SPIN DYNAMICS AND SOLITON MOTION IN TRANS-(CH)x

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SPIN DYNAMICS AND SOLITON MOTION IN TRANS-(CH)x

M. Nechtschein, F. Devreux, F. Genoud, M. Guglielmi, K. Holczer

To cite this version:

M. Nechtschein, F. Devreux, F. Genoud, M. Guglielmi, K. Holczer. SPIN DYNAMICS AND SOLI- TON MOTION IN TRANS-(CH)x. Journal de Physique Colloques, 1983, 44 (C3), pp.C3-209-C3-216.

�10.1051/jphyscol:1983342�. �jpa-00222694�

JOURNAL DE PHYSIQUE

Colloque C3, supplément au n°6, Tome 44, juin 1983 page C3-209

SPIN DYNAMICS A N D SOLITON MOTION IN TRANS ~ ( C H )K

M. Nechtschein*, F. Devreux , F. Genoud*, M. Guglielmi and K. Holczer

Centre d'Etudes Nucleaires de Grenoble, Departement de Recherche Fondamentale, Section de Resonance Magnetique, 85X, 38041 Grenoble Cedex, France

Résumé - Des résultats de résonance magnétique, comprenant des mesures de relaxation nucléaire (Ti), de relaxation électronique, de largeur de raie RPE et de polarisation dynamique nucléaire, sont passés en revue et analysés. Ils sont expliqués en termes de spins diffusifs unidimensionnels. Les propriétés de ces spins sont en complet accord avec le modèle des solitons, à condition de tenir compte d'effets de piégeage. A une température donnée la population des spins dans l'état piégé dépend de deux paramètres : la concentration de sites avec piège et l'énergie de piégeage. Ces paramètres sont évalués à partir de la dépendance thermique de la largeur de raie RPE et du temps de relaxation nucléaire. On donne également une détermination expérimentale de la variation thermique du coefficient de diffusion des solitons, ainsi que de leur extension.

Abstract - Magnetic resonance data in undoped trans-(CH)x, including nuclear and electron relaxation times (Ti, and Tie), ESR linewidth, and Dynamic Nuclear Polarization are reviewed and analyzed. The results are comprehensively ex- plained in terms of highly one dimensional diffusive spins, the properties of which are consistent with the soliton picture, provided that trapping effects are taken into account. At a given temperature, the population of the spins in the trapped state depends on two parameters : the trap-site concentration and the trapping energy. These parameters are evaluated from the temperature dependence of both the ESR line-width and Ti. We also give experimental determination of the diffusion coefficient as a function of temperature and of the soliton extension.

The aim of this paper is to review magnetic resonance results obtained in trans- (CH)X which give evidence for highly-one-dimensional diffusive spins. While the presence of unpaired spins has been known for many years to be a general feature in conjugated polymers /!/, fast spin motion seems to be a peculiarity of tra»s-{CH)x, likely connected to the possibility of structural degeneracy.

First, it has been proposed that the narrowing of the ESR line observed upon isome- rization from the cis- to the trans-form was a signature of a cross-over from fixed to mobile spins /2-6/. A striking evidence for the specificity of the spin charac- teristics in trans-(CH)x has been provided by the completely different effects obtained by Dynamic Nuclear Polarization (DNP) experiments performed on cis-rich-, and on trans-(CH)x, respectively 111. The DNP experiment consists of observing the NMR (at the nuclear Larmor frequency, q\j) while pumping with microwave power near the electronic Larmor frequency (oje). Two limiting results may occur according to whether the electron-nuclear coupling is static or dynamic. In the static case, the electronic spin is fixed (at least its hopping frequency is less than w|\j) and for- bidden transitions at a)e±u)«, can be induced. They give rise to a NMR enhancement which is negative, or positive, for pumping at OJ +a>N, o r W e ~uN ' r e sPe ctively. This

is the so-called "solid-state effect" (SEE) / 8 / . On the other hand, if the electronic spin is mobile such that energy exists at -fiwe in the motion spectrum one gets an en- hancement of the NMR signal by pumping justatue. This is the Overhauser effect (OE).

