Carbon-13 Spin Relaxation Parameters of Semicrystalline Polymers

10 Carbon-13 Spin Relaxation Parameters of Semicrystalline Carbon-13 NMR in Polymer Science Downloaded from pubs.acs.org by UNIV OF MASSACHUSETTS AMHERST on 09/25/18. For personal use only.

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D. E. AXELSON and L. MANDELKERN Department of Chemistry and Institute of Molecular Biophysics, Florida State University, Tallahassee, FL 32306 The overall molecular structure and morphology of a semicrystalline polymer is generally admitted to represent a very complex situation. (1)(2)(3) Crystallinity is rarely if ever complete and, depending on molecular weight and crystallization conditions, can range from about 30 to 90% for homopolymers. (1)(4)(5) Above the level of the unit cell a lamella-like crystallite is the usual predominant feature of homopolymer crystallization, and is considered to be the primary structural entity. In addition, however, the crystallites can be organized into higher levels of morphology, or supermolecular structure such as spherulites or other geometrical forms. (6)(7)(8) There are, therefore, regions of different chain structures present in dif ferent proportions, within a semicrystalline polymer. In the most rudimentary way they can be characterized as an ordered crystalline region, a relatively diffuse interfacial region and an interzonal or amorphous region, wherein the chain units are in non-ordered conformations and connect crystallites. (1)(9) The structure and amounts of these regions determine properties. The crucial question that still needs to be resolved is the detailed structure of the non-crystalline regions, the influence of higher levels of morphology on this structure and its relation to the completely amorphous polymer at the same temperature and pressure. The thermodynamic, spectral and electromagnetic scattering prop erties of a large number of semicrystalline polymers have been studied for many different polymers over the last few decades. (1) (j4) (5) It has been generally concluded that the degree of crystallinity is a quantitative concept. (1) {3) However, the finer details of the different structures present, and their relationship to crystallite organization, are s t i l l in need of more quantitative assessment. Carbon-13 nuclear magnetic resonance has become an important tool with which to study the microstructure and molecular dynamics 1

Current address: DuPont of Canada Research Center, Kingston, Ontario, Canada K7L5A5 0-8412-0505-l/79/47-103-181$08.50/0 © 1979 American Chemical Society

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of s y n t h e t i c polymers. (10)(11) The u t i l i z a t i o n of s p i n r e l a x a t i o n techniques to study the motions and to deduce the s t r u c t u r a l f e a t u r e s of bulk s y n t h e t i c polymers has been demonstrated. It is p o s s i b l e to observe what are e s s e n t i a l l y high r e s o l u t i o n 13c spectra of bulk amorphous polymers (11)(12)(13)(14)(15) and the n o n - c r y s t a l l i n e regions o f polymers (13) (16)(17) by r e l a t i v e l y simple techniques. The o b s e r v a t i o n of C spectra f o r t h i s purpose can be c a r r i e d out with j u s t complete s c a l a r proton decoup l i n g . The major advantages i n using C are the i d e n t i f i c a t i o n of resonant l i n e s f o r the d i f f e r e n t i n d i v i d u a l carbon atoms i n the chain, and d e s p i t e the very o f t e n high v i s c o s i t y of the medium, a l a c k of averaging of the r e l a x a t i o n parameters due to s p i n d i f f u s i o n . To study g l a s s y polymers or the c r y s t a l l i n e regions, more complicated methods u s i n g d i p o l a r decoupling, c r o s s p o l a r i z a t i o n and magic angle spinning need to be used.(18)(19)(20) In the present work we r e s t r i c t our s t u d i e s to s c a l a r proton decoupled s p e c t r a and the determination o f the s p i n r e l a x a t i o n parameters under these experimental c o n d i t i o n s . We are thus l i m i t i n g o u r s e l v e s a t present to probing motions, and r e l a t i n g them to s t r u c t u r e , w i t h i n the mobile non-ordered regions of the s e m i c r y s t a l l i n e polymers a t temperatures w e l l above the g l a s s temperature. In f a c t only the r e s u l t s a t r e l a t i v e l y h i g h temperatures w i l l be d i s c u s s e d here t o avoid complications caused by t r a n s i t i o n s observed a t lower temperatures. (21) Low temperature s t u d i e s of l i n e a r and branched p o l y e t h y l e n e as w e l l as t h e i r copolymers w i l l be reported subsequently. (22) 1 3

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Proton decoupled n a t u r a l abundance C F o u r i e r transform NMR spectra were obtained on a Bruker HX270 a t 67.9 MHz» Whenever p o s s i b l e the samples were s t u d i e d as powders but molded f i l m s were a l s o used. I t was found t h a t no lock m a t e r i a l was necessary f o r f i e l d frequency s t a b i l i z a t i o n . D r i f t t e s t s showed that f i e l d f l u c t u a t i o n s were orders of magnitude smaller (< 0.5 Hz) than the t y p i c a l linewidths i n v e s t i gated, which were the order of s e v e r a l hundred Hz. Finely powdered p o l y ( v i n y l c h l o r i d e ) was used to suspend chunks or p e l l e t s of p o l y e t h y l e n e f o r cases of sample l i m i t a t i o n . The l i n e widths were found to be independent of the f i l l e r used as long as temperature v a r i a t i o n s due to decoupling were minimal. The l i n e width measurements were obtained under i d e n t i c a l experimental c o n d i t i o n s as p o s s i b l e with p a r t i c u l a r a t t e n t i o n being p a i d to noise modulation, bandwidth and decoupling f i e l d s t r e n g t h . When comparisons were important the samples were i n v e s t i g a t e d consecut i v e l y , i f p o s s i b l e . Otherwise, polymer samples of known l i n e width were used as standards. With t h i s procedure, v a r i a t i o n s were kept to a minimum and meaningful comparisons could be made. Two-level decoupling was used to minimize sample h e a t i n g . (23) Quadrature d e t e c t i o n was employed with the a p p r o p r i a t e s p e c t r a l

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widths and data p o i n t s to produce a w e l l - d e f i n e d resonance i n the frequency domain. Linewidths were measured d i r e c t l y from the p l o t t e d spectra, with allowance being made f o r the a r t i f i c i a l l i n e broadening caused by applying an e x p o n e n t i a l l y decaying f u n c t i o n to the f r e e i n d u c t i o n decay. In some instances a computer gener ated l e a s t squares f i t t i n g r o u t i n e was used with e s s e n t i a l l y identical results. S p i n - l a t t i c e r e l a x a t i o n times were measured by the f a s t i n v e r s i o n - r e c o v e r y method (24) with subsequent data a n a l y s i s by a n o n - l i n e a r three parameter l e a s t squares f i t t i n g r o u t i n e . (25) Nuclear Overhauser enhancement f a c t o r s were measured using a gated decoupling technique with the p e r i o d between the end of the data a c q u i s i t i o n and the next 90° p u l s e equal t o about four times the Tj_ v a l u e . Most of the data used a d e l a y of about ten times the T i v a l u e . (26) High temperature measurements were c a r r i e d out using a Bruker B-ST 100/700 v a r i a b l e temperature u n i t . S e l e c t i v e s a t u r a t i o n experiments were performed with the HX270 employing the homonuclear decoupling mode a v a i l a b l e with the instrument but s u b s t i t u t i n g the u s u a l 1H - 1H s i t u a t i o n by 13c - 13c double resonance. A Schomandl type ND100M power a m p l i f i e r provided the second frequency. A spurious peak was g e n e r a l l y observed a t the i r r a d i a t i n g frequency which could be attenuated by a s l i g h t change i n delay times used. However, these have been removed from the spectra reproduced here f o r p u r e l y cosmetic reasons. The p r o p e r t i e s o f a l l but the two lowest molecular weight l i n e a r p o l y e t h y l e n e samples have been p r e v i o u s l y d e s c r i b e d . (17) These i n c l u d e molecular weight, degree o f c r y s t a l l i n i t y and morphological form. (8) (17) The f r a c t i o n Μ = 8.6 χ 10 was obtained by column f r a c t i o n a t i o n and c h a r a c t e r i z e d i n the u s u a l manner. (27)(28) The sample l a b e l e d 1 χ 1 0 i s a l s o known as Polywax 1000. I t i s manufactured by the P e t r o l i t e C o r p o r a t i o n . I t s a c t u a l molecular weight, as obtained from g e l permeation chromatography, i s M = 1263; M = 1136. (29) I t s m e l t i n g temper ature, under the c o n d i t i o n s of the NMR measurements, was 108.8°C as determined by d i f f e r e n t i a l c a l o r i m e t r y . The low d e n s i t y (branched) p o l y e t h y l e n e s studied here were commercial v a r i e t i e s whose molecular weights, d i s t r i b u t i o n and s i d e group concentra t i o n s have been reported. (_30) The ethylene-butene-1 copolymers were a g i f t from the Exxon Chemical C o r p o r a t i o n . The four p o l y e t h y l e n e oxide samples were obtained from the Union Carbide C o r p o r a t i o n , and were used i n the powdered form i n which they were r e c e i v e d . T h e i r molecular weights were obtained i n the c o n v e n t i o n a l manner and are r e s p e c t i v e l y M^ = 3.2 χ 10 ; M = 2.7 χ 10 ; M = 6.0 χ 10 ; M = 6.67 χ 10 ; M = 6.0 χ 10 ; M = 3.3 χ 10 ; M = 1.2 χ 1 0 f o r the samples s t u d i e d . The enthalpy of f u s i o n of the samples, i n the o r i g i n a l powder form, ranged from 37.8 to 39.6 c a l / g , i n d i c a t i n g that there was not very much d i f f e r e n c e i n the l e v e l o f c r y s t a l l i n i t y among the samples 3

