Relaxation Studies in the System Poly(ethyl methacrylate) - American

8 Relaxation Studies in the System Poly(ethyl methacrylate)Chloroform by Carbon-13 and Proton

Downloaded by NORTH CAROLINA STATE UNIV on May 3, 2015 | http://pubs.acs.org Publication Date: July 2, 1979 | doi: 10.1021/bk-1979-0103.ch008

L E N A S J. H E D L U N D ,

R O B E R T M. R I D D L E , and

NMR

WILMER

G.

MILLER

Department of Chemistry, University of Minnesota, Minneapolis, MN 55455

Nuclear magnetic resonance spectroscopy of d i l u t e polymer solutions is utilized routinely for analysis of tacticity, of copolymer sequence d i s t r i b u t i o n , and of polymerization mechanisms. The dynamics of polymer motion in d i l u t e solution has been in vestigated also by proton and by carbon-13 NMR spectroscopy. To a lesser extent the solvent dynamics in the presence of polymer has been studied.16-18 Little systematic work has been carried out on the dynamics of both solvent and polymer in the same system. The concentration dependence of polymer or solvent motion has been studied only rarely over a wide range i n concentration. Typically, polymer carbon-13 relaxationisnotconcentration de pendent up to 20-30 percent polymer. L i t t l e i s known concerning the concentration dependence of the solvent motion. Carbon-13 relaxation depends predominantly on intramolecular contributions, whereas proton relaxationissensitive to inter molecular as w e l l as intramolecular interactions. However, by use of isotope dilution23 the two types of interactions may be separated. Studies utilizing both nuclei can thus y i e l d compli mentary information. The experimental design was to study both the carbon-13 and proton relaxation as a function of temperature for both polymer and solvent, and to extend these to as high a polymer concentration as the available equipment permitted. Inasmuch as the mechanical properties of polymers can be affected considerably by small amounts of diluents, we would ultimately l i k e to approach the bulk polymer state, where use of strong dipolar decoupling and magic angle spinning are necessary.2^ We chose the system poly(ethyl methacrylate)-chloroform (PEMA-CHCI3) for several reasons. Karim and Bonner,— using a ΡΕΜΑ packed gas chromatography column, have shown that CHCI3 has the strongest interaction with bulk ΡΕΜΑ out of the t h i r t y s o l vents investigated. Secondly, although ΡΕΜΑ has not been so thoroughly studied as poly(methyl methacrylate), PMMA, i t s chain dynamics i n solution should resemble PMMA, which i n bulk has also been s t u d i e d . ^ F i n a l l y , the dynamics of neat chloroform has been studied by NMR22-12. and by d i e l e c t r i c relaxation. 21'— 1-7

5-15

19-22

0-8412-0505-l/79/47-103-143$05.00/0 © 1979 A m e r i c a n C h e m i c a l Society

In Carbon-13 NMR in Polymer Science; Pasika, W.; ACS Symposium Series; American Chemical Society: Washington, DC, 1979.

CARBON-13 NMR IN POLYMER SCIENCE

144

Experimental P o l y ( e t h y l methacrylate) (Cellomer A s s o c i a t e s ) was vacuum d r i e d at 50 C. The molecular weight (M^) was determined to be 3.3 χ 1 0 from i t s i n t r i n s i c v i s c o s i t y i n e t h y l acetate. ~ Chloroform ( s p e c t r a l grade) and deuterochloroform (MSD Isotopes) were used as r e c e i v e d . P r i o r to sample p r e p a r a t i o n the solvent was degassed using f i v e freeze-thaw c y c l e s . The solvent was vacuum d i s t i l l e d onto the polymer i n a 12 nm NMR tube, and sealed. H and C s p i n - l a t t i c e r e l a x a t i o n times were made on a V a r i a n A s s o c i a t e s XL-100 - 15/VFT-100 Spectrometer operating at 100.1 and 25.2 MHz, r e s p e c t i v e l y , using d i f f e r e n t i a l mode — i n v e r s i o n recovery or s a t u r a t i o n r e c o v e r y using homospoil. H and C T j measurements were made using e i t h e r an e x t e r n a l F or an i n t e r n a l H f i e l d frequency l o c k . E i t h e r i n t e g r a t e d peak areas or peak i n t e n s i t i e s were used to determine T j from a l i n e a r p l o t of i n t e n s i t y versus delay depending on the l i n e w i d t h o f the resonance. For sharp resonances no d i f f e r e n c e was found i n T^'s determined from i n t e g r a t e d areas or i n t e n s i t i e s . 5


