Study of molecular motion in polymers by the paramagnetic probe method

2238 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.

A. 1~. VASSERMANP.~a~.

F. HUMBEL, F. JONA and P. SCHERRER, Helv. Phys. acta 26: 1, 1953 K. Z. FATT~KHOV, Zh. tekhn, fiziki 22: 313, 1952 {~. C. GARTON, Trans. F a r a d a y Soc. A42: 56, 1946 G. F R E L I g H , Teoriya dielektrikov (Theory of Dielectrics). Izd. inostr, lit., 1960 G.P. MI~HAILOV and A. M. LOBANOV, Sb. Fizika dielektrikov (Physics of Dielectrics). p. 92, Izd. A N SSSR, 1960; Zh. tekhn, fiziki 28: 2, 1958 R. J. ME/tgINS, Progress in dielectrics 3: 151, 1961 G. P. MI~HAILOV and T. I. BORISOVA, Uspekhi fiz. nauk 83: 63, 1964 G. P. MIKHAILOV, A. M. LOBANOV and M. P. PLATONOV, Vysokomol. soyed. 8: 692, 1377, 1966 (Translated in Polymer Sei. U.S.S.R. 8: 4, 760, 1966) M. V. VOL'KENSHTEIN, Konfiguratsionnaya statistika polimernykh tsepei (Configurational Statistics of Polymer Chains). Izd. A N SSSR, 1959 I. L N0VAK, Zh. tekhn, fiziki 24: 18, 1954; 25: 1854, 1955 T. N. P L I E r , Dokl. A N SSSR 169: 626, 1966 T. M. BIRSHTEIN and O. B. PTITSYN, Konformatsiya makromolekul (Macromolecular Conformation). Izd. " N a u k a " , 1964 M. BACCAREDDA, E. BUTTA and V. FROSINI, J. Polymer Sci. B3: 189, 1965 E. BUTTA and V. FROSINI, Ric. Sci. 6: 3, 1964 B. I. HUNT, J. G. POWLES and A. E. WOODWARD, Polymer 5- 323, 1964 J. M. CRISSMAN, A. E. WOODWARD and J. A. SAUER, J. Polymer Sci. 9: 2693, 1965

STUDY OF MOLECULAR MOTION IN POLYMERS BY THE PARAMAGNETIC PROBE METHOD* A. M. VASSERMA~,A. L. BUCHACHENKO,A. L. KOVARSKIIand M. B. NEIMA~ (dec.) Institute of Chemical Physics, U.S.S.R. Academy of Sciences

(Received 30 September 1967) R~.LAXATIO~ properties of polymers depend on the intensity of the molecular motion of macromolecules, segments, and units and are determined by intraand intermolecular reaction potentials of atoms and groups of macromolecules. IR spectroscopy, methods of dielectric and mechanical losses, NMR were developed and are being widely used to study these. EPR has also been used to study molecular motion in polymers [1]. By this method the temperature variations of line width of the signal formed during polymer irradiation are determined. This is only possible at temperatures below the glass temperature (Tg), since polymer radicals intensively recombine on incresing temperature. The use of stable radicals as paramagnetic probes considerably widens the possibilities of the EPR method and makes it possible to examine molecular motion at temperatures higher than T~. * Vysokomol. soyed. A10: No. 8, 1930-1936, 1968.

Study of molecular motion in polymers b y the paramagnetie probe method

2239

T h e i d e a o f a p r o b e h a s n o t u p t o r e c e n t l y b e e n f u r t h e r d e v e l o p e d in p r a c t i c e . In view of the extensive study of stable organic radicals the practical possibility o f u s i n g t h e s e r a d i c a l s a s p r o b e s h a s o n l y r e c e n t l y e m e r g e d in p r a c t i c e .