* ER CNRS 2 1 6

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983342

C3-210 JOURNAL DE PHYSIQUE

The DNP r e s u l t s a r e shown i n F i g . 1. The OE i s observed i n a t r a n ~ - ( C H ) ~ sample w h i l e a c i s - r i c h (CH), sample g i v e s r i s e t o t h e SSE. This demonstrates c o n c l u s i v e l y t h a t a t room temperature t h e spins a r e mobile i n t r a n ~ - ( C H ) ~

-

a t l e a s t a t t h e r a t e o f we % 10'' r a d s e c - l

-

and f i x e d i n ~ i s - ( c H ) ~ . We p o i n t o u t t h a t t h e e l e c t r o n s p i n - s p i n exchange i n t e r a c t i o n s , which do n o t g i v e r i s e t o any d e t e c t a b l e d e v i a t i o n from t h e Curie law, a r e much t o o small t o be r e s p o n s i b l e f o r t h e OE.

r i

Such completely d i f f e r e n t behaviours o f t h e spins upon a change o f t h e geometry o f t h e (CH), backbone can be simply explained i f we a s s o c i a t e t h e unpaired spin t o a bond a l t e r n a t i o n d e f e c t , i.e. a w a l l between two domains, A and B, which d i f f e r from each o t h e r by t h e phase o f t h e s i n g l e / d o u b l e bond a l t e r n a t i o n . I n t h e case of trans-(CH),, t h e two domains, A and B, a r e degenerated. One, thus, imagine t h a t t h e s p i n d e f e c t , which can be described i n terms o f t h e s o l i t o n p i c t u r e /9/, i s a b l e t o m i g r a t e q u i t e f r e e l y along t h e chain. On t h e o t h e r hand, f o r cis-(CH),, domains A and B have no more t h e same energy, namely t h e energy o f t h e c i s - t r a n s o i d form

(A)

1 ie s below the energy o f t h e t r a n s - c i s o i d form (B). Consequently, t h e s p i n d e f e c t w i l l tend t o change i t s place i n such a way t h a t domain (A) increases t o t h e d e t r i m e n t o f domain 6, u n t i l i t reaches t h e c h a i n end, where i t w i l l be trapped.

I P-Po

Fig. 2

-

Bond a l t e r n a t i o n d e f e c t i n f a ) t r a n s - , and (b) cis-(CH),. I n t r a n ~ - ( C H ) ~ domains A and B being degenerated, d e f e c t s i n ('a) I and 2 correspond t o t h e same energy. I n cis-(CHIx EA

<

EB, so d e f e c t w i l l t e n d t o m i g r a t e towards t h e end o f the chain : ( b ) 2.

F i g . 1

-

Enhancement o f proton NMR amp1 i t u d e

(P) a t 300 K as a func- t i o n o f t h e microwave pumping frequency v near w /ZTI = 8240 M ~ Z

f o r (me c i s - r i c h (AH % 7.8 G) and ( r ) t r a l ! (AH % 0.8 G) undoped (El?),. Po i s t h e NMR signal ampl i t u d e w i t h o u t pumping.

6 ^{P - P o}

i! '0 40-

7 1 \- ³⁰

^-

-1 0 20

-

- 5

^/a

,='

,is 1 0 -

' d '

dm i 8 ' I

* =

^a\

-ad .-.-e- 8- ,

\

e ^a, a\*

v p [MHz1

-

0 ^{0 -}

8220

;

8240

\,

8260 i

\ Y ~ ? Y N

.\ ^'

^..a' .,m'

--5 ",-.I.-

Q u a n t i t a t i v e s t u d i e s of t h e s p i n m o b i l i t y and o f i t s d i m e n s i o n a l i t y i n trans-(CH), have been performed from t h e frequency dependence of t h e p r o t o n n u c l e a r r e l a x a t i o n t i m e (TI

1.