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i n t h i s form on t h i s b a s i s o f c a l c u l a t i o n . I f 45 c a l / g i s taken as the heat o f f u s i o n f o r the completely c r y s t a l l i n e sample (4), then the degree o f c r y s t a l l i n i t y i s about 0.85 f o r these samples. The p o l y t r i m e t h y l e n e oxide sample was a g i f t from P r o f e s s o r J . E. Mark. I t s v i s c o s i t y average molecular weight was 100,000. Care was taken t o check p e r i o d i c a l l y , by d i f f e r e n t i a l scan ning c a l o r i m e t r y and small angle l i g h t s c a t t e r i n g , whether any changes occurred i n the l e v e l o f c r y s t a l l i n i t y or morphology. I f such changes occurred, then the samples were no longer used. Results Linewidths. The major i n t e r e s t s i n the experimental l i n e widths o f s e m i c r y s t a l l i n e polymers are how they depend on the morphology and l e v e l o f c r y s t a l l i n i t y , t h e i r v a r i a t i o n with temperature, and whether they are a continuous f u n c t i o n through the melting temperature. Experiments have been designed t o e l u c i d a t e these f a c t o r s and t o supplement and make c l e a r e r those p r e v i o u s l y reported. (16)(Γ7) The temperature dependence o f the l i n e w i d t h on molecular weight and l e v e l o f c r y s t a l l i n i t y , o f l i n e a r p o l y e t h y l e n e , i s i l l u s t r a t e d i n F i g u r e 1. The very high molecular weight sample, M = 2 χ 10 , has a degree o f c r y s t a l l i n i t y , l-λ, o f about 0.51, i s n o n - s p h e r u l i t i c , and does not possess any w e l l - d e f i n e d supermolecular s t r u c t u r e . (17) F o r t h i s sample the l i n e w i d t h i s a smoothly monotonicly decreasing f u n c t i o n of the temperature. There i s no i n d i c a t i o n o f any d i s c o n t i n u i t y at elevated temperatures or upon m e l t i n g . An asymptotic value f o r the l i n e w i d t h o f about 200 Hz i s reached a t 128°C. The i n t e r mediate sample o f low molecular weight, M = 8.6 χ 1 0 , w i t h 1-λ of about 0.90 should have a r o d - l i k e morphology. (8)(31) In t h i s case, a r e s o l v a b l e spectrum cannot be obtained below 90°C. Above t h i s temperature the l i n e w i d t h r a p i d l y approaches the l i m i t i n g value c h a r a c t e r i s t i c o f the much higher molecular weight sample, M = 2 χ 1 0 . Thus i n the melt, or completely amorphous s t a t e , the l i n e w i d t h s f o r these two polymers are e s s e n t i a l l y i d e n t i c a l d e s p i t e the almost three orders o f magnitude d i f f e r e n c e i n mole c u l a r weight. The very lowest molecular weight sample studied, designated as 1 χ 1 0 , with a very s i m i l a r l e v e l o f c r y s t a l l i n i t y and morphology as the 8.6 χ 103 sample does not y i e l d r e s o l v a b l e s p e c t r a u n t i l a temperature o f 75-80°C i s reached. Above the melting temperature f o r t h i s polymer, a constant much lower l i m i t i n g value o f about 50 Hz i s found f o r the l i n e w i d t h . Since i n t h i s case s p e c t r a cannot be obtained below 75°C, a c l e a r d e c i s i o n cannot be made as t o whether a d i s c o n t i n u i t y i n the l i n e w i d t h s occurs upon m e l t i n g . The data are suggestive, however, that a d i s c o n t i n u i t y does i n f a c t e x i s t . In the molten s t a t e there i s a very l a r g e d i f f e r e n c e i n l i n e w i d t h f o r Μ = 1 χ 1 0 as compared t o the other samples. However, the asymptotic value has 3

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already been obtained f o r only a very s l i g h t l y higher molecular weight, M = 8.6 χ Ι Ο . The i n f l u e n c e o f morphology on the linewidth-temperature r e l a t i o n s i s i l l u s t r a t e d i n F i g . 2 f o r two high molecular weight samples which have the same degree o f c r y s t a l l i n i t y a t room temperature. (17) The major i n f l u e n c e o f the morphology on the observed l i n e w i d t h s , that have been p r e v i o u s l y reported (17), manifests i t s e l f below 90°C. As the temperature i s decreased the l i n e w i d t h d i f f e r e n c e s become c o n t i n u o u s l y g r e a t e r between the two samples. In the v i c i n i t y o f 30-40°C the d i f f e r e n c e s correspond to the values p r e v i o u s l y reported. (17) Above 90°C the l i n e widths o f the two samples are i n d i s t i n g u i s h a b l e from one another, and both have the same value i n the melt. The continuous char a c t e r of both curves i n d i c a t e s that e i t h e r the f u s i o n process with regard t o morphology i s d i f f e r e n t i n the two cases; or i f the morphological forms are maintained, the s t r u c t u r e s i n the non c r y s t a l l i n e regions possess a d i f f e r e n t temperature dependence. More d e t a i l e d s t u d i e s which r e l a t e any changes i n morphology with the course o f f u s i o n f o r these kinds o f samples are necessary t o r e s o l v e these p o i n t s . F o r present purposes, the major, d e f i n i t i v e conclusions are that the temperature dependence o f the l i n e w i d t h i s continuous through the melting temperature f o r these two extremes i n morphology. Moreover, depending on the morphology, s i g n i f i c a n t d i f f e r e n c e s i n the magnitude o f the l i n e w i d t h are observed below 90°C. 3

F i g . 3 represents a s i m i l a r phenomenon f o r two samples which possess s p h e r u l i t i c morphologies but have d i f f e r e n t l e v e l s of c r y s t a l l i n i t y . A t the intermediate temperatures the i n c r e a s e d degree o f c r y s t a l l i n i t y y i e l d s only a s l i g h t l y g r e a t e r l i n e w i d t h f o r the same morphology. T h i s small d i f f e r e n c e remains constant u n t i l the m e l t i n g i s reached, a t which p o i n t the two curves merge. A t the lower temperatures, the same high value charac t e r i s t i c o f s p h e r u l i t e s and independent of the l e v e l o f c r y s t a l l i n i t y i s observed as was p r e v i o u s l y reported. (17) The p l o t i n F i g . 4 represents i n the same diagram the i n f l u e n c e o f both the degree o f c r y s t a l l i n i t y and morphology, from examples taken from the previous two f i g u r e s . As would be a n t i c i p a t e d from the previous r e s u l t s , the d i f f e r e n c e s i n the l i n e w i d t h s below the melting range are g r e a t l y enhanced when the data are examined i n t h i s manner. However, as i s e q u a l l y c l e a r , the r e s u l t s would be d i f f i c u l t t o s o r t out f o r i n t e r p r e t i v e purposes i f a c l e a r d i s t i n c t i o n was not made between the l e v e l s of c r y s t a l l i n i t y and morphology, o r l a c k t h e r e o f , as d i s t i n c t l y d i f f e r e n t , independent q u a n t i t i e s . The linewidth-temperature r e l a t i o n o f the p o l y e t h y l e n e oxide samples are given i n F i g . 5. Despite the l a r g e d i f f e r e n c e s i n molecular weight, these samples have about the same l i n e w i d t h , 300-350 Hz, i n the c r y s t a l l i n e s t a t e a t 25°C. They a l l a l s o possess a s p h e r u l i t i c type of morphology. The i n f l u e n c e on the l i n e w i d t h o f the d i f f e r e n t types o f supermolecular s t r u c t u r e s


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Figure 2. Plot of linewidth, W , against temperature at 67.9 MHz for two linear PE samples of same degree of crystallinity (0.51) but differing morphologies: spherulitic, (Ο); no morphology (%). %

Figure 3. Plot of linewidth, W , against temperature at 67.9 MHz for two linear PE samples having a spherulitic morphology but differing levels of crystallinity: degree of crystallinity 0.78, (Ο); degree of crystallinity 0.50, (Φ). %


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Figure 4. Plot of linewidth, W , against temperature at 67.9 MHz for two linear PE samples of differing morphologies and levels of crystallinity. No morphology, degree of crystallinity 0.50, ( Ο ); spherulitic morphology, degree of crystallinity 0.78, (Φ). %


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Figure 5. Plot of linewidth, W , against temperature at 67.9 MHz for PEO samples of indicated molecular weights: 3.3 X 10 mol wt; (Φ), 6 X 10 mol wt; (•), θχΙΟ mol wt; (Ο), 3 Χ 10 mol wt. %

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that can be developed i n p o l y e t h y l e n e oxide has not as yet been i n v e s t i g a t e d . For the two highest molecular weight samples studied here, the l i n e w i d t h s are a c o n t i n u o u s l y decreasing func t i o n of temperature. A l i m i t i n g value o f approximately 135 Hz i s a t t a i n e d at the elevated temperatures i n the melt. There i s no evidence of any d i s c o n t i n u i t y i n t h i s q u a n t i t y i n the m e l t i n g region of 60-70°C. However, although a l l four samples have e s s e n t i a l l y the same l i n e w i d t h i n the c r y s t a l l i n e s t a t e , there i s a d e f i n i t e d i s c o n t i n u i t y upon m e l t i n g f o r the two lowest molecu l a r weight samples. The change i n l i n e w i d t h i s g r e a t e s t f o r the lowest molecular weight sample and i s independent of temperature above i t s m e l t i n g temperature. The l i m i t i n g l i n e w i d t h s i n the molten s t a t e are 80-90 Hz f o r M = 6 χ 1 0 and are reduced t o 47 Hz f o r M = 3 χ 10 . In c o n t r a s t to l i n e a r p o l y e t h y l e n e the asymp t o t i c l i n e w i d t h f o r the melt of p o l y e t h y l e n e oxide i s a t t a i n e d at higher molecular weights. However, f o r both polymers the asymp t o t i c l i n e w i d t h s are r e l a t i v e l y broad. 4

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Because of the u l t i m a t e i n t e r e s t i n understanding the seg mental motions t h a t c o n t r i b u t e to l i n e w i d t h s and the apparently broad l i n e s t h a t are observed f o r both l i n e a r p o l y e t h y l e n e and polyethylene oxide, we have a l s o s t u d i e d a s e r i e s of random ethylene-butene-1 copolymers. Because of the h i g h c o - u n i t content of these samples and the temperature range s t u d i e d , i f these polymers are c r y s t a l l i n e a t a l l , the l e v e l i s very low. Above 50°C they are e s s e n t i a l l y completely amorphous. (32) The l i n e width measurements f o r four such copolymers are given i n F i g . 6. Above 50°C the l i n e w i d t h s only change s l i g h t l y and are i n the range of 180-200 Hz, s i m i l a r to the melt of the homopolymer. As the temperature i s lowered w e l l below 35°C c r y s t a l l i n i t y begins to develop. T h i s problem w i l l be d i s c u s s e d i n d e t a i l i n a sub sequent paper. (22) For present purposes, f o r these copolymers, we are mainly concerned with the l i n e w i d t h s i n the amorphous state. S p i n - L a t t i c e R e l a x a t i o n Parameters, T-^. In F i g . 7 the NT^ values f o r p o l y e t h y l e n e oxide samples are p l o t t e d as a f u n c t i o n of temperature. A l s o p l o t t e d are the average values f o r the two d i f f e r e n t carbons of p o l y t r i m e t h y l e n e oxide. Except f o r the very lowest molecular weight p o l y e t h y l e n e oxide sample (which cor responds to a degree of p o l y m e r i z a t i o n of only 4.5), the s p i n l a t t i c e r e l a x a t i o n time i s the same f o r a l l the samples at a given temperature and i s a l s o a continuous f u n c t i o n of the tem p e r a t u r e . The r e s p e c t i v e m e l t i n g temperatures of each of the polymers i s i n d i c a t e d by the v e r t i c a l arrows i n the f i g u r e . I t thus becomes abundantly c l e a r from ;his extensive s e t of data t h a t the T^'s are continuous f u n c t i o n s through the m e l t i n g tem p e r a t u r e . The segmental motions of the n o n - c r y s t a l l i n e regions which are represented by t h i s parameter are not dependent on the s t a t e of the polymer. The lowest molecular weight p o l y e t h y l e n e