1

1 3

3 7

1

1 3

1 9

2

Results 1 3

The C spectrum of 6, 20 and 40 wt. % ΡΕΜΑ s o l u t i o n s at 34 C are shown i n F i g u r e 1. A l l of the resonances a r e e a s i l y d i s c e r n i b l e except f o r the backbone methylene at 40%. At low concentration the polymer 01-CH3, quaternary carbon, and backbone methylene carbon e x h i b i t r e s o l v e d or p a r t i a l l y r e s o l v e d chemical s h i f t s due to the various stereochemical sequences s i n c e the polymer was not s t e r e o r e g u l a r . A rough estimate i n d i c a t e s the polymer i s e s s e n t i a l l y a t a c t i c . The C r e l a x a t i o n behavior of chloroform as a f u n c t i o n of temperature and polymer c o n c e n t r a t i o n i s shown i n Figure 2, and the corresponding nuclear Overhauser enhancement f a c t o r s i n F i g u r e 3. The values f o r the neat s o l v e n t a r e i n rather good agreement with l i t e r a t u r e v a l u e s . — A d d i t i o n o f as l i t t l e as three percent polymer i s seen to have a measurable a f f e c t on the solvent r e l a x a t i o n . As the polymer concentration i s increased f u r t h e r there i s a systematic lowering o f T j . At 30% and higher, a T j minimum i s observed. In Figures 4-6 the temperature and concentration dependence of the quaternary carbon, α and e s t e r methyls, and e s t e r methylene C r e l a x a t i o n s are shown. Data on the backbone methylene have not y e t been accumulated, nor have the nuclear Overhauser en hancements on the polymer carbons. At low polymer concentration the d i f f e r e n c e i n Τχ among the s t e r e o t r i a d s f o r a given C was l e s s than experimental e r r o r . At higher concentration only an average could be determined. In general the concentration de pendence of T i i s considerably l e s s than that observed with the s o l v e n t . A T j minimum i s found f o r the e s t e r methylene, and the quaternary carbon r e l a x a t i o n . The minimum moves to higher tem perature with i n c r e a s i n g polymer concentration, analogous to the 1 3

1 3

1 3


HEDLUND ET AL.

Poly(ethyl

ΡΕΜΑ

-

CHCI

2

methacrylate)-Chloroform

3


6% 6 CH»

,c=o 0 3

ÇH

2

7CH3

Jl

20%

40%

I Figure I.

2

34 5

67

C-13 spectrum of 6,20, and 40 wt % ΡΕΜΑ solutions at 34°C


146



Τ (°C)

Figure 2.

Chloroform C-13 relaxation as a function of temperature. The polymer concentration (weight percent) is as indicated.



HEDLUND ET AL.

Poly(ethyl


V

Figure 3.

Chloroform nuclear Overhauser enhancement factor as a function temperature at the indicated polymer concentrations.

American Chemfcaf Society Library

1155 16th St. N. w. In Carbon-13 NMR in Polymer Science; Pasika, W.; ACS Symposium Series; Washington, American Chemical D. C. 20038 Society: Washington, DC, 1979.


148


T,

(sec)

Figure 4.

Temperature and concentration dependence of the quaternary C-13 rehxation: (Φ), 10%; (X), 20%; (O), 30%.