THEORETICAl. PRINCIPLES OF THE PARAMAGNETIC PROBE METHOD W h e n an unpaired electron of a paramagnetic particle is in a g-orbital, its anisotropie hyper-fine interaction ( H F I ) with magnetic nuclei and the anisotropy of spin-orbital interaction m a y not be neutralized b y molecular motion to zero in condensed media, which results in wide lines of hyper-fine structure (HFS). This widening depends on the nature of the orbital of the unpaired electron (anisotropy of H F I and g-factor) and is simply determined b y the correlation time of rotational motion of the paramagnetic particle. Correlation time means the time between two intermittent reorientations with a rotation amplitude of approxim a t e l y u/2; it depends on the intensity of molecular motion in the medium in which the paramagnetic particle is situated. Thus, the paramagnetie particle functions as a probe to s t u d y the molecular motion of the matrix. Stable organic radicals, nitroxides in particular, are convenient for use as probes. These radicals readily dissolve in most liquids and can easily be a d d e d to polymers. They are stable over a wide range of temperature and their E P R spectrum can be analysed with comparative ease. The correlation time Tc is determined from the analysis of line width of the H F S . The theory of line width has been described in a general form in a separate paper [2]; for aliphatic nitroxide radicals of general formula

H3c
H3C~ N" "CH3 "O using an expression for rc, it can be obtained from another study [3]: "rc=8"4× lO-1%tHmax I' / I + ~ - - 1 )

(l)

where ztHmax is the width of the spectrum component m~ = + 1 (in oersteds), I+1 is the intensity of first derivatives of the outer components situated in a high m N = -- 1 and low (m/~ = + 1) fields.

METHODS OF EXPERIMENT Stable radicals of various structures were used in the s t u d y

H

HsC'%/N",d/Ca H~C/~/J"CH3 ~ O I

CHs C~ 3 I CH3 II

O

H3C CH3

N--C) ~--~--O~N--6 cCI~
H3C~CH3 H3c" "~" "cH3 o"

Ill

2240

A.M.

VASSERMAN et ad.

The radicals were added to the polymer by joint solution in organic solvents, or by swelling the polymer in a radical solution with subsequent elimination of solvent. The radical concentration in the polymer was 1 × 101'-1 × 101~ spin/em s. Rubbers with different molecular network densities were prepared by 6°Co ?-irradiation of the initial polymer (polydimethylsiloxane) or by irradiation with fast electrons (SKD). The concentration of crosslinks was calculated from the Flory formula [4]. Samples with added radicals were placed in thin-waUed ampoules which were evacuated. E P R spectra at different temperatures were recorded by an EPR-2-IKhF radiospectrometer.

ISled *

I

Fzo. 1. E P R spectra of radical I in atactic polypropylene at different temperatures,°K:

1--332, ~--344, 3--361. Figure 1 illustrates typical E P R spectra of radical I in polymer matrices: a symmetrical widening of outer components is due to auisotropy of H F I ; assymetric widening to anisotropy of the g-factor. From an analysis of the spectra according to equation (1) the value of ~c can easily be found. The value Vrot, which is the inverse of ~c, will be conventionally referred to as the rotation frequency of the radical. Expression (1) is suitable for determination of Vrotin the range of N 1 × 10°-5 × 10l° sec -1, i.e. when the anisotropy of H F I and the g-factor influence widening to an extent which is insu~cient to change the shape of the spectral lines. EXPERIMENTAL RESULTS AND DISCUSSION

Linear polymers. T h e t e m p e r a t u r e d e p e n d e n c e o f t h e r o t a t i o n f r e q u e n c y o f radical I in v a r i o u s p o l y m e r s is satisfactorily described b y t h e A r r h e n i u s e q u a t i o n . A c t i v a t i o n energies a n d p r e - e x p o n e n t i a l f a c t o r s are g i v e n in T a b l e 1. R e s u l t s in T a b l e 1 indicate t h a t t h e p r e - e x p o n e n t i a l f a c t o r s a r e a b n o r m a l l y high a n d c o n s i d e r a b l y exceed t h e frequencies o f r o t a t i o n a l v i b r a t i o n s o f t h e particle in t h e condensed p h a s e (1012 sec -1) [51. T h e a c t i v a t i o n energies a n d p r e e x p o n e n t i a l f a c t o r s m a r k e d l y exceed t h e c o r r e s p o n d i n g v a l u e s for t h e r o t a t i o n o f t h e radical in liquids [6]. I n addition, log v0 err shows a linear r e l a t i o n s h i p w i t h a c t i v a t i o n energy, i.e. t h e c o m p e n s a t i n g effect (CE) is o b s e r v e d (Fig. 2a). All this p o i n t s to t h e f a c t t h a t t h e a c t i v a t i o n energies a n d premexponential f a c t o r s s h o w n in T a b l e 1 are effective.