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Figure 6. Plot of linewidth, W , against temperature at 67.9 MHz for ethylenebutene-1 random copolymers. Co-unit contents: (H), 10; ( Q ) , 7; (Φ), 21; (O), 26. %

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Figure 8. Plot of spin-lattice relaxation time against temperature, at 67.9 MHz, for linear and branched PE. Linear PE from Ref. 17, (%); linear PE this work, ( Ο ); branched PE this work, (Q)-

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oxide sample g i v e s s i g n i f i c a n t l y higher NT-^ values a t the e l e v a t e d temperatures. A s i m i l a r c o n t i n u i t y i n the C T^'s through the melting temperature was p r e v i o u s l y reported f o r l i n e a r p o l y e t h y l e n e . (17) We have now i n v e s t i g a t e d the temperature dependence of t h i s quan t i t y , f o r t h i s polymer, i n more d e t a i l and have a l s o s t u d i e d a low d e n s i t y (branched) p o l y e t h y l e n e . The r e s u l t s f o r the p o l y ethylenes are summarized i n F i g . 8. The new data reported here s u b s t a n t i a t e the c o n c l u s i o n p r e v i o u s l y reached f o r l i n e a r p o l y ethylene. A s i m i l a r c o n c l u s i o n can now be reached f o r the back bone carbons of low d e n s i t y (branched) p o l y e t h y l e n e . The melting temperature f o r t h i s p a r t i c u l a r sample, under the c r y s t a l l i z a t i o n c o n d i t i o n s s t u d i e d , i s l e s s than 110°C. (33) Thus, the C s p i n l a t t i c e r e l a x a t i o n parameters f o r the backbone carbons are the same f o r both the l i n e a r and branched polymers over the tempera ture range s t u d i e d here. Changes t h a t occur i n T± as the tem perature i s reduced below 0°C i n v o l v e other c o n s i d e r a t i o n s and w i l l be d i s c u s s e d i n d e t a i l elsewhere. (22) 1 3

1 3

Nuclear Overhauser Enhancement F a c t o r . The n u c l e a r Overhauser enhancement f a c t o r , N0EF, has not been as e x t e n s i v e l y s t u d i e d f o r the pure s e m i - c r y s t a l l i n e polymers as have the other 1 C r e l a x a t i o n parameters. The p r e v i o u s l y reported r e s u l t s f o r l i n e a r polyethylenes (17), with v a r y i n g l e v e l s of c r y s t a l l i n i t y and d i f f e r e n t supermolecular s t r u c t u r e s , are i n c l u d e d i n the summary of Table I . For t h i s polymer a t 45°C and 67.5 MHz, w i t h i n the l i m i t s of the experimental r e s u l t s p r e s e n t l y a v a i l a b l e , the N0EF appears to depend p r i m a r i l y on the l e v e l of c r y s t a l l i n i t y and not on any other morphological, s t r u c t u r a l or molecular f a c t o r s . The samples with the lowest l e v e l of c r y s t a l l i n i t y t h a t could be a t t a i n e d with t h i s polymer, 0.50, possess f u l l NOEF's which are a l s o found i n the pure melt. (34) For the higher c r y s t a l l i n i t y samples the NOEF i s reduced, l e a d i n g to the sug g e s t i o n t h a t the degree of c r y s t a l l i n i t y could be an important f a c t o r i n determining t h i s q u a n t i t y . We have explored the tem perature dependence of the sample which had an NOEF of 1.5 at 45°C. Although the NOEF i n c r e a s e d s l i g h t l y to 1.7 a t 100°C, i t has not yet achieved i t s maximum value a t t h i s p o i n t . Since the f u l l NOEF must be a t t a i n e d i n the pure melt, i t i s not as y e t c l e a r whether or not the change w i l l be continuous. The NOEF s f o r two of the polyethylene oxide samples, M = 3.2 χ 10 and 6.67 χ 10 , were determined, as a f u n c t i o n of temperature, from room temperature through the melting p o i n t . In both cases f u l l NOEF s were observed a t room temperature and i n the melt. Schaefer and Natusch have reported e s s e n t i a l l y a f u l l NOEF, 1.7 ± 0.1, f o r a 1000 molecular weight polyethylene oxide which i s a l i q u i d a t room temperature. (35) I t i s c l e a r t h a t more extensive s t u d i e s are needed b e f o r e any d e t a i l e d i n t e r p r e t a t i o n can be given to the NOEF s, or trends d i s c e r n e d , r e l a t i v e to the amorphous s t r u c t u r e o f the 3

1

4

5

1

1

a

e

1.0

503 945

352

None Rod

.94

e

a

-

C

d

d

.70

* U n f r a c t i o n a t e d sample e s t i m a t e d accuracy +10% êstimated accuracy ±5-10% êstimated accuracy ±0.1 estimated accuracy ±0.2 estimated

4

6

2.75 χ 1 0

6.1 x 10

500

-

None

.54

6

6.1 x 1 0

496

358

None

.72

6

*2.0 χ 1 0

2.0 501

369

None

.51

-

700

356

Spher.

.68

5

*1.7 χ 1 0

6

1.5

695

348

Spher.

.81

5

*1.7 χ 1 0

2.0 χ 10

2.0

625

355

Spher.

.51

5

2.5 χ 1 0

*

C

NOEF

622

b

343

(Hz)

Spher.

Linewidth

0.57

T-^msec)

Morph.

4

ά

8.1 χ 1 0

(1-λ)

Carbon-13 Spin R e l a x a t i o n Parameters o f L i n e a r Polyethylene (17) at 45°C and 67.9 MHz

Table Ι·


196

s e m i c r y s t a l l i n e polymers. However, there are c e r t a i n inherent r e s t r a i n t s which make d i f f i c u l t the determination and c o l l e c t i o n of as much data as would be d e s i r e d . There are no problems with systems which can be described by a o n e - c o r r e l a t i o n time model, such as l i n e a r polyethylene of low l e v e l s of c r y s t a l l i n i t y (17) and the polyethylene oxide samples j u s t d e s c r i b e d . However, when 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 are necessary to d e s c r i b e the r e s u l t s , complications can e x i s t . For example, even i n the com p l e t e l y amorphous s t a t e c i s polyisoprene at 40° and 0°C possesses low NOEF s which are very c l o s e to the t h e o r e t i c a l l y allowed minimum. These r e s u l t s are a consequence of the d i s t r i b u t i o n of r e l a x a t i o n times that are r e q u i r e d to d e s c r i b e the system, ^ i i ) ( i ) ( λ Ε ) Consequently, upon c r y s t a l l i z a t i o n very l i t t l e change can be expected, as i s observed experimentally. (16) Thus the number of systems t h a t can be e f f e c t i v e l y s t u d i e d , to assess the i n f l u e n c e of c r y s t a l l i n i t y on the NOEF's, are l i m i t e d . These w i l l have to be i n t e n s i v e l y s t u d i e d i n more d e t a i l before any general conclusions can be deduced. 1

3

Discussion S p i n - L a t t i c e Relaxation Parameters. As i s summarized i n Table I, i t was p r e v i o u s l y shown f o r l i n e a r polyethylene t h a t a t f i x e d temperature, the T s are constant f o r a wide range i n the l e v e l of c r y s t a l l i n i t y and molecular weight and f o r d i f f e r e n t morphologies or l a c k thereof. (17) The l e v e l s of c r y s t a l l i n i t y v a r i e d from 0.50 to 0.94 i n t h i s study. Thus the segmental motions, r e f l e c t e d i n Τχ, are dependent only on the p r o p e r t i e s of the amorphous s t a t e . T h i s c o n c l u s i o n i s f u r t h e r s u b s t a n t i a t e d by the temperature dependence of Τχ, which i s i l l u s t r a t e d i n F i g . 8. These data c l e a r l y demonstrate the c o n t i n u i t y of T through the melting temperature f o r both l i n e a r and branched polyethylene. Consequently as f a r as the Τχ measurements are concerned, the segmental motions from the n o n - c r y s t a l l i n e regions that c o n t r i b u t e to t h i s q u a n t i t y are i d e n t i c a l to those of the pure melt. The amount of c r y s t a l l i n i t y , the o r g a n i z a t i o n of the c r y s t a l l i t e s and the temperature, t h e r e f o r e , have no i n f l u e n c e on the high f r e quency segmental motions i n the n o n - c r y s t a l l i n e regions. These conclusions are f u r t h e r g e n e r a l i z e d by the more exten s i v e data presented i n F i g . 7 f o r polyethylene oxide and p o l y trimethylene oxide. The continuous nature of the Τχ f u n c t i o n f o r both these polymers over a l a r g e temperature range i s q u i t e d e f i n i t e and i s emphasized by the d e t a i l e d data i n the v i c i n i t y of the r e s p e c t i v e melting temperatures. This i s true even f o r the polyethylene oxide samples where d i s c o n t i n u i t i e s i n the l i n e w i d t h are c l e a r l y i n d i c a t e d i n F i g . 7. Obviously, the type of segmental motions which c o n t r i b u t e to the two d i f f e r e n t r e l a x a t i o n param e t e r s are i n f l u e n c e d q u i t e d i f f e r e n t l y by the presence of crystallinity. The T-, values f o r the very low molecular weight polyethylene ,

1

1

10.