8.

HEDLUND ET AL.

Poly(ethyl

-0-CH -CH 2

.5-

149


3

X

T, (sec)

X o

0 X

X .05'

ι

3.3

1

1

3.5 3.7 l/T χ K)

1

3.9

1

4.1

1 4.3

3

Figure 5.

Temperature and concentration dependence of the ester methylene C-13 rehxation: (Φ), 10%;(χ), 20%;(0), 30%.



• X x

-0-CH -CH

ο

2


X

οχ

3

β

? χ χ

T, -CH

-

3

·

ο

χ

ο χ

ι 3.3

ι 35

ι 3.9

3.7 Ι/Τ χ Ι Ο

ure 6.

χ

ι 4.1

ι 4.3

3

Temperature and concentration dependence of the methyl C-13 re laxation: (Φ), 10%;(X),

20%;(0),

30%.


8.

HEDLUND ET AL.

Poly(ethyl

151


r e s u l t s f o r the s o l v e n t . The e s t e r methyl has a considerably l a r g e r T j than the e s t e r methylene due to the i n t e r n a l r o t a t i o n of the methyl. The 01-CH3 T i i s more than an order of magnitude smaller than that o f the e s t e r methyl, as i t r e f l e c t s more closely the backbone motion and probably a higher b a r r i e r f o r i n t e r n a l r o t a t i o n as w e l l . In Figure 7 i s shown the s o l v e n t H r e l a x a t i o n time as a f u n c t i o n o f temperature and polymer c o n c e n t r a t i o n . Analogous to the C r e s u l t s , the proton r e l a x a t i o n i s a f f e c t e d by a d d i t i o n of only a small amount of polymer. Further a d d i t i o n o f polymer decreases T j s y s t e m a t i c a l l y . The neat chloroform proton T^ data a r e i n s u b s t a n t i a l agree ment with those of Bender and Z e i d l e r . 2 J U n l i k e chloroform * C r e l a x a t i o n , which i s almost e x c l u s i v e l y by i n t r a m o l e c u l a r d i p o l e d i p o l e r e l a x a t i o n , H r e l a x a t i o n has i n t e r m o l e c u l a r as w e l l as i n t r a m o l e c u l a r c o n t r i b u t i o n s . By means of d i l u t i o n with C D C I 3 one can o b t a i n s e p a r a t e l y the i n t r a m o l e c u l a r and the v a r i o u s i n t e r m o l e c u l a r contributions.£Z A d d i t i o n a l i n t e r m o l e c u l a r terms must be i n c l u d e d i n the presence o f polymer. Expressed i n terms of r e l a x a t i o n r a t e s , 3 8

1


1 3

3

1

w w

= a/T

l ) i n t r a

+

d/T

(i)

l ) l n t e r

where (l/Tj). , = intra

(

1

1

/

T

) 1

s p i n rotation intra

+

(

;

}

H-C1 intra

(

2

)

1

and 1

H

(1/Τχ). _ - (Ι/Τχ)^ inter inter 1

+ (l/Ti) ^ inter

1

S

1

+ (1/T!) I inter. H

1

(3)

The s u p e r s c r i p t s H-Cl r e f e r s to s o l v e n t p r o t o n - c h l o r i n e i n t e r a c t i o n , H-HS to solvent proton-proton i n t e r a c t i o n , and H-P to i n t e r a c t i o n of the s o l v e n t proton with the polymer. The l a t t e r should be dominated by solvent proton-polymer proton i n t e r a c t i o n . Upon a d d i t i o n of C D C I 3 , followed by e x t r a p o l a t i o n to pure C D C I 3 , the extrapolated r a t e [ ( I / T ^ Q ] i s given by