The e l ectron-spin-motion-induced n u c l e a r r e 1 a x a t i o n r a t e i s given by

/ l o /

:

where a and d a r e t h e i s o t r o p i c and d i p o l a r e l e c t r o n i c spin-proton h y p e r f i n e cou- p l ings, r e s p e c t i v e l y , and

x

= Xmol ar/N(gugI2. The s p e c t r a l d e n s i t y f u n c t i o n f o r the magnetic f i e l d f l u c t u a t i o n s a t t h e nucleus, f ( w ) , depends s e n s i t i v e l y on t h e dimen-

s i o n a l i t y of t h e s p i n motion ( f o r w < d i f f u s i o n r a t e ) . I n p a r t i c u l a r f o r a one-dimen- sional (ID) d i f f u s i o n , one has

f ( w ) = (2D u ) - ' / ~

//

( 2 )

where D i s t h e i n t r a c h a i n d i f f u s i o n r a t e .

//

I n F i g . 3 we see data of T;' versus v i 1 / 2 f o r t ~ a n s - ( C H ) ~ (VN = wN/2r). The room

F i g . 3

-

Proton r e l a x a - t i o n r a t e i n trans-(CH),, Ti1, p l o t t e as a func- t i o n o f ^F-I

51

f o r T = 295, 77, 30, and 4.2 K

temperature data gives c l e a r evidence f o r I D d i f f u s i v e s p i n motion. Using Eq. ( 1 ) and ( 2 ) , w i t h values f o r a and d corresponding t o an unpaired s p i n i n a 2pz o r b i t a l as explained p r e v i o u s l y /7/ and the, s p i n s u s c e p t i b i l i t y corresponding t o a s p i n c o n c e n t r a t i o n p e r u n i t CH o f n = as measured by t h e Schumaker-Slichter method, t h e T1 data a t room temperature y m 5 D r (3-6) x 1013 rad/s, t h a t i s a d i f f u s i o n c o e f f i c i e n t = b 2 D

// //, b// being t h e Ynter-CH u n i t d i s t a n c e l a ^% 5 x cm2/s.

//

The transverse d i f f u s i o n r a t e and, hence, t h e a n i s o t r o p y o f t h e s p i n motion can be estimated from t h e c u t - o f f frequency wc, i.e. t h e frequency a t which t h e divergence o f f (w) as w ⁺ 0 i s truncated. The v a l u e o f wc i s o f t h e order o f 10' rad/s as determined from t h e r e l a x a t i o n t i m e i n t h e r o t a t i n g frame /11/, o r from d i r e c t determination o f t h e c u t - o f f frequency by measuring TI i n

/12/. One deduces a considerable a n i s o t r o p y f o r t h e s p i n motion which i s a l s o c o n s i s t e n t w i t h t h e assignment o f t h e spins

because they a r e thus supposed t o be c o n f i n e d i n s i d e given chains.

The e l e c t r o n s p i n motion being a l s o t h e main source o f t h e e l e c t r o n s p i n - l a t t i c e r e l a x a t i o n , another and independent e v a l u a t i o n o f t h e d i f f u s i o n r a t e can be obtained from the e l e c t r o n r e l a x a t i o n time

Tie.

The e l e c t r o n r e l a x a t i o n r a t e induced by the modulation of t h e e l e c t r o n spin-spin d i p o l a r i n t e r a c t i o n s i s given by :

JOURNAL DE PHYSIQUE

where

R2

i s a geometrical f a c t o r (see Appendix B i n ref. /13/) which can be computed from t h e s t r u c t u r e /14/. Considering t h e d i p o l a r i n t e r a c t i o n s t h a t a given s i t e undergoes from each of t h e n e a r e s t neighbouring (n.n) carbones l o c a t e d on t h e 8 n.n.

