h i g h e r t e m p e r a t u r e s p o p u l a t i o n s i n s t a t e s o t h e r t h a n g g o r g'g w o u l d become l a r g e r a l l o w i n g f o r t h e more common o c c u r r e n c e o f c o n f o r m a t i o n a l changes o t h e r t h a n t h o s e l i s t e d i n e q . 6. T h i s w o u l d r e s u l t i n e f f e c t i v e l y c o m p l e t e r o t a t i o n i n agreement w i t h t h e s i m u l a t i o n f r o m 60 t o 120 d e g r e e s . These arguments w o u l d a c c o u n t f o r t h e s h i f t f r o m r e s t r i c t e d r o t a t i o n t o c o m p l e t e a n i s o t r o p i c r o t a t i o n , b u t why i s t h e c h o i c e o f t h e o x y g e n - o x y g e n a x i s made? I n f a c t , i t c a n o n l y be a r o u g h a p p r o x i m a t i o n , s i n c e t h e ends o f t h e f o r m a l g r o u p must move d u r i n g these c o n f o r m a t i o n a l changes. The t i m e s c a l e f o r t h e f o r m a l g r o u p c o n f o r m a t i o n a l changes a r e o n l y somewhat more r a p i d r e l a t i v e t o t h e t i m e s c a l e o f s e g m e n t a l m o t i o n and p h e n y l g r o u p r o t a t i o n , s o p h e n y l g r o u p s a r e o n l y somewhat s l u g g i s h w i t h r e s p e c t t o t h e f o r m a l g r o u p . A more d e t a i l e d and a c c u r a t e model f o r t h e f o r m a l g r o u p m o t i o n c o u l d be u n d e r t a k e n b u t t h e d a t a i n hand do n o t warrant i t . The p r e s e n t p i c t u r e p o i n t s t o s i n g l e c o n f o r m a t i o n a l t r a n s i t i o n s a t t h e f o r m a l group which r e s u l t i n o n l y p a r t i a l s p a t i a l averaging of d i p o l a r i n t e r a c t i o n s a t lower temperatures.


f

Acknowledgments The r e s e a r c h was c a r r i e d o u t w i t h f i n a n c i a l s u p p o r t o f N a t i o n a l S c i e n c e F o u n d a t i o n G r a n t DMR-790677, o f N a t i o n a l S c i e n c e F o u n d a t i o n Equipment G r a n t No. CHE 77-09059, o f N a t i o n a l S c i e n c e F o u n d a t i o n G r a n t No. DMR-8108679, and o f t h e U.S. Army R e s e a r c h O f f i c e G r a n t DAAG 29-82-G-0001.

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(2)

R.P. Lubianez, A.A. Jones and M. B i s c e g l i a , Macromolecules (1980) 12, 1141.

(3)

A.A. Jones and M. B i s c e g l i a , Macromolecules (1979) 12, 1136.

(4)

J . F . O'Gara, S.G. Desjardin and A.A. Jones, Macromolecules (1980) 14, 64.

(5)

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(6)

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(7)

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(8)

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(9)

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(10)

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(11)

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(12)

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(1962)

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36,

180, 54,

results. (1977)

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1. (1978)

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(17)

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(18)

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72,

1 (1980)

RECEIVED September 22, 1983


5489.

99.

Spin Relaxation and Local Motion in a Dissolved Aromatic Polyformal

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