(l/T

l ) o

=

d/W

intra

+

(1/Τΐ>ί£

Γ

+ d / T l ^ e r

+

^ ^ t e r

Equations 1-4, plus a knowledge^ of the t h e o r e t i c a l 1

(I/TO ?""? 1

/arti)i n~* ter

inter/

R

N

1 7

and a/Ti) ~ inter/ E

v

i y

C1

H

v

/(l/Ti) "~? inter' 1

ratios

, allows the


4


152


t

• •

i T, (sec) 10

χ χ

•

χ χ

A

Α

χ

Δ • Δ Δ

•

Ο 1° 3.5

*Ι 3.7

I 3.9 Ι / Τ χ ΙΟ

ι 4.1

ι 4.3

ι 4.5

3

Figure 7. Temperature and concentration dependence of the chloroform H relaxation: 0%; 3%; « ) , 6%; (χ), 10%; (A), 20%; (A), 30%; (*), 1

40%;(O),50%.


8. HEDLUND ET AL.

Poly(ethyl

i n t r a m o l e c u l a r and i n t e r m o l e c u l a r c o n t r i b u t i o n s to T j to be a s sessed. In pure chloroform the i n t r a m o l e c u l a r r e l a x a t i o n i s found to be dominated by s p i n r o t a t i o n . — The i n t e r m o l e c u l a r c o n t r i b u t i o n s dominate the i n t r a m o l e c u l a r a t a l l temperatures, with the proton-proton i n t e r a c t i o n being the major c o n t r i b u t o r to the i n t e r m o l e c u l a r r e l a x a t i o n mechanisms. In the presence o f polymer the quantity , H-P . ... (1/Τχ). _ + (1/Ti). _ i s more e a s i l y inter intra determined from the experimental data than the proton-polymer i n t e r a c t i o n alone. Shown i n Figure 8 i s the solvent protonsolvent proton c o n t r i b u t i o n as a f u n c t i o n o f polymer concentra t i o n . Shown i n F i g u r e 9 i s the s o l v e n t proton-polymer c o n t r i b u t i o n , where we have assumed the i n t r a m o l e c u l a r c o n t r i b u t i o n i s s m a l l , and a l s o s c a l e d the r e s u l t s to r e f l e c t the number o f polymer protons present. Λ

J

v


153


N

1

λ

v

1

J

Discussion In a polymer s o l u t i o n the t r a n s l a t i o n a l d i f f u s i o n of solvent i s w e l l known to be r e l a t e d t o the i n t e r n a l motion o f the polymer, and i t s concentration dependence.—""— I t would not be s u r p r i s i n g to f i n d a r e l a t i o n s h i p between solvent r o t a t i o n a l motion and polymer segmental motion, p a r t i c u l a r l y a t high polymer concentra t i o n . There i s l i t t l e systematic l i t e r a t u r e bearing on t h i s p o i n t . R o t h s c h i l d , i t by a n a l y z i n g the band shape o f a f a r i n f r a red band o f CH Cl2, found only a small change i n solvent r o t a t i o n a l c o r r e l a t i o n time upon a d d i t i o n o f up to 60% p o l y s t y r e n e . Anderson and Liu,î-§ studying the proton r e l a x a t i o n o f benzene i n the presence o f PMMA, found a systematic decrease i n with i n c r e a s i n g polymer c o n c e n t r a t i o n . A d d i t i o n o f 35% PMMA r e s u l t e d i n a f a c t o r o f three r e d u c t i o n i n Τχ. Through the use o f isotope d i l u t i o n they were able to separate the r e l a x a t i o n i n t o i n t r a molecular and i n t e r m o l e c u l a r c o n t r i b u t i o n s . Inasmuch as t h e i r a n a l y s i s i n d i c a t e d that the i n t r a m o l e c u l a r r e l a x a t i o n was inde pendent o f polymer c o n c e n t r a t i o n , they concluded that up to 35% PMMA had no e f f e c t on the r o t a t i o n a l motion of benzene. F i n a l l y we turn to the work o f Heatley and S c r i v e n s , — who measured the C and H r e l a x a t i o n i n acetone at 0, 5, 10 and 20% PMMA. At high temperatures s p i n r o t a t i o n dominated the r e l a x a t i o n and l i t t l e information was obtainable concerning solvent motion. At low temperatures, where d i p o l a r r e l a x a t i o n dominated, no e f f e c t o f polymer on acetone r o t a t i o n was evident up to 10% PMMA, but q u i t e p e r c e p t i b l e at 20% PMMA. 3