chains, one o b t a i n s /15/ R/ye = 2440 G. I n Eq. ( 3 ) f ' (w ) i s t h e c o r r e l a t i o n func- t i o n f o r t h e r e l a t i v e p o s i t i o n s between two m o b i l e spin$. F o r two d i f f u s i v e s p i n s w i t h i n d i v i d u a l d i f f u s i o n r a t e D //, one has :

Using a s a t u r a t i o n technique we have measured on d i f f e r e n t samples : T I e = 6-10 ps, which i s i n agreement w i t h o t h e r r e p o r t e d data /16/. It i s noteworthy t h a t t h e same values have been measured i n b o t h (CH), and (CD)&, which i s an evidence t h a t t h e modulation o f t h e hyperfine c o u p l i n g i s a n e g l i g ~ b l e phocess f o r t h e e l e c t r o n r e l a x a t i o n . From t h e measured Tie, which should be 2 TIe, and using Eqs. (3) and (4) one o b t a i n s :

which i s i n good agreement w i t h t h e NMR determination.

F o l l o w i n g a s i m i l a r approach as f o r t h e n u c l e a r and t h e e l e c t r o n s p i n - l a t t i c e r e l a - x a t i o n , t h e ESR l i n e - w i d t h can be expressed as

For t h e d i f f e r e n t parameters e n t e r i n g i n t o Eq. ( 5 ) one uses t h e values already given, i n p a r t i c u l a r those f o r D determined from T1 and Tle, one expects AM

-

0.2 Gauss. Although i n a f e 4 special cases, ESR l i n e s as narrow as 0.28 and 0.44 Gauss have been r e p o r t e d /13,16/, g e n e r a l l y t h e measured l i n e - w i d t h s a r e s i g n i f i c a n t l y l a r g e r . Furthermore they a r e spread over q u i t e a wide range, say up t o 1.6 Gauss.

These f a c t s suggest t h a t i n usual samples t h e d i f f u s i v e s p i n c o n t r i b u t i o n t o t h e 1 ine-width, as expressed by Eq. ( 5 ) , i s s t r o n g l y masked by e x t r i n s i c c o n t r i b u t i o n s due t o f i x e d spins connected t o u n c o n t r o l l e d defects, o r i m p u r i t i e s . I n p a r t i c u l a r i t has been shown, q u a l i t a t i v e l y /13/, and i n r e c e n t s t u d i e s /17/ q u a n t i t a t i v e l y , t h a t oxygen contamination has a d r a s t i c e f f e c t on t h e l i n e - w i d t h . Due t o t h e absence o f motional narrowing, even a small amount o f f i x e d s p i n s can dominate t h e l i n e - width, about p r o p o r t i o n a l l y t o t h e i r concentration. On t h e o t h e r hand, t h e spin- l a t t i c e r e l a x a t i o n , T1 as w e l l as TIe, i s m a i n l y governed by t h e d i f f u s i v e spins, which a r e much more e f f i c i e n t t o p r i v i d e t h e necessary spectrum components a t t h e Larmor frequencies. Thus, by t a k i n g i n t o account t h e presence o f b o t h mobile and f i x e d spins, one resolves t h e apparent c o n t r a d i c t i o n between p r o p e r t i e s which a r e concerned w i t h low frequency f l u c t u a t i o n s

-

ESR 1 ine-width, ENDOR, e l e c t r o n spin- echo

-

on t h e one side, and those which r e f l e c t more dynamical processes

-

spin- l a t t i c e r e l a x a t i o n , Overhauser e f f e c t

-

on t h e o t h e r side.

I n a f u r t h e r step /18/ we have r e f i n e d t h i s model i n o r d e r t o account f o r t h e temperature dependence o f t h e l i n e - w i d t h . I n s t e a d o f two d i f f e r e n t s p i n species, m o b i l e and f i x e d , a more a p p r o p r i a t e d e s c r i p t i o n c o n s i s t s o f spins being e i t h e r i n mobile ( d i f f u s i v e ) , o r i n f i x e d ( l o c a l i z e d ) s t a t e s . The l a t t e r s t a t e s a r e associated w i t h s i t e s on which t r a p s have been created by defects, o r i m p u r i t i e s . Assuming

t h a t f o r a given chain t h e r e i s a given t r a p p i n g energy E, t h e thermal p o p u l a t i o n of t h e spins i n l o c a l i z e d s t a t e s , denoted as C, i s expressed as f o l l o w s :

where p i s t h e t r a p - s i t e c o n c e n t r a t i o n and g(E) t h e d i s t r i b u t i o n f u n c t i o n o f t h e t r a p p i n g energy.