Semicrystalline

Polymers

197

oxide sample are e s s e n t i a l l y the same as the high molecular weight ones a t low temperatures. However, above 50°C the NT^ i n c r e a s e s . Since the degree of p o l y m e r i z a t i o n f o r t h i s sample i s very low, being only a few repeating u n i t s , o v e r a l l molecular r e o r i e n t a t i o n can take p l a c e a t these e l e v a t e d temperatures. Thus i n d i v i d u a l molecular c o n t r i b u t i o n s are being made. A s i m i l a r behavior f o r low molecular weight polyethylene oxide has been reported (36) as have proton T-^ measurements f o r low molecular weight p o l y ethylene. (37) The major r e s u l t s d e s c r i b e d could be p a r t i a l l y a n t i c i p a t e d from those p r e v i o u s l y reported f o r l i n e a r polyethylene (17) as w e l l as those f o r c i s p o l y i s o p r e n e . (16) For the l a t t e r polymer, by t a k i n g advantage of i t s c r y s t a l l i z a t i o n k i n e t i c c h a r a c t e r i s t i c s , i t was p o s s i b l e to compare the C r e l a x a t i o n parameters of the completely amorphous and p a r t i a l l y c r y s t a l l i n e polymer (31% c r y s t a l l i n i t y ) a t the same temperature, 0°C. This i s a unique s i t u a t i o n and allows f o r some unequivocal comparisons. I t was d e f i n i t i v e l y observed t h a t f o r a l l the carbons of c i s p o l y isoprene the T-^'s d i d not change with c r y s t a l l i z a t i o n . Based on the r e s u l t s obtained to date, which have been sum marized above f o r s e v e r a l d i f f e r e n t s e m i c r y s t a l l i n e p o l y m e r s — l i n e a r and low d e n s i t y (branched) polyethylene, p o l y t r i m e t h y l e n e oxide, polyethylene oxide and c i s p o l y i s o p r e n e — i t i s concluded that the r e l a t i v e l y f a s t segmental motions, as manifested i n Τχ, are independent of a l l aspects of the c r y s t a l l i n i t y and are the same as the completely amorphous polymer a t the same temperature. Furthermore, i t has p r e v i o u s l y been shown t h a t f o r polyethylene, the motions i n the n o n - c r y s t a l l i n e regions are e s s e n t i a l l y the same as those i n the melts of low molecular weight n-alkanes. (17) Proton NMR r e l a x a t i o n parameters have a l s o been determined f o r polyethylene (38) and polyethylene oxide {39) i n the melting r e g i o n . The apparent c o n t r a d i c t i o n between the proton s p i n l a t t i c e r e l a x a t i o n parameter f o r a high molecular weight l i n e a r polyethylene sample at i t s melting p o i n t , with the relaxation measurements, has p r e v i o u s l y been p o i n t e d out. (17) This discrep ancy i s s t i l l maintained with the more d e t a i l e d r e s u l t s reported here f o r both types of p o l y e t h y l e n e . For the proton r e l a x a t i o n a small, but d i s t i n c t , d i s c o n t i n u i t y i s reported a t the melting temperature. (38) On the other hand, Connor and Hartland (39) have reported r e s u l t s of a proton NMR study f o r a s e r i e s of polyethylene oxide samples by r o t a t i n g frame proton r e l a x a t i o n time T-^ measurements. T i was a l s o determined. For t h e i r lowest molecular weight sam p l e , M = 550, the T values d i s p l a y a f a i r l y sharp d i s c o n t i n u i t y at about 12°C. T h i s temperature i s c l o s e to the independently determined melting range of 15-25°C. However, there i s no e v i dence f o r a d i s c o n t i n u i t y i n the T-^ measurements f o r t h i s sample. Above the melting temperature the values found f o r Τχ and T were s i m i l a r . T e x h i b i t e d a very pronounced d i s c o n t i n u i t y a t about 63°C f o r the sample M = 6000. T h i s d i s c o n t i n u i t y occurs 1 3

l p

l p

l p


198

w i t h i n the reported m e l t i n g range of 60-63°C. Although there i s a minimum of T-^ i n t h i s temperature r e g i o n , there i s no i n d i c a t i o n of any d i s c o n t i n u i t y . In c o n t r a s t to these two lower molecular weight samples, f o r a high molecular weight sample that was a l s o s t u d i e d , M = 2.8 χ 10^, no sharp d i s c o n t i n u i t y was observed i n T i n the v i c i n i t y of the melting temperature and T-L was con tinuous. In summary, f o r the two lowest molecular weight samples, Tip d i s p l a y e d a d i s c o n t i n u i t y i n the melting region while T-^ was continuous. For the very high'molecular weight sample both of these r e l a x a t i o n parameters were continuous with temperature. These r e s u l t s are reminiscent of and very s i m i l a r to those reported here f o r the r e l a x a t i o n parameters of polyethylene oxide as i l l u s t r a t e d i n F i g s . 5 and 7. We have found that the Τχ s are continuous with temperature over a very wide molecular weight range. However, as i s shown i n F i g . 5, there are d i s c o n t i n u i t i e s i n l i n e w i d t h s a t the melting temperatures f o r the low molecular weight samples, but the l i n e w i d t h s are continuous f o r the higher molecular weight samples. The T^p r e s u l t s of Connor and Hartland (39) d i s p l a y v i r t u a l l y the same behavior. These s i m i l a r i t i e s do not appear to be c o i n c i d e n t a l since the l i n e w i d t h i s d i r e c t l y r e l a t e d to the s p i n - s p i n r e l a x a t i o n param e t e r , T , which i s s e n s i t i v e to low frequency motions. The Τ χ values are a l s o more s e n s i t i v e to the lower frequency motions and would thus be expected to behave s i m i l a r l y to T , or l i n e widths, i n the l c r e l a x a t i o n s t u d i e s . l p

1

2

ρ

2

3

Linewidths. I d e a l l y the s p i n - s p i n r e l a x a t i o n time, T , can be obtained from the l i n e w i d t h W^ by the r e l a t i o n T = V^W^) · Although i n the present work we are mainly i n t e r e s t e d i n the i n f l u e n c e of the d i f f e r e n t aspects of c r y s t a l l i n i t y on T , i t i s i n f o r m a t i v e to examine the l i n e w i d t h i n the completely amorphous s t a t e above the melting temperature. T h i s s t a t e conveniently serves as a reference p o i n t f o r the subsequent d i s c u s s i o n . As we s h a l l deduce i n the subsequent d i s c u s s i o n , i t i s a l s o very impor tant i n e s t a b l i s h i n g an understanding of the c o n d i t i o n s f o r a d i s c o n t i n u i t y to be observed i n the v i c i n i t y of the melting temperature. We have p r e v i o u s l y reported (15) that f o r non c r y s t a l l i n e p o l y i s o b u t y l e n e samples, a t 45°C and 67.9 MHz, the l i n e w i d t h s f o r a l l the carbons are independent of chain length f o r molecular weights greater than about 4-5 χ 1 0 . Below t h i s molecular weight the l i n e w i d t h s are s u b s t a n t i a l l y reduced with decreasing chain l e n g t h . The l i m i t i n g , or l e v e l i n g - o f f , value f o r the methylene carbons i s about 200 Hz f o r t h i s polymer. For l i n e a r polyethylene, we observed a very s i m i l a r e f f e c t , as was i l l u s t r a t e d i n F i g . 1. In the pure melt above the melting temperature a t 140°C, and a t the same frequency, a l i m i t i n g value of about 200 Hz f o r the l i n e w i d t h i s observed. The l i m i t i n g value i s a t t a i n e d a t a much lower molecular weight f o r t h i s polymer under these c o n d i t i o n s . For the very low molecular weight sample, Μ = 1 χ 10 , the l i n e w i d t h i s s u b s t a n t i a l l y reduced 2

2

2

4

3

10.


SemicrystalUne

Polymers

199

to about 50 Hz. The completely amorphous ethylene-butene-1 copolymers, whose molecular weights are i n the asymptotic r e g i o n , have l i n e w i d t h s o f the order of 180-200 Hz above 50°C. These are very s i m i l a r to the completely amorphous homopolymer. The r e s u l t s for polyethylene oxide f o l l o w the same p a t t e r n s . An asymptotic l i n e w i d t h of 135 Hz i s reached i n the molten s t a t e between 6 χ 10 and 6 χ 10 . A monotonie decrease i n l i n e w i d t h i s observed below t h i s molecular weight. For high molecular weight c i s p o l y i s o p r e n e , i n the completely amorphous s t a t e a t 40°C and at 67.9 MHz, the l i n e w i d t h s f o r a l l the carbons are only about 40 Hz. (16) Although a d d i t i o n a l type polymers should be s t u d i e d before f i r m g e n e r a l i z a t i o n s can be made, the data i n hand i n d i cate c e r t a i n s a l i e n t f e a t u r e s r e l a t i v e to the amorphous s t a t e s . There i s a low c r i t i c a l molecular weight, whose exact value v a r i e s with polymer type, above which the l i n e w i d t h and thus T i s independent of chain l e n g t h . T h i s behavior has now been observed with the three d i f f e r e n t polymers s t u d i e d i n d e t a i l and could be expected to be u n i v e r s a l . Except f o r c i s - p o l y i s o p r e n e , the l i n e w i d t h s f o r the other polymers are r e l a t i v e l y broad compared to other type molecular systems. The r a t h e r narrow l i n e s observed f o r the methylene carbons of c i s p o l y i s o p r e n e , about 40 Hz a t 67.9 MHz and 20 Hz a t 22.9 MHz (16), are a l s o found i n the melt of other diene polymers. (22) They would appear from the data obtained so f a r to be a t y p i c a l of polymers and a consequence of the double bond i n the c h a i n . 5

2

In c o n t r a s t to the s p i n - l a t t i c e r e l a x a t i o n parameters, which remain i n v a r i a n t , a s u b s t a n t i a l broadening of the resonant l i n e s occurs upon c r y s t a l l i z a t i o n . The e f f e c t i s r e l a t i v e l y modest f o r c i s p o l y i s o p r e n e a t 0°C and 67.9 MHz, where comparison can be made a t the same temperature. Here there i s about a 50% i n c r e a s e i n the l i n e w i d t h s upon the development of 30% c r y s t a l l i n i t y . Schaefer (13) r e p o r t s approximately 3- to 5 - f o l d broader l i n e s (but they are s t i l l r e l a t i v e l y narrow) f o r the c r y s t a l l i n e t r a n s polyisoprene r e l a t i v e to the completely amorphous c i s p o l y i s o p r e n e at 40°C and 22.6 MHz. I t i s i n t e r e s t i n g to note i n t h i s con n e c t i o n that f o r carbon b l a c k f i l l e d c i s p o l y i s o p r e n e the l i n e widths are g r e a t e r by f a c t o r s of 5-10 r e l a t i v e to the u n f i l l e d polymer. In the present work the l i m i t i n g value of the l i n e w i d t h s f o r polyethylene oxide i n c r e a s e s from 135 Hz i n the melt above 70°C, to the range 300-350 Hz i n the c r y s t a l l i n e s t a t e a t room tempera t u r e . As i s i n d i c a t e d i n Table I, the resonant l i n e w i d t h s f o r l i n e a r p o l y e t h y l e n e i n c r e a s e s u b s t a n t i a l l y upon c r y s t a l l i z a t i o n and a t t a i n values i n the range 500-900 Hz a t 45°C and 67.9 MHz. As has been emphasized p r e v i o u s l y (17), the l e v e l o f c r y s t a l l i n i t y i s not the major determinant of the l i n e w i d t h i n the s e m i c r y s t a l l i n e s t a t e . Rather the supermolecular s t r u c t u r e or morphology i s a major f a c t o r i n governing the magnitude o f the l i n e w i d t h . S t r u c t u r a l f a c t o r s and c r y s t a l l i z a t i o n c o n d i t i o n s under which low d e n s i t y (branched) p o l y e t h y l e n e forms