2

1 3

2

Returning to our data, i t i s e s p e c i a l l y i n t e r e s t i n g that we f i n d a systematic r e d u c t i o n i n solvent C r e l a x a t i o n upon i n crease i n polymer concentration, even at low polymer concentration, inasmuch as the r e l a x a t i o n should be almost e x c l u s i v e l y by i n t r a molecular d i p o l a r r e l a x a t i o n . — The existence o f a T\ minimum a t higher polymer concentration permits us to make a meaningful com p a r i s o n with v a r i o u s models. I f the chloroform C relaxation 1 3

1 3




154

Figure 9. Temperature and concentration dependence of the solvent protonpolymer proton relaxation rate: 10% polymer; (χ), 20% polymer.


8.

HEDLUND ET AL.

Poly(ethyl

155


was d e s c r i b a b l e by a s i n g l e i s o t r o p i c r o t a t i o n a l c o r r e l a t i o n time, τ , the s p e c t r a l d e n s i t i e s J (ω) would be given by


J

n

( a ) )

=

τ

/ 0

(

1

+

ω

2

τ

2 0

)

( 5 )

'

l e a d i n g to a minimum of 0.040 sec. The f a c t that the Τχ min imum i s more than 4 times l a r g e r i n i t s e l f r u l e s out a s i n g l e ro t a t i o n a l c o r r e l a t i o n time. The next l o g i c a l step i s to assume a d i s t r i b u t i o n of c o r r e l a t i o n times, as i t w i l l r a i s e the Tj minimum. The appropriate s p e c t r a l d e n s i t i e s f o r both symmetric and asymmetric d i s t r i b u t i o n s of i s o t r o p i c r o t a t i o n s have been given ° , wherein the r e l a x a t i o n s are c h a r a c t e r i z e d by a mean c o r r e l a t i o n time and a d i s t r i b u t i o n width parameter. Keeping the width parameter and type of d i s t r i b u t i o n f u n c t i o n f i x e d , T^ as a f u n c t i o n of mean c o r r e l a t i o n time may be c a l c u l a t e d . Assuming, f o r instance, the symmetric Cole-Cole d i s t r i b u t i o n , a width parameter of 0.25 w i l l give a Τχ minimum i n agreement with the 30% ΡΕΜΑ data. However, upon keeping the width parameter constant; a mean c o r r e l a t i o n time of l e s s than 1 0 " sec. would be required to y i e l d a c a l c u l a t e d Ti i n agreement with the 20 C date. T h i s i s c l e a r l y a meaningless value as solvent r o t a t i o n a l c o r r e l a t i o n times are never that s m a l l . As an example, f o r pure deuterochloroform at 20°, H u n t r e s s ^ c a l c u l a t e s τ± to be 1.8 χ 1 0 ~ sec. and T u to be 0.92 χ 1 0 " sec. I t i s h i g h l y u n l i k e l y that the r o t a t i o n a l d i f f u s i o n of the solvent i n a polymer s o l u t i o n could p o s s i b l y exceed that of the pure solvent. A d d i t i o n a l l y the c a l culated corresponding to t h i s mean τ and d i s t r i b u t i o n width i s much lower than the experimental value at 20 C of n e a r l y 2. Unsymmetric d i s t r i b u t i o n s give u n s a t i s f a c t o r y r e s u l t s a l s o . The assumption of i s o t r o p i c motion i s not a s i g n i f i c a n t source of e r r o r , as chloroform r o t a t i o n d i f f u s i o n c o e f f i c i e n t s d i f f e r by l e s s than a f a c t o r of two.?-? Relaxation by s c a l a r coupling and s p i n r o t a t i o n i s small i n pure c h l o r f o r m — , and we can see l i t t l e reason why i t should be more s i g n i f i c a n t i n the presence of polymer. Hence another mechanism must be devised to e x p l a i n the experimental r e s u l t s . 1