The r e s u l t i n g ESR l i n e - w i d t h can be expressed as an a d d i t i v e f u n c t i o n o f a l o c a l i z e d s p i n c o n t r i b u t i o n AHL and a d i f f u s i o n s p i n c o n t r i b u t i o n AHD :

AH = C AHL + ( 1

-

C)AHD (7)

I n Eq. (7) AHL and AHD a r e n o t temperature independent. I n p a r t i c u l a r t h e d i f f u s i v e c o n t r i b u t i o n depends on temperature through D (see Eq. (5) ). Furthermore, t h e spin-spin d i p o l a r i n t e r a c t i o n s , which should ffe taken i n t o account, depend on whether t h e i n t e r a c t i o n s r e f e r s t o f i x e d t o fixed, f i x e d t o mobile, o r m o b i l e t o m o b i l e spins. Consequently, these c o n t r i b u t i o n s t o t h e l i n e - w i d t h a r e temperature dependend through t h e r e 1 a t i v e f ixed/mobil e population. The d i f f e r e n t mechanisms i n v o l v e d i n AH have been discussed i n d e t a i l s i n Ref. /18/. One can f i n a l l y express AH(T) as a f u n c t i o n o f C(T) and D(T). These two q u a n t i t i e s a r e a l s o i n v o l v e d i n the n u c l e a r r e l a x a t i o n r a t e i f ones takes i n t o account t h a t o n l y t h e spins i n t h e d i f f u - s i v e state, i .e. t h e f r a c t i o n 1-C(T) o f t h e t o t a l s p i n s u s c e p t i b i l i t y , c o n t r i b u t e t o t h e r e l a x a t i o n . Thus, from experimental data o f b o t h AH(T) (Fig. 4) and t h e frequency dependence o f TI a t d i f f e r e n t temperatures (Fig. 31, C(T) and D(T) can be extracted.

I n Fig. 4 we g i v e AH(T) f o r ( a ) vacuum-seal ed and ( b ) a i r contaminated samples. I t i s noteworthy t h a t t h e zero-temperature l i m i t i s about t h e same f o r t h e two samples.

T h i s i s c o n s i s t e n t w i t h t h e ideas t h a t a t low temperature a l l spins a r e trapped (C(0) = 1 ) and t h e l i n e - w i d t h reduces t o t h a t o f f i x e d spins : AH(O) = aHL(0). The t h e o r e t i c a l curves have been c a l c u l a t e d assuming t h a t t h e t r a p p i n g energy i s equal- l y d i s t r i b u t e d from Eo 1 0.06 eV t o zero. The two curves ( a ) , and ( b ) , correspond t o t r a p - s i t e c o n c e n t r a t i o n o f 5 %, and 25 %, r e s p e c t i v e l y .

Fig. 4

-

ESR 1 in e w i d t h AH vs temperature, as compared t o t h e o r e t i c a l curves c a l c u l a t e d w i t h a d i s t r i b u t i o n f u n c t i o n f o r t h e t r a p p i n g energy as shown i n t h e i n s e r t . ( a ) Vacuum sealed sample and t r a p - s i t e concentra- t i o n p = 5 %, (b) a i r contaminated sampl e and p = 25 %.