200

e i t h e r s p h e r u l i t e s or no w e l l - d e f i n e d morphology have r e c e n t l y been e s t a b l i s h e d . (33) Samples from each of these s t r u c t u r a l c a t e g o r i e s y i e l d l i n e w i d t h s which are v i r t u a l l y i d e n t i c a l with the corresponding values l i s t e d i n Table I f o r the l i n e a r polymer. A morphological map, s i m i l a r to those developed f o r l i n e a r and branched polyethylene (8)(33), has not as yet been completed f o r polyethylene oxide. Thus a f u r t h e r g e n e r a l i z a t i o n of these important f i n d i n g s to t h i s polymer cannot be made as y e t . The r e s u l t s that have been obtained i n d i c a t e that the major i n f l u e n c e of the c r y s t a l l i n e regions on segmental motions, and hence to the s t r u c t u r e of the n o n - c r y s t a l l i n e regions, i s i n the l i n e w i d t h and T . The d i f f e r e n t morphologies are r e f l e c t e d i n d i f f e r e n t values of T2The segmental motions i n long chain molecules which exert major i n f l u e n c e on the s p i n - l a t t i c e r e l a x a t i o n times and the nuclear Overhauser enhancements are not i n general the same motions which determine the resonant l i n e w i d t h . Tl i s i n general greater than T . This d i f f e r e n c e can i n p a r t be a consequence of the slower modes of polymer motion, which are c h a r a c t e r i z e d by c o r r e l a t i o n times s u f f i c i e n t l y long that they do not c o n t r i b u t e s i g n i f i c a n t l y to Τχ but do to T2I t i s there f o r e important, i n terms of d e s c r i b i n g the f i n e s t r u c t u r e of the n o n - c r y s t a l l i n e regions, to understand the type motions which c o n t r i b u t e to T and to develop a r a t i o n a l e f o r the r e l a t i v e l y broad l i n e s that are observed f o r most c r y s t a l l i n e polymers. There are many p o s s i b l e f a c t o r s that can c o n t r i b u t e to the linewidths. I t i s important, t h e r e f o r e , that the p e r t i n e n t ones be discerned and understood i f the molecular i n t e r p r e t a t i o n s are to be e v e n t u a l l y deduced. The task i s a formidable one and the complete s o l u t i o n of the problem i s not as yet i n hand. Many of the p o s s i b l e c o n t r i b u t i o n s to the l i n e w i d t h , and reasons f o r the apparently excessive broadening, have been p r e v i o u s l y d i s cussed. (11)(13)(17) Several mechanisms have emerged as being most l i k e l y c o n t r i b u t o r s . One must, however, be w i l l i n g to accept the concept that s e v e r a l d i f f e r e n t mechanisms can be simultaneously involved and c o n t r i b u t i n g to the l i n e broadening. Therefore i t i s necessary that a d i v e r s e set of experiments be designed and c a r r i e d out, to s u b s t a n t i a t e or dismiss the d i f f e r e n t p o s s i b i l i t i e s . A unique process i s not n e c e s s a r i l y r e q u i r e d and should not be e s t a b l i s h e d as an o b j e c t i v e . A l a r g e number of d i f f e r e n t type experiments are necessary to s o r t out the d i f ferent p o s s i b i l i t i e s . In c o n s i d e r a t i o n of the amount of work i n v o l v e d , the problem has not as yet been completely r e s o l v e d . Line broadening due to inhomogeneity i n the s t a t i c magnetic f i e l d , Ho, as w e l l as i n the r f pulse H can c o n t r i b u t e to the observed resonance. However, s t u d i e s of standard samples, of known n a t u r a l l i n e w i d t h s , enable the c o n t r i b u t i o n s from t h i s source to be determined. In the present case these causes con t r i b u t e only a few percent, i . e . , a few Hz, to the t o t a l l i n e w i d t h and are thus i n c o n s e q u e n t i a l to the present problem. Before d i s c u s s i n g the d i f f e r e n t motional c o n t r i b u t i o n s to the l i n e w i d t h , 2

2

2

lf

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the p o s s i b i l i t y t h a t non-motional or s t a t i c phenomena can a l s o make a s u b s t a n t i a l c o n t r i b u t i o n needs to be given s e r i o u s cons i d e r a t i o n . (40)(41) D i f f e r e n c e s i n bulk magnetic s u s c e p t i b i l i t y w i t h i n the same volume element can r e s u l t i n d i f f e r e n c e s i n nuclear screening among n u c l e i i n d i f f e r e n t regions o f the sample, r e s u l t i n g i n a broadening of the resonance l i n e s . (40)(41)(42) Although such broadening can occur from the i r r e g u l a r macroscopic sample c o n f i g u r a t i o n , i t most l i k e l y a r i s e s from microscopic s t r u c t u r a l d i f f e r e n c e s w i t h i n the sample. Broadening from t h i s cause alone w i l l vary l i n e a r l y with the a p p l i e d f i e l d . (41) Thus, because of the high f i e l d used i n the present work, i f t h i s process were o p e r a t i v e , i t could be q u i t e severe, and would have escaped n o t i c e i n most previous s t u d i e s which have been conducted a t much lower f i e l d s t r e n g t h s . Consequently, we have c a r r i e d out a d e t a i l e d study of the frequency dependence of the l i n e w i d t h s f o r the polymers studied here. P a r t i c u l a r a t t e n t i o n has been given to the i n f l u e n c e of c r y s t a l l i n i t y , morphologic form and temperature. An extensive s e t of data has now been c o l l e c t e d and analyzed. We s h a l l l i m i t o u r s e l v e s here to a b r i e f summary of the major f i n d i n g s as they p e r t a i n to the major themes of the present work. A more d e t a i l e d r e p o r t of these f i n d i n g s w i l l be presented elsewhere. (43) A s u b s t a n t i a l e f f e c t of the f i e l d on the resonant l i n e widths was found f o r the c r y s t a l l i n e p o l y e t h y l e n e s and p o l y ethylene oxides. The magnitude of the changes with frequency i s i n q u a l i t a t i v e accord with t h e o r e t i c a l e x p e c t a t i o n . I f other molecular and c o n s t i t u t i o n a l f a c t o r s are h e l d constant, then the i n f l u e n c e of the morphology on the l i n e w i d t h , which was p r e v i o u s l y observed a t 67.9 MHz, i s s t i l l maintained at the lower frequenc i e s . Thus, the low frequency segmental motions of the nonc r y s t a l l i n e regions are d e f i n i t e l y i n f l u e n c e d by the morphology; the previous c o n c l u s i o n was not a consequence of the high f i e l d s that were used. T h i s f a c t thus has important molecular i m p l i c a t i o n s with r e s p e c t to the s t r u c t u r e . For these samples the e x t r a p o l a t i o n of the l i n e w i d t h to zero frequency does not pass through the o r i g i n . Rather large r e s i d u a l v a l u e s , about 100 Hz f o r the c r y s t a l l i n e polyethylenes and about 25 Hz f o r c r y s t a l l i n e polyethylene oxides, are found. T h i s r e s u l t i s c o n s i s t e n t with a r e s i d u a l d i p o l a r c o u p l i n g c o n t r i b u t i o n to the resonant l i n e width. P r e l i m i n a r y magic angle s p i n n i n g experiments that we have performed with c r y s t a l l i n e p o l y e t h y l e n e oxide a t low s p i n n i n g frequencies s u b s t a n t i a t e that the field-dependent broadening has a major s t a t i c c o n t r i b u t i o n from microscopic inhomogeneities. Thus, there are a t l e a s t s e v e r a l c o n t r i b u t i o n s to the resonant l i n e w i d t h and i t s broadening. The homopolymers of low l e v e l s of c r y s t a l l i n i t y , as w e l l as the ethylene-butene-1 copolymers, which are e i t h e r completely amorphous, or s l i g h t l y c r y s t a l l i n e a t the temperatures of measurement, a l s o d i s p l a y frequency-dependent l i n e w i d t h s . Although these e f f e c t s are not n e a r l y as severe as i n the more

202


c r y s t a l l i n e samples, they are not e a s i l y understood. R e s i d u a l d i p o l a r couplings could r e a d i l y account f o r a p o r t i o n of the l i n e w i d t h s i n these cases. The frequency dependence of the l i n e w i d t h and the c o n t r i b u t i o n s from microscopic inhomogeneities s t r o n g l y suggest s i g n i f i cant inhomogeneous broadening. I f these c o n t r i b u t i o n s are not completely averaged i n an experiment, they w i l l g i v e r i s e to a d i s t r i b u t i o n of chemical s h i f t s and an inhomogeneous resonant l i n e . (13) Bloembergen, P u r c e l l and Pound (44) have shown that s i n g l e frequency i r r a d i a t i o n of a l i n e whose width i s dominated by magnetic f i e l d inhomogeneities r e s u l t s i n the l o c a l s a t u r a t i o n of the l i n e . T h i s i s the s o - c a l l e d "hole burning" experiment and has been c a r r i e d out s u c c e s s f u l l y by Schaefer f o r s e v e r a l polymer systems. (13) In t h i s experiment i t i s p o s s i b l e to determine the n a t u r a l d i p o l a r l i n e w i d t h i n the presence of m a c r o s c o p i c a l l y or m i c r o s c o p i c a l l y inhomogeneous magnetic f i e l d s . (415) However, when attempting to s a t u r a t e a resonance whose width i s determined by strong s p i n - s p i n i n t e r a c t i o n s , r a t h e r than f i e l d inhomogen e i t i e s , the e n t i r e l i n e becomes saturated. In t h i s s i t u a t i o n the energy absorbed by the spins i s no longer l o c a l i z e d ; i n s t e a d , the temperature of the s p i n system as a whole i s r a i s e d . This s i t u a t i o n i s i l l u s t r a t e d i n F i g . 9 f o r dioxane (15% acetone-d^, 85% dioxane, ambient temperature, 67.9 MHz). T h i s homogeneous resonant l i n e was chosen f o r i l l u s t r a t i o n and f o r comparison with a l i n e a r p o l y e t h y l e n e sample. The s p e c t r a on the r i g h t demons t r a t e t h a t an i n c r e a s e i n the s a t u r a t i n g r f f i e l d causes a decrease i n the i n t e n s i t y of the resonance. Simultaneously, however, the l o c a t i o n of the l i n e , i . e . , the p o i n t of maximum i n t e n s i t y , as w e l l as the l i n e w i d t h remain constant, because of the homogeneity. The r e s u l t s of t h i s type experiment f o r a l i n e a r , nons p h e r u l i t i c p o l y e t h y l e n e sample are shown i n F i g s . 10 and 11. In F i g . 10 the r f i r r a d i a t i o n was a p p l i e d a t approximately the l o c a t i o n o f the maximum i n the l i n e i n t e n s i t y . The power l e v e l s were p r o g r e s s i v e l y increased to saturate the major p o r t i o n of the resonance. An i r r e g u l a r l y shaped resonance i s observed. F i g . 11 demonstrates more c l e a r l y the inhomogeneous nature of the i n i t i a l polyethylene resonance. In t h i s i n s t a n c e , the p o s i t i o n of the i r r a d i a t i n g r f i s p r o g r e s s i v e l y moved u p f i e l d , as i s i n d i c a t e d by the v e r t i c a l arrows, from the p o s i t i o n of maximum l i n e i n t e n s i t y i n the unperturbed spectrum. D i f f e r e n t power l e v e l s were used c o n c u r r e n t l y . The uppermost spectrum i n F i g . 11 was obtained with no s e l e c t i v e r f i r r a d i a t i o n being a p p l i e d and i s the r e f e r ence against which the remaining s p e c t r a should be compared. I t i s again apparent from these r e s u l t s that the resonant l i n e i s inhomogeneous since the symmetry, l i n e w i d t h at h a l f - h e i g h t , and peak maxima change with the p o s i t i o n and s t r e n g t h of the i r r a d i ation. The i n a b i l i t y to "burn" a narrow hole i n the p o l y e t h y l e n e spectrum i s an i n d i c a t i o n t h a t the " n a t u r a l homogeneous linewidth"