Study of molecular motion in polymers b y the paramagnetic probe method

2241

Eeff, kcal/mo/e

ZO-

f

I

I

5"0

fO

3"5-

%

3"0200

/

I

fS

ZO ^ ~ x,\~ZY£~

~Xu

250

f

~ °e~"

~c*~× 3

~ 300 "~ dYO

~'00

~50

FIe. 2. Dependence of effective activation energy on log voeff for the rotation of radical I in linear polymers (a); variation of the actual activation energy of rotation of radicals I in linear polymers as a function of temperature (b): / - - p o l y s t y r e n e , 2--atactic polypropylene, 3--isotactie polypropylene, 4--polybutadiene rubber (SKB), 5--polyisobutylene, 6 - - n a t u r a l rubber, 7 - - d i v i n y l rubber (SKI)). T~LE

1.

ACTIVATIONENERGIES AND PRE-EXPONENTIALFACTORSOF R O T A T I O N FREQUE~rCIES OF RADICALI IN Lrm~xR POLYMERS

Polymer

Temperature range,

Yoeff, sec -1

Ee~t, kcal/mole

°K Polystyrene Atactic polypropylene Isotactic polypropylene SKB Polyisobutylene NR SKD

380-450 I 4 × 10~8 325-360 2-2 × 102~ 320-395 9.0 × 101~ 305-350 1.52× 1017 300-355 315 × 10:e 270-330 2 × 101. 230-280 1.6 × 1014

dE (T) dT ' keal/

Ts, °K

/mole. deg. 18.2 18.7 10.5 11.5 10.5 8.5 5.8

3.4 × 4.6 × 2× 2.6× 2.4 × 1.8 × 1.6 ×

10 -2 10 -3 10 -3 10 -3 10 -3 10 -~

10 -B

354 238 443 (m.p) 221 202 203 155

* Certain polymer characteristics are given below: polystyrene--density 1"05 g/cms, atactic low molecular weight polypropylcne, isotactlc polypropylene from which atactlc material has been washed out, [~]ffi3.1, SKB--molocular woight 200-250,000, polyisobutylene--molecular weight ~ 118,000; NR--denslty 0.92 g/cms, [TI]=8.2; SKD--molecular weight ~ 250,000.

O n e o f t h e p o s s i b l e c a u s e s o f C E is t h e v a r i a t i o n o f a c t u a l a c t i v a t i o n e n e r g y w i t h t e m p e r a t u r e . T h i s a s s u m p t i o n w a s first s u g g e s t e d i n a n e a r l i e r s t u d y [7] a n d h a s r e c e n t l y b e e n e x p e r i m e n t a l l y c o n f i r m e d [8]. W i t h t h i s a s s u m p t i o n t h e

2242

A.M. VASS~.I~M_¢~e~ a/.

effective activation energies and pre-exponential factors are determined b y the equations:

aE(T) Ee.=E(T)--~ aT ]nv0err=lnv o

1

aE(T)

R

~T

(a) '

where v0 and E(T) are the actual pre-exponent and activation energy. When the temperature dependence of E (T) is linear, no deviation from the Arrhenius equation is observed, i.e. a2E/aT2=O. Since the actual activation energy decreases with increase of temperature, aE/aT
Study of molecular motion in polymers by the paramagnetic probe method

2243

dependes considerably on t h e c o n c e n t r a t i o n of crosslinks in t h e p o l y m e r . T h e v a r i a t i o n o f actual a c t i v a t i o n e n e r g y does n o t exceed 1-2 kcal/mole. T h e a c t u a l a c t i v a t i o n e n e r g y of radical rotation, as p o i n t e d o u t previously, is d e t e r m i n e d

E elf, kca//rnole /

/~-

J

fZE~kcal/mole 6"0

2"0

~

-

¢0

× , ~ ~

I

LSO

1

300

t

8

I

350'

I

1¢00

l~SO

~

"l/

13

IS

l?

7~ ~ °K FxG. 3

FIG.

I

19 Zf loft vo e¢¢

4

FIo. 3. Dependence of the actual activation energy of the rotation of radical I in polymers when Vrot--const on temperature T (see designation of points in Fig. 2): log Vrot= 8.6 (1); 9.0 (2) and 9.4 (3). FIG. 4. Dependence of the activation energy on log Veffin crossllnked polymers: in polydimethylsiloxane:/--radical TII, 2--radical II and 3--radical I; 4--radical I in SKD. b y t h e m o b i l i t y o f m a c r o m o l e c u l a r segments. Since during s t r u c t u r e f o r m a t i o n in p o l y m e r s a n e t w o r k is f o r m e d in which the molecular weight o f the section b e t w e e n t h e crosslinks is higher t h a n the molecular weight o f t h e segment, the p o t e n t i a l barrier o f radical r o t a t i o n varies to a negligible e x t e n t .