,lfi+

15

12

12

A p o s s i b l e step i n t h i s d i r e c t i o n can be made through use of e a r l i e r r e l a x a t i o n studies on other systems. Hunt and P o w l e s , — when studying the proton r e l a x a t i o n i n l i q u i d s and g l a s s e s , found the r e l a x a t i o n best described by a " d e f e c t - d i f f u s i o n " model, i n which a non-exponential c o r r e l a t i o n f u n c t i o n corresponding to d i f f u s i o n i s included together with the usual exponential f u n c t i o n corresponding to r o t a t i o n a l motion. The c o r r e l a t i o n f u n c t i o n i s taken as the product of the two independent r e o r i e n t a t i o n pro cesses. This type of model has more r e c e n t l y been a p p l i e d to C r e l a x a t i o n i n p o l y m e r s , ^ where the nonexponential part c o r r e sponds to conformational jumps i n a Monnerie t y p e — l o c a l mode 1 3



156


mechanism plus an exponential contribution corresponding to over all tumbling. A continium version of this has recently been given.— This can at least qualitatively explain the experimental data in that the Tj minimum can be significantly increased over a single exponential model while keeping the nuclear Overhauser enhancement factor much closer to the experimental values, while at the same time not leading to physically absurd values for the exponential reorientation. One can give a physical picture to this scheme which makes some intuitive sense. In the presence of polymer the solvent is relaxed by two mechanisms. One is the rotation of the solvent, an exponential reorientation contribu tion. The nonexponential or diffusive contribution could result from the reorientation when the solvent drops into the hole re sulting from the conformational jump of the polymer. This would be compatible with the mechanisms used to explain the relation ship between solvent translational diffusion and polymer segment motion, as mentioned earlier. The solvent proton results can also be analyzed in terms of this mechanism, as well as the poly mer backbone motion. We are currently trying to quantitatively analyze the data from this viewpoint. References 1. K. J. Liu and R. Ullman, J. Chem. Phys., 48, 1158 (1968). 2. K. J. Liu and W. Burlant, J. Polym. Sci., Part A-1, 5, 1407 (1967). 3. K. Hatada, Y. Okamoto, K. Ohta, and H. Yuki, J. Polym. Sci., Polym. Letters Ed., 14, 51 (1976). 4. F. Heatley and M. K. Cox, Polymer, 18, 225 (1977). 5. D. Ghesquiere, B. Ban, and C. Chachaty, Macromolecules, 10, 743 (1977). 6. J. Spevacek and B. Schneider, Polymer, 19, 63 (1978). 7. D. Doskocilova, B. Schneider, and J. Jakes, J. Mag. Res., 29, 79 (1978). 8. J. Schaefer, Macromolecules, 6, 882 (1973). 9. J. R. Lyerla and T. T. Horikawa, J. Polym. Sci., Polym. Letters Ed., 14, 641 (1976). 10. F. Heatley and A. Begum, Polymer, 17, 399 (1976). 11. F. A. Bovey, F. C. Schilling, T. K. Kwei and H. L. Frisch, Macromolecules, 10, 559 (1977). 12. K. Hatada, T. Kitayama, Y. Okamoto, K. Ohta, Y. Umemura and H. Yuki, Makromol. Chem., 178, 617 (1977). 13. R. E. Cais and F. A. Bovey, Macromolecules, 10, 752 (1977). 14. R. E. Cais and F. A. Bovey, Macromolecules, 10, 757 (1977).