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Figure 9. Selective irradiation of dioxane. Homonuclear irradiation of a homo geneously broadened resonance at 67.9 MHz. Spectral details: PW = 40 psec (90°C), D2 = 10 sec, 4 scans accumuhted, quadrature detection; 15% acetone-d , 85% dioxane mixture. 6

ι

Figure 10. Selective irradiation of linear PE (2 χ JO mol wt,l — λ ~ 0.5). Spec tral details are: 35° C; 67.9 MHz; sweep width ± 5 KHz (quadrature detection); line broadening 9.7 Hz; pulse width 35 êc (90°C = 48 êc); delay = 1.0 sec, 4K data points; 1024 scans accumulated; 10-mm sample tube. Decoupling: 7W (forward), 0.4W (reflected), broad band noise modulated decoupling. 6

204


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f o r the p a r t i c u l a r sample s t u d i e d i s q u i t e l a r g e . T h i s c o n c l u s i o n i s c o n s i s t e n t with the large l i n e w i d t h obtained by extrap o l a t i n g the frequency data to zero frequency. On the other hand, Schaefer (13) has shown from s e l e c t i v e s a t u r a t i o n experiments of amorphous c i s p o l y i s o p r e n e , c r y s t a l l i n e trans p o l y i s o p r e n e , as w e l l as carbon b l a c k f i l l e d c i s p o l y i s o prene, t h a t the resonant l i n e s are homogeneous. The l i n e w i d t h s i n these cases are thus not caused by inhomogeneous broadening r e s u l t i n g from e q u i v a l e n t n u c l e i being s u b j e c t to d i f f e r i n g l o c a l magnetic f i e l d s . The r e s u l t s f o r these systems are thus c o n t r a r y i n p a r t to what has been found here. At t h i s p o i n t i t has been e s t a b l i s h e d that there are a t l e a s t two b a s i c mechanisms which c o n t r i b u t e to the broad l i n e s that are observed f o r the c r y s t a l l i n e polymers. The r e s i d u a l zero frequency l i n e broadening component can be analyzed i n more d e t a i l . S p e c i f i c a t t e n t i o n can be given to f a c t o r s which are a consequence of the c h a i n - l i k e c h a r a c t e r of the molecules. The l o c a l f i e l d a t a given nucleus i s the sum of the i n d i v i d u a l f i e l d s c o n t r i b u t e d by the neighboring magnetic n u c l e i . Segmental motions w i l l induce a time dependence to the v a r i a b l e s so t h a t the i n d i v i d u a l c o n t r i b u t i o n s can be d e s c r i b e d by the equation:(46) H

i:j

(t) = ± P i j / r 3

i : j

(t)[3 cos2e

i : J

( t ) - ΐΊ

(D

I f r ^ j i s assumed to be constant, i . e . , the d i r e c t l y bonded protons provide the dominant c o n t r i b u t i o n , and 0 i j ( t ) i s only time dependent, the time averaged l o c a l f i e l d i s given by 3

T

2

( V i j / r ^ ) / 2(3 c o s 0 ( t ) - l ) d t . i j

(2)

Here T i s the order of time i n which the nucleus r e s i d e s i n a given s p i n s t a t e . I f there are no r e s t r i c t i o n s on the d i r e c t i o n s a v a i l a b l e to the i n t e r n u c l e a r v e c t o r , then the time average can be r e p l a c e d by a space average, with the r e s u l t t h a t 2

(y

i j

/r

3 i j

)

£

π

2

(3 c o s 0

i : j

- l ) s i n 0d0 = 0.

(3)

For non-viscous l i q u i d s , where the above c o n d i t i o n w i l l be expected to be f u l f i l l e d , narrow resonances are observed, when only t h i s source of l i n e broadening i s i n v o l v e d . Other types of r e s t r i c t i o n s can be thought of being imposed on the parameters o f Eq. (1), when polymeric systems are i n v o l v e d . For example, the o r i e n t a t i o n angles may be u n r e s t r i c t e d with respect to a c c e s s i b i l i t y but the segmental motions may not be s u f f i c i e n t l y r a p i d to average 0^j over the angular range 0 to π i n the time i n t e r v a l T . Conversely the motions may be r e l a t i v e l y r a p i d but the angular range may be r e s t r i c t e d . I t has been c a l c u l a t e d t h a t e x c l u d i n g 0— from but a few o r i e n t a t i o n s , i . e . , excluding the magnetization v e c t o r s from s o l i d s e c t o r s of only a few degrees, i s s u f f i c i e n t to produce broadening by about an order 2

206


of magnitude. (13)(46) T h i s l a t t e r process has been termed incomplete motional narrowing. I t was a l s o noted (Γ3) that i n a s e l e c t i v e s a t u r a t i o n experiment a p a r t i a l l y motionally-narrowed l i n e can be expected t o behave as 3 s i n g l e dipolar-broadened NMR line. Schaefer (13)(41) has i n t e r p r e t e d the l i n e w i d t h s o f c i s p o l y i s o p r e n e i n t h i s context and concluded t h a t the data c o u l d be explained by assuming t h a t not a l l s p a t i a l o r i e n t a t i o n s were a c c e s s i b l e t o the c h a i n u n i t s as a consequence o f r e s t r i c t i o n s imposed on the segmental motions. Chain entanglements were p o s t u l a t e d t o be the major source o f these r e s t r i c t i o n s f o r t h i s amorphous polymer. In the carbon b l a c k f i l l e d c i s p o l y i s o p r e n e , the f i l l e r i t s e l f was considered t o be an a d d i t i o n a l source o f entanglements. F o r s e m i c r y s t a l l i n e polymers, the presence o f c r y s t a l l i t e s and t h e i r r e l a t i v e arrangement c o u l d p l a y a s i m i l a r r o l e as w e l l as i n t r o d u c i n g inhomogeneities i n t o the system which can serve as another source o f broadening. The l i n e broadening caused by p a r t i a l motional narrowing can be d i s t i n g u i s h e d from t h a t due t o i s o t r o p i c r e o r i e n t a t i o n a t a reduced r a t e by a p p r o p r i a t e magic angle s p i n n i n g experiments. (13)(47) Random i s o t r o p i c motion a t reduced r a t e s covers f r e quencies o f the order o f the i n v e r s e o f the c o r r e l a t i o n time, i . e . o f the order o f 1 0 - 1 0 Hz. Hence, sample r o t a t i o n a t the u s u a l l y a c c e s s i b l e r a t e s o f 1 0 - 1 0 Hz a t the magic angle w i l l have no i n f l u e n c e s i n c e the l i n e w i d t h s are determined by f r e q u e n c i e s s e v e r a l orders o f magnitude g r e a t e r . P a r t i a l motional narrowing, however, r e s u l t s i n the l i n e w i d t h being determined i n p a r t by very low or zero frequency components. These are a f f e c t e d by f a s t magic angle s p i n n i n g . The extent o f l i n e narrowing t h a t i s obtained depends on the d i s t r i b u t i o n o f the f r e q u e n c i e s generated by the r e s i d u a l d i p o l a r i n t e r a c t i o n r e l a t i v e t o the s p i n n i n g frequency. 5

7

2

4

The concept o f c h a i n entanglements i n f l u e n c i n g the l i n e widths, o r T 2 s , can be examined more d i r e c t l y by studying the i n f l u e n c e o f molecular weight. I t i s w e l l e s t a b l i s h e d t h a t the zero shear bulk v i s c o s i t y o f a l l amorphous polymers i s d i r e c t l y p r o p o r t i o n a l t o the molecular weight below a c r i t i c a l low mole c u l a r weight, M , and above t h i s molecular weight i n c r e a s e s as the 3.5 power o f M. (48)(49)(50) M represents approximately twice the molecular weight between c h a i n entanglements. The mole c u l a r weight dependence o f the v i s c o s i t y r e s u l t s from the f r a c t i o n a l l o s s i n the two d i f f e r e n t molecular weight r e g i o n s . (48) T h i s molecular weight dependence manifests i t s e l f q u i t e d i s t i n c t l y i n the C l i n e w i d t h s i n the completely amorphous s t a t e and i s c o n s i s t e n t with c e r t a i n proton NMR T2 s t u d i e s t h a t have been r e p o r t e d . F o r p o l y i s o b u t y l e n e the C l i n e w i d t h s a r e i n v a r i a n t a t 45°C f o r each o f the carbons f o r molecular weights g r e a t e r than 4.5 χ 1 0 over a 6 0 - f o l d change i n molecular weight. (15) T h i s range corresponds t o a change o f e i g h t orders o f f

c

c

1 3

1 3

4

10.


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magnitude i n the bulk v i s c o s i t y . There i s a decrease i n the l i n e widwth below t h i s molecular weight. From bulk v i s c o s i t y measure ments, M i s found to be 1.5 χ 1 0 (5>1) (52) , which i s the same order o f magnitude that was found f o r the i n v a r i a n t l i n e w i d t h . The polyethylene l i n e w i d t h s , as i l l u s t r a t e d i n F i g . 1, c l e a r l y i n d i c a t e that a constant value i s a t t a i n e d i n the melt between 1-8 χ 10 . Proton T measurements a t 150°C i n d i c a t e t h a t there i s a change i n slope i n t h i s q u a n t i t y as a f u n c t i o n of molecular weight a t about M = 6 χ 10 . (37) The c r i t i c a l molecular weight as determined from bulk v i s c o s i t y measurements f o r t h i s polymer has been given as 2 χ 1 0 (53) and 3.8 χ 1 0 . (52) These values are very c l o s e to those which would be deduced from the l i n e w i d t h measurements. For polydimethyl s i l o x a n e the break i n the proton T - m o l e c u l a r weight curve occurs a t about M = 5 χ Ι Ο . (37) M i s about 2.5 χ 10 from v i s c o s i t y measurements. (52) F i g . 5 i n d i c a t e s that f o r polyethylene oxide a t 90°C the l i n e w i d t h becomes constant between 6 χ 10 and 6 χ 10 . The v i s c o s i t y data i n d i c a t e s that the c r i t i c a l molecular weight i s about 10 . (54)(55)(56) For a l l the cases c i t e d above, which represent those data f o r which a comparison can be p r e s e n t l y made, there i s a d i r e c t connection between the c r i t i c a l molecular weight r e p r e s e n t i n g the i n f l u e n c e of entanglements on the bulk v i s c o s i t y and other p r o p e r t i e s , and the NMR l i n e w i d t h s , or s p i n - s p i n r e l a x a t i o n parameters of the amorphous polymers. Thus the entanglements must modulate the segmental motions so that even i n the amorphous s t a t e they are a major reason f o r the incomplete motional nar rowing, as has been p o s t u l a t e d by Schaefer. (13) T h i s e f f e c t would then be f u r t h e r accentuated w i t h c r y s t a l l i z a t i o n . 4