E, kcoymole

3.53"0 ~.S

ZOO

~3 Z f 3 300 T,°K

FIG. 5. Dependence of actual activation energy of rotation of radical I on temperature in crosslinl~ed polyflimethylsiloxanes. Network density: 1 - 3"5 × 10=x, 2--3"7 X 10zx, 3--3"5 X 10~°, 4--1.5 × 10l° links/cmS; 5--initial polymer.

A . M . V A S S E R ~ ~ ~.

2244

It is interesting to compare

Compar¢son ~ t h r ~ I t s obtained by other methods.

t h e results obtained by the paramagnetic probe method with results obtained

by other methods, NMR in particular. It is well known that NMR data on molecular motion in polymers are satisfactorily correlated with results obtained by methods of mechanical and dielectric losses [9, 10]. log,~

lb

lfl

3b

~z,, '~& [

8Z

3

%,e i

~ i/T,fOa

FIG. 6. Dependenceof log v-- 1IT: 1--isotactic polypropylene,2--atactie polypropylene, 3--natural rubber, d--divinyl rubber; a--a~cordlng to NI~R data [10, 11]; b--a~cording to data obtained by the paraxm~gneticprobe method. The most accurate correlation times in polymers were obtained from the temperature dependence of spin-lattice relaxation times T 1, determined by the spin-echo method. It is well known that the high temperature part of the curve showing the variation of T 1 corresponds to the motion of polymer chain segments. Figure 6 illustrates a comparison of temperature dependences of radical correlation frequencies with the correlation frequencies of polymer segments which were derived from the data in former papers [10, 11]. A comparison of activation energies of pre-exponents determined by two methods is shown in Table 3. These results indicate that there is a correlation between the temperature variation vrot of the radical and segments (straight lines in coordinates log fro~ - - l I T for a radical and polymer segments are approximately parallel). This is further proof that the frequency of rotation of the radical is determined by mobility of polymer segments. Since the effective activation energies determined by NMR and the paramegnetic probe method are silimilar, it may be assumed that the actual potential barriers of segment motion and radical rotation also differ to a negligible extent. This means that the paramagnetic probe method enables the potential barrier of macromolecular segment motion to be evaluated.

Study of molecular motion in polymers by the paramagnetic probe method However,

the

correlation

from correlation

frequencies

due

radical

to different

frequencies of segmental

and

segment

of radical motion;

motion

2245

somewhat

differ

the differences are apparently

dimensions.

T A B L E 2. A C T I V A T I O I ~ E N E R G I E S A N D P R E - E X P O N E N T I A : L FACTORS OF ROTATIOI~ F R E Q U E N C I E S OF A R A D I C A L I N C R O S S L I N K E D P O L Y M E R S

Concentration Radical

Polymer

o f erosslinks,

Voeff,

-~eff,

see -1

keal/mole

links/cma I

II

LII

I

Thus,

Polydimethylsiloxane

,,

SKD

the par,magnetic

tion in polymers;

probe

method

it can also be employed

bility of macromolecular

chains

TABLE 3, C O ~ I S O N

3.2 x 1011 5.9 x 101' 4.5 x 101' 8"6 X 101' 2 . 6 × 101' 6.1 × 101' 3.8 × 101' 2.5 x 10 TM 1"75 X 10 TM 7"6 X 1011 7"0 X 101' 9"3 × 1014 2"1 X 101' 7"7 X 1011 1"6 X 101' 4.9 X 10 TM 2.04 x 10 TM 3-3 x 1014 1-7 X 1014

2.1 14.3 6.6 3'2 2"8 4.6 9.6 4"9 3"3 2"9 13"8 6"8 4"3 3"4 5"8 9.6 8.3 6.2 6.0

can be used to study to investigate

in biopolymers

[12].

OF m~SVLTS OBT~r~rSD BY N M R ~ n D T ~ .