8. 15.


16. 17. 18. 19. 20. 21. 22. 23. 24. 25.

HEDLUND ET AL.

Poly(ethyl methacrylate)-Chloroform

157

W. H. Stockmayer, A. A. Jones and T. L. Treadwell, Macromolecules, 10, 762 (1977). J. Ε. Anderson and Κ. J. Liu, J. Chem. Phys., 49, 2850 (1968). K. Sato and A. Nishioka, J. Polym. Sci. Part A-2, 10, 489 (1972). F. Heatley and J. H. Scrivens, Polymer, 16, 489 (1975). W. P. Slichter and D. D. Davis, Macromolecules, 1, 47 (1968). F. Heatley, Polymer, 16, 493 (1975). T. Cosgrove and R. F. Warren, Polymer, 18, 255 (1977). R. Kimmich and Kh. Schmauder, Polymer, 18, 239 (1977). G. Bowers and A. Rigamonti, J. Chem. Phys., 42, 171 (1965). J. Schaefer, in "Structural Studies of Macromolecules by Spectroscopic Methods", K. J. Irvin, Ed., John Wiley & Sons, 1976, pp 201-226. A. K. Karim and D. C. Bonner, Soc. Plast. Eng., Tech. Pap., 22, 3 (1976).

26.

D. W. McCall, Natl. Bur. Stand. (U.S.) Spec. Publ. No. 301, 475 (1969). 27. H. J. Bender and M. D. Zeidler, Ber. Bunsenges Physik. Chem., 75, 236 (1971). 28. R. Shoup and T. Farrar, J. Mag. Res., 7, 48 (1972). 29. W. T. Huntress, J. Phys. Chem., 73, 103 (1969). 30. D. E. O'Reilly and G. E. Schacher, J. Chem. Phys., 39, 1768 (1963). 31. G. Bowers and A. Rigamonti, J. Chem. Phys., 42, 175 (1965). 32. K. Gillen, M. Schwartz and J. Noggle, Mol. Phys., 20, 899 (1971). 33. S. Mallikarjun and Ν. E. Hill, Trans. Faraday Soc., 61, 1389 (1965). 34. S. Mallikarjun and Ν. E. H i l l , Rheologica Acta, 5, 232 (1966). 35. J. Brandrup and H. Immergut, Polymer Handbook, 2nd ed., Interscience, New York, 1975. 36. R. Freeman and H. D. W. H i l l , J. Chem. Phys., 54, 3367 (1971). 37. J. L. Markley, W. J. Horsley, and M. P. Klein, J. Chem. Phys., 55, 3604 (1971). 38. J. R. Lyerla, T. T. Horikawa and D. E. Johnson, J. Am. Chem. Soc., 99, 2466 (1977).



158


39. A. Abragam, The Principles of Nuclear Magnetism, Oxford (1961). 40. R. S. Moore and J. D. Ferry, J. Phys. Chem., 66, 2699 (1962). 41. C. P. Wong, J. L. Schrag, and J. D. Ferry, J. Polym. Sci. Part A-2, 8, 991 (1970). 42. J. D. Ferry, "Viscoelastic Properties of Polymers," Wiley, New York (1970). 43. W. G. Rothschild, Macromolecules, 1, 43 (1968). 44. J. Schaefer, Macromolecules, 6, 882 (1973). 45. Β. I. Hunt and J. G. Powles, Proc. Phys. Soc., 88, 513 (1966). 46. B. Valur, J. P. Jarry, F. Geny and L. Monnerie, J. Polym. Sci., Polym. Phys. Ed. 13, 667, 675 (1975). 47. J. T. Bendler and R. Yaris, Macromolecules, 11, 650 (1978). RECEIVED

March 13,

1979.


Relaxation Studies in the System Poly(ethyl methacrylate) - American

Recommend Documents