c

3

2

3

R

3

3

4

2

c

4

4

5

4

From the above, the observations t h a t i n some cases a d i s c o n t i n u i t y a t the melting temperature i s observed i n the C l i n e w i d t h s , while i n other s i t u a t i o n s the l i n e w i d t h i s continuous, can be r e a d i l y e x p l a i n e d . For polyethylene oxide the l i n e w i d t h s i n the c r y s t a l l i n e s t a t e , f o r the samples s t u d i e d to date, are a l l about the same, presumably due to the s i m i l a r i t y i n morphology and l e v e l o f c r y s t a l l i n i t y . However, due to the d i f f e r e n c e s i n the l i n e w i d t h i n the amorphous s t a t e , the lower molecular weight samples must e x h i b i t a d i s c o n t i n u i t y a t the melting temperature, while the higher ones w i l l be continuous. A s i m i l a r s i t u a t i o n w i l l e x i s t f o r p o l y e t h y l e n e . In t h i s case i t has been seen i n F i g . 1 that the major i n f l u e n c e of morphological form on the l i n e w i d t h a t lower temperatures has disappeared f o r the h i g h molecular weight sample. Thus i t i s continuous upon m e l t i n g . The c o n t i n u i t y of the C l i n e w i d t h over a l a r g e temperature range, above room temperature, that has p r e v i o u s l y been reported (17) and i s f u r t h e r d e t a i l e d here does not r e v e a l any change i n the v i c i n i t y of the α t r a n s i t i o n r e g i o n (80-100°C). Major changes are found i n broad l i n e proton NMR experiments, which measure l i n e w i d t h s or second moments. (57) There i s , however, no discrepancy between these r e s u l t s s i n c e the α t r a n s i t i o n i s a property of the c r y s t a l l i n e r e g i o n s . The proton measurements 1 3

1 3


208

1 J

examine the complete sample, while the proton decoupled C s t u d i e s reported here are r e s t r i c t e d t o motions w i t h i n the non c r y s t a l l i n e regions. These are u n a f f e c t e d by the α t r a n s i t i o n . The proton s p i n - s p i n r e l a x a t i o n decay o f u n f r a c t i o n a t e d polyethylene melts have been s t u d i e d by F o l l a n d and Charlesby (58) who i n t e r p r e t e d t h e i r data i n terms o f the broad molecular weight d i s t r i b u t i o n . The system was p o s t u l a t e d t o c o n s i s t o f high molecular weight entangled molecules which c o e x i s t e d with lower molecular weight s p e c i e s . Thus they argue f o r the presence o f a more mobile component as w e l l as one which i s subject to motional c o n s t r a i n t s due t o the entanglements. Other processes could be i n v o l v e d , but very l i k e l y f o r the same molecular reasons, such as a 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 times (59) and incomplete motional averaging o f the d i p o l a r i n t e r a c t i o n s . (60) I t does not appear necessary t o r e q u i r e the e x i s t e n c e o f d i s c r e t e l y d i f f e r e n t s t r u c t u r a l e n t i t i e s , as has been argued. (61) Further evidence f o r the d i r e c t i n f l u e n c e o f c h a i n entangle ments on the l i n e w i d t h i n the proton s p e c t r a f o r some completely amorphous polymers has been demonstrated by Cohen-Addad and c o l l a b o r a t o r s . (60)(62)(63) S p e c t r a l narrowing, as a consequence of r e s i d u a l d i p o l a r broadening, was observed i n magic angle spinning experiments, f o r p o l y i s o b u t y l e n e , polydimethyl s i l o x a n e and c i s 1,4 polybutadiene. The s i g n i f i c a n t r e s u l t here i s not simply t h a t the resonant l i n e w i d t h was narrowed upon magic angle spinning but t h a t t h i s e f f e c t was o n l y observed over the concen t r a t i o n and molecular weight range where the chains were known to be entangled. For d i l u t e d systems, or f o r the pure polymers whose molecular weights were lower than the c r i t i c a l value f o r chain entanglement, no i n f l u e n c e o f the magic angle spinning was observed. In the amorphous s t a t e , t h e r e f o r e , a t s u f f i c i e n t l y h i g h molecular weights, polymer chains e x h i b i t both l i q u i d - l i k e and s o l i d - l i k e p r o p e r t i e s from the p o i n t o f view o f NMR measurements. The l i q u i d - l i k e p r o p e r t i e s are manifested i n the h i g h frequency segmental motions, and r e f l e c t e d i n the s p i n - l a t t i c e r e l a x a t i o n measurements. The s o l i d - l i k e p r o p e r t i e s , as i n d i c a t e d by the l i n e broadening, are a r e s u l t o f r e s i d u a l d i p o l a r couplings caused by incomplete motional narrowing. T h i s l a t t e r e f f e c t i s removed as soon as the molecular b a s i s f o r the entangled system does not e x i s t . Conclusion The r e s u l t s d i s c u s s e d above i n d i c a t e that the f u r t h e r study of the C s p i n r e l a x a t i o n parameters possess the p o t e n t i a l to develop our understanding o f the s t r u c t u r e o f the n o n - c r y s t a l l i n e regions o f s e m i c r y s t a l l i n e polymers. S i g n i f i c a n t progress has already been made i n r e l a t i n g the s p i n - l a t t i c e r e l a x a t i o n parameters with that o f the pure melt. The l i n e w i d t h s , o r s p i n s p i n r e l a x a t i o n parameters, o f s e m i c r y s t a l l i n e polymers have been 1 3

10.


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shown to contain contributions from several major sources. The pathways and methods by which to sort these out have been set forth. Of particular importance is the influence of morphology, or crystallite arrangement, rather than the degree of crystallinity on the linewidths, which should be reflected in other properties. An inhomogeneous resonant line is typical of most semicrystalline polymers. A more detailed analysis of the line shapes that have been observed will be discussed elsewhere together with a more detailed discussion of the influence of field strength. (43) A clear picture has not as yet appeared on the influence of crystallinity and morphology on the nuclear Overhauser enhancement factor. More detailed work remains to be done in this area. However, preliminary results indicate that there is a major influence of the level of crystallinity. Acknowledgement This work was supported by the National Science Foundation under Grant No. DMR 76-21925. Literature Cited 1. L. Mandelkern, Morphology of Semicrystalline Polymers, in Characterization of Materials in Research: Ceramics and Polymers, Syracuse University Press, p. 369 (1975). 2. E. W. Fischer, Prog. Colloid and Polymer Sci. 57, 149 (1975). 3. J. H. Magill in Treatise in Material Science, V. 10, Part A, Academic Press, p. 1 (1977). 4. L. Mandelkern, Crystallization of Polymers, McGraw-Hill (1964). 5. L. Mandelkern, Acc. Chem. Res. 9, 81 (1976). 6. S. Go, R. Prud'homme, R. Stein and L. Mandelkern, J. Polym. Sci., Polym. Phys. Ed. 12, 1185 (1974). 7. L. Mandelkern, S. Go, D. Peiffer and R. S. Stein, J . Polym. Sci., Polym. Phys. Ed. 15, 1189 (1977). 8. J. Maxfield and L. Mandelkern, Macromolecules 10, 1141 (1977) 9. L. Mandelkern, J. Phys. Chem. 75, 3909 (1971). 10. V. D. Mochel, J. Macromol. Sci.-Revs. Macromol. Chem. C8, 289 (1972). 11. J. Schaefer, in Topics in Carbon-13 NMR Spectroscopy, Vol. 1, G. C. Levy, ed., Wiley-Interscience, New York, p. 149 (1974). 12. M. W. Duch and D. M. Grant, Macromolecules 3, 165 (1970).

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13. J. Schaefer, Macromolecules 5, 427 (1972). 14. J. Schaefer, Macromolecules 6, 882 (1973). 15. R. A. Komoroski and L. Mandelkern, J. Poly. Sci., Polym. Symp. C54, 201 (1976). 16. R. A. Komoroski, J. Maxfield and L. Mandelkern, Macro molecules 10, 545 (1977). 17. R. A. Komoroski, J. Maxfield, F. Sakaguchi and L. Mandelkern, Macromolecules 10, 550 (1977). 18. J. Schaefer, E. O. Stejskal and R. Buchdahl, Macromolecules 8, 291 (1975). 19. J. Schaefer and E. O. Stejskal, J. Amer. Chem. Soc. 98, 2035 (1976). 20. H. A. Resing and W. B. Moniz, Macromolecules 8, 560 (1975). 21. D. E. Axelson and L. Mandelkern, J. Polym. Sci., Polym. Phys. Ed. 16, 1135 (1978). 22. D. E. Axelson and L. Mandelkern, to be published. 23. G. C. Levy, I. R. Peat, R. Rosanske and S. Parks, J. Magn. Reson. 18, 205 (1975). 24. D. Canet, G. C. Levy and I. R. Peat, J. Magn. Reson. 18, 199 (1975). 25. J. J. 26. S. 64,

Kowalewski, G. C. Levy, L. F. Johnson and L. Palmer, Magn. Reson. 26, 533 (1977). J. Opella, D. J. Nelson and O. Jardetzky, J. Chem. Phys. 2533 (1976).

27. J. G. Fatou and L. Mandelkern, J. Phys. Chem. 69, 71 (1965). 28. E. Ergőz, J. G. Fatou and L. Mandelkern, Macromolecules 5, 147 (1974). 29. S. Go, F. Kloos and L. Mandelkern, to be published. 30. D. E. Axelson, G. C. Levy and L. Mandelkern, Macromolecules, in press. 31. J. D. Hoffman, L. J. Frolen, G. S. Ross and J. I. Lauritzen, Jr., J. Res. Natl. Bur. Stand., Sect. A 79, 671 (1975).