Atactic polypropylene Isotactie polypropylene Natural rubber Divinyl rubber

Ee~t, k c a l / m o l e probe method NMR 18.7 10-5 8.5 5.8

17-0 8.2 10.5 6.5

Voe~, sec -1 probe method NMR 2.2 x 9x 2x 1.6 x

10 '1 10 TM 1014 1014

0 3-3 x 1 0 - ' 1 x 10-' 4 × 10 -s 2 × 10 -s 0.6 × 1 0 - ' 1.4 x 1 0 - ' 4 X 10 -s 1"5 × 1 0 - a 0 3 X 10-'

9 X 10 -s 3 × 10-' 0 1"2 X 10 -s 2.4 × 1 0 - 2 1.9 × 1 0 - ' 1.3 × 1 0 -2 1"2 X 1 0 - z

molecular

the structure

PARA~AGNETIC PROBE METHOD

Polymer

~T

'

/mole. deg

Initial polymer 1.5 × 101' 3.5 x 10 '0 3 . 5 x 10 '1 3.7 x 10 '1 Initial polymer 1.5 x I019 3.5 x 10 '° 3"5 x 10 '1 3"7 x 10 '1 1"5 × 101' 3"5 x 10 'o 3 . 5 x 10 '1 3"7 x 10 '1 3 x 10 TM 1 x 1017 Initial polymer 3.5 × 101' 1.42 x 10 'o

Same

b E (T) kcal/

2.2 x 10 TM 1 X 10 TM 1 x 101~ 1 X 1018

and

momo-

2246

A . M . VASSER~__~Neta/.

Finally, the a u t h o r s consider it their pleasant d u t y to t h a n k E. G. R o z a n t s e v for providing the radicals, T. S. Fedoseyev, for providing the crosslinked polymers a n d discussing the results, a n d T. N. K h a z a n o v i e h for discussion of results a n d valuable advice. CONCLUSIONS

(1) The p a r a m a g n e t i c p r o b e m e t h o d was used to s t u d y the mobility o f macromolecular segments in polymers. I t is p o i n t e d out t h a t the a c t i v a t i o n energies observed for the r o t a t i o n o f a stable radical are effective, whereas t h e actual a c t i v a t i o n energies v a r y with t e m p e r a t u r e . (2) The f r e q u e n c y of r o t a t i o n of the radical a n d t h e actual a c t i v a t i o n e n e r g y are p a r a m e t e r s d e t e r m i n e d b y the mobility of m a c r o m o l e e u l a r segments. (3) Variation in the molecular n e t w o r k density of polymers has little effect on the actual a c t i v a t i o n energy, b u t considerably alters the effective a c t i v a t i o n e n e r g y a n d OE/OT. (4) A correlation is established between the p a r a m e t e r s characterizing molecular segmental mobility using the p a r a m a g n e t i c probe and N M R methods.

Translated by E. SEMERE REFERENCES 1. G. M. Z I ~ D O ~ O V ,

Yu. D. TSYETKOV and Ya. S. LEBEDEV, Z h . strukt, khimii

2" 696, 1961 2. J. H. FREED and G. K. FRAENKEL, J. Chem. Phys. 39: 326, 1963 3. A. L. BUCHACHENKO and A. M. VASSERMAN, Zh. strukt, khimii 8: 27, 196"/ 4. P. J. FLORY, Principles of Polymer Chemistry, p. 507, New York, 1953 5. ¥. S. STARUNOV, Optika i spektroskopiya 18: 300, 1965 6. A. L. RUCHACHENKO and L. S. TROITSKAYA, Izv. AN SSSR, seriya khimich., 602, 1966 7. Ya. S. LEBEDEV, Yu. D. TSVETKOV and V. V. VOYEVODSKII, Kinetika i kataliz 1: 496, 1960 8. A. I. MIKItAILOV and Ya. S. LEBEDEV, Zh. fiz. khimii 45: 1005, 1968 9. I. Ya. SLONIM and A. N. LYUBIMOV, Yadornyi magnitnyi rozonans v polimerakh (Nuclear Magnetic Resonance in Polymers). "Khimiya", 1966 10. P. SLICHTER, J. Polymer Sci. 14" 33, 1966 11. I. KAWAI, Y. YOSHII~_[ and A. HIRAI, Phys. Soc. Japan 16: 2356, 1966 12. R.I. SUKItORUKOV, A. M. YASSER~IAI~I, L. A. KOZLOVA and A. L. BUCHACHEI~IKO, Dokl. AN SSSR 177: 454, 1967