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32. F. Sakaguchi and L. Mandelkern, unpublished observations. 33. J . Maxfield and L. Mandelkern, J. Polym. Sci., Polym. Phys. Ed., in press. 34. Y. Inoué, A. Nishioka, and R. Chujo, Makromol. Chem. 168, 163 (1973). 35. J. Schaefer and D. F. S. Natusch, Macromolecules 5, 416 (1972). 36. J. J. Lindberg, I. Sirén, E. Rahkamaa and P. Tormala, Die Angewandte Makromolekulare Chemie 50, 187 (1976). 37. D. W. McCall, D. C. Douglass and E. W. Anderson, J. Polym. Sci. 59, 301 (1962). 38. C. L. Beatty and M. F. Froix, Polym. Prepr. Am. Chem. Soc. Div. Polym. Chem. 16, 628 (1975). 39. T. M. Connor and A. Hartland, J. Polym. Sci., Polym. Phys. Ed. 7, 1005 (1969). 40. J. A. Pople, W. G. Schneider and A. Bernstein, High Resolution Nuclear Magnetic Resonance, McGraw-Hill, p. 80 (1959). 41. J. K. Becconsall, P. A. Curnuck and M. C. McIvor, Appl. Spec. Rev. 4, 307 (1971). 42. C. P. Poole and H. A. Farrach, Relaxation in Magnetic Resonance, Academic Press (1971). 43. D. E. Axelson, R. A. Komoroski and L. Mandelkern, to be published. 44. N. Bloembergen, Ε. M. Purcell and R. V. Pound, Phys. Rev. 73, 679 (1948). 45. J. Schaefer, J. Magn. Resonance 6, 670 (1972). 46. S. Kaufman, W. P. Slichter and D. D. Davis, J . Polym. Sci., Polym. Phys. Ed. 9, 829 (1971). 47. J. Schaefer, S. H. Chin and S. I. Weissman, Macromolecules 5, 798 (1972). 48. F. Bueche, Physical Properties of Polymers, Interscience, p. 65ff (1962). 49. F. Bueche, J . Chem. Phys. 20, 1959 (1952); ibid., 25, 599 (1956).

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50. W. W. Graessley, Adv. Polym. Sci. 16, 1 (1974). 51. J. D. Ferry, Viscoelastic Properties of Polymers, 2nd edition, Wiley (1970). 52. G. C. Berry and T. G. Fox, Adv. Polym. Sci. 5, 261 (1968). 53.

R. S. Porter and J. F. Johnson, J. Appl. Polym. Sci. 3, 194 (1960).

54. R. S. Porter and J. F. Johnson, Trans. Soc. Rheol. 6, 107 (1962); Soc. Plast. Eng. Trans. 3, 18 (1963). 55. H. Markovitz, T. G. Fox and J. D. Ferry, J. Phys. Chem. 66, 1567 (1962). 56. T. P. Yin, S. E. Lovell, and J. D. Ferry, J. Phys. Chem. 65, 534 (1961). 57. H. G. Olf and A. Peterlin, J . Polym. Sci. A-2 8, 753, 771 (1970). 58. R. Folland and A. Charlesby, J. Polym. Sci., Polymer Lett. Ed. 16, 339 (1978). 59. F. Horii, R. Kitamaru and T. Suzuki, J. Polym. Sci., Polym. Lett Ed. 15, 65 (1977). 60. J. P. Cohen-Addad, M. Domard and J. Herz, J. Chem. Phys. 68, 1194 (1978). 61. W. L. F. Gőlz, H. G. Zachmann, Kolloid-Z.Z. Polym. 247, 814 (1971). 62. J. P. Cohen-Addad and C. Roby, J . Chem. Phys. 63, 3095 (1975). 63.

J. P. Cohen-Addad and J. P. Faure, J. Chem. Phys. 61, 1571 (1974). Discussion

J. Guillet, University of Toronto, Ontario: Just one com ment about your glass transition temperatures. Surely because the frequency with which you are working is so high, the glass transition temperature will occur at a much lower temperature rather than at a much higher one. Would this not be correct? D. Axelson: The glass temperature usually increases with increasing frequency. However, in the present problem our conclusions are based on the correlation time, which is a frequency-independent quantity. J. Guillet: What is the essential frequency of your measure ment? Presumably i t is not the frequency of the radiation.

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D. Axelson: These s p e c t r a were obtained a t 67.9 MHz, but t h a t ' s not the problem. We can measure c o r r e l a t i o n times regardl e s s of the frequency. The c o r r e l a t i o n time at the g l a s s temperature i s very long. From a measurement of the c o r r e l a t i o n time we should be able to t e l l whether i t i s a t r u e g l a s s . In a l l these cases the c o r r e l a t i o n times are s i x to nine orders of magnitude lower than can p o s s i b l y e x i s t i n a g l a s s . For t h i s reason I t h i n k the c o r r e l a t i o n between the NMR measurement and d i e l e c t r i c r e l a x a t i o n and dynamic mechanical do not r e l a t e one to one because of the frequency e f f e c t s i n the other measurements. J. Guillet: But you would expect a frequency e f f e c t i n t h i s one as w e l l , i f o n l y the frequency of the motion i t s e l f . D. Axelson: The r e l a x a t i o n parameters are frequency dependent but not the c o r r e l a t i o n time. J . C. R a n d a l l , P h i l l i p s Petroleum, Oklahoma: I was i n t e r ested i n your l i n e w i d t h curves vs temperature i n which you essent i a l l y had the melting p o i n t curves. Did you do any f r e e z i n g p o i n t curves? D. Axelson: These were obtained f o r branched polyethylene and were s i m i l a r to the melting p o i n t curves. The c o n d i t i o n s were such that e i t h e r d i r e c t i o n gave i d e n t i c a l l i n e w i d t h s . J . C. R a n d a l l : Yes, I could see t h a t i n the low d e n s i t y p o l y e t h y l e n e . I t would be i n t e r e s t i n g to compare a system o f s p h e r u l i t e s vs known morphology f o r e s s e n t i a l l y the same c r y s t a l l i n i t y . What r e s u l t would those c o n d i t i o n s give? D. Axelson: T h i s would be a very i n t e r e s t i n g experiment to c a r r y out but t e c h n i c a l l y somewhat d i f f i c u l t f o r us a t present. We have plans to c a r r y out such measurements i n the near f u t u r e . C. J . Carman, B. F. Goodrich, Ohio: Since Tg i s a zero frequency measurement and s i n c e the NMR experiment i s a t a higher frequency, I think Tg would go to a higher v a l u e . In other words, your apparent Tg with an NMR measurement would be higher than a Tg as measured with a zero frequency measurement (DSC). Therefore I don't t h i n k the numbers you presented are too surp r i s i n g i n view o f the f a c t that you are a t a higher frequency. Your Tc should be a pseudofunction of Tg a t higher temperatures than o f a Tg measured by a thermal measurement. D. Axelson: Based on c o r r e l a t i o n time measurements the upper l i m i t Tg's that we r e p o r t are frequency-independent. The r e s u l t s would only be s u r p r i s i n g to those who argue f o r a much higher Tg f o r the p o l y e t h y l e n e s . A. Jones, C l a r k U n i v e r s i t y , Massachusetts: Is the dominant e f f e c t on T2 morphological and the dynamics of low frequency motions somewhat d i f f i c u l t to e x t r a c t from T ? D. Axelson: For the p o l y e t h y l e n e s , a t l e a s t , there i s a major e f f e c t of morphology on l i n e w i d t h . T h i s i s going to make more d i f f i c u l t a d e t a i l e d d e s c r i p t i o n of the dynamics of the low frequency motion r e l a t i v e to a completely amorphous polymer. J. Guillet: I thank Dr. Carman f o r p o i n t i n g out my e r r o r caused by the e a r l y hour of the morning, I t h i n k . I t i s q u i t e c o r r e c t that Tg should be higher and, as I r e c a l l from the work on d i e l e c t r i c and other measurements of the g l a s s t r a n s i t i o n , a 2

214


ten degree r i s e i n the g l a s s t r a n s i t i o n might be expected f o r every l o g h e r t z . T h i s would correspond to a g l a s s t r a n s i t i o n a t about ten to the f o u r t h or f i f t h c y c l e s per second, which sounds about the r i g h t range f o r the NMR. F i f t y degrees' d i f f e r e n c e would be expected, ten degrees f o r each order o f magnitude change i n the frequency. I t could c o r r e l a t e q u i t e w e l l with the g l a s s t r a n s i t i o n temperature. D. Axelson: As we have a l r e a d y p o i n t e d out, the c o r r e l a t i o n time i s frequency-independent. The longest c o r r e l a t i o n time that we have measured i s about 10" s. Whether the r e s u l t s c o r r e l a t e w e l l with the g l a s s temperature depends on the value one accepts f o r l i n e a r and branched p o l y e t h y l e n e . Those values have been a c o n t r o v e r s i a l matter. J. Guillet: I t seems to me i n t e r e s t should be focused on only one kind of c o r r e l a t i o n time and that i s the one that r e l a t e s to the motions of long segments i n the polymer. Obviously, the g l a s s t r a n s i t i o n s are not going to be a f f e c t e d by r o t a t i o n s o f methyl groups and phenyl groups. The motion t h a t r e a l l y r e l a t e s to the g l a s s t r a n s i t i o n i s whether or not a complete r e o r d e r i n g of segments of ten- to fifty-monomer u n i t s takes p l a c e . This c o r r e l a t e s w i t h the g l a s s t r a n s i t i o n . D. Axelson: Carbon-13 NMR allows f o r the measurement o f the average c o r r e l a t i o n time f o r each i n d i v i d u a l carbon atom. For the g l a s s temperature problem we are o b v i o u s l y o n l y concerned with the c o r r e l a t i o n time of the backbone carbons. C. J . Carman: E a r l i e r i n your t a l k you showed the carbon Τχ data and NOEF f o r p a r t i a l l y c r y s t a l l i n e and amorphous p o l y isoprenes. Was t h i s a n a t u r a l rubber which had been allowed to c r y s t a l l i z e to d i f f e r e n t degrees or was t h i s a s y n t h e t i c rubber? D. Axelson: The sample studied was a s y n t h e t i c c i s p o l y i s o p r e n e . I t s c i s - 1 , 4 content was g r e a t e r than 99%. C. J . Carman: How was the c r y s t a l l i n i t y c o n t r o l l e d and how was the c r y s t a l l i n i t y a s c e r t a i n e d ? As I r e c a l l the data, the T-^'s were not a f f e c t e d ; n e i t h e r were the NOEF's. In examining the amorphous r e g i o n how can one be c e r t a i n the c r y s t a l l i n e r e g i o n i s p a r t i c i p a t i n g i n the data anyway? D. Axelson: D e t a i l e d answers to these questions can be found i n Macromolecules 10, 545 (1977); i b i d . , 10, 55 (1977). P. Sipos, Dupont, O n t a r i o : In the case of p o l y e t h y l e n e what was the o r i g i n of the sample? Because i t makes a d i f f e r e n c e as f a r as being c a t a l y t i c or f r e e r a d i c a l . D. Axelson: The low d e n s i t y (branched) p o l y e t h y l e n e s were f r e e r a d i c a l i n i t i a t e d ; the l i n e a r polymers were d e r i v e d from commercial sources and p u r i f i e d and c h a r a c t e r i z e d as d e s c r i b e d (Macromolecules 1.0, 550(1977)). 6

RECEIVED M a r c h 13,

1979.

Carbon-13 Spin Relaxation Parameters of Semicrystalline Polymers

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