C3-214 JOURNAL DE PHYSIQUE

The good f i t obtained i n Fig. 4 supports t h e f o l l o w i n g p i c t u r e f o r s o l i t o n t r a p p i n g upon oxygen e f f e c t . The f i r s t e f f e c t o f oxygen i s t o compensate spins, as we show i n another work presented a t t h i s conference. T h i s e f f e c t may be reasonably under- stood i n terms o f a c h a r g e - t r a n s f e r between adsorbed oxygen and (CH)x a t t h e p l a c e o f a s o l i t o n , r e s u l t i n g i n a s p i n - l e s s charged s o l i t o n . T h i s charged s o l i t o n d i s t u r b s t h e neighbouring chains, c r e a t i n g t r a p s f o r those s o l i t o n s which remain n e u t r a l . The t r a p p i n g energy decreases from EO s 0.06 eV f o r t h e n.n. chains, t o about zero f o r chains f a r away.

The temperature dependence o f D i s g i v e n i n F i g . 5 i n a double l o g a r i t h m t c p l o t . We n o t i c e t h a t D i s an i n c r e a s i n g (rad/sec) f u n c t i o n o f ternpgrature which seems t o

s a t u r a t e a hiclh temoerature. From soin-

L e t us now consider t h e n u c l e a r r e l a x a t i o n data i n more d e t a i l s . They a r e given versus v - l l 2 a t 295, 77, 30 and 4.2 K as shown i n Fig. 3. The one-dimensional d i f - f u s i v e behaviour, as expressed by Eqs. ( 1 ) and ( 2 ) , i s observed a t h i g h temperature.

For T = 30 and 4.2 K, t h e data can s t i l l be f i t t e d w i t h s t r a i g h t l i n e s , b u t non zero i n t e r c e p t w i t h t h e frequency a x i s i s d e f i n i t e l y present. The i n t e r c e p t d e f i n e s a h i g h frequency c u t - o f f wmax, because f o r w

>

t h e motion spectrum vanishes.

B a s i c a l l y ,,,u,, i s t h e r a t e a t which t h e e l e c t r o n i c magnetic f i e l d seen by a given proton f l u c t u a t e s when a mobile s p i n i s near-by. I f t h e s p i n wave f u n c t i o n i s peaked on o n l y one CH u n i t , t h i s r a t e i s n o t h i n g b u t t h e d i f f u s i o n r a t e i t s e l f , and one has

wax

% D. On t h e o t h e r hand i f t h e s p i n i s extended over R

>>

1 l a t t i c e constants t h e r e w i l l be no change o f t h e induced magnetic f i e l d u n t i l t h e s p i n has moved by a distance o f t h e order o f i t s extension. Due t o t h e random walk character o f t h e motion t h i s r e q u i r e s a t i m e R2D-I, which leads t o % D / R ~ . Exact deriva- t i o n o f t h i s problem has been given by one o f us (F.D.) /20/. I n t h e random-wal k model f o r a p a r t i c u l e d e l o c a l i z e d over 2e s i t e s t h e r e s u l t i s t h a t t h e l o c a l s p i n c o r r e l a t i o n f u n c t i o n i s expressed as :

1oq3

1 0 ' ~

to"

l 0 ' O

which should increase w i t h decreasing Fig. 5

-

Temperature dependence of t h e temperature /19/, f o r t h e b a s i c reason s p i n d i f f u s i o n r a t e i n trans-(CHIx, as t h a t t h e mean f r e e path 1 i s expected determined from combined a n a l y s i s o f t o increase s t e e p l y w i t h decreasing tem-

Tl(w,T) and

AH(T).

perature. Experimental r e s u l t s a r e i n

c o n t r a d i c t i o n w i t h such an expectation. I n c o n t r a s t , t h e slowing down o f t h e motion w i t h decreasing temperature suggests a phonon a s s i s t e d process.

-

-

-

t

, 8 , , , . ,

f

f

+ f

-+

3 10 30 " ' ' 3 i 0 case (b) leads t o a d i f f u s i o n c o e f f i c i e n t

-

;

: -

-

I

-

dynamics r e s u i t s it' i s n o t p o s s i b l e ' t o decide whether t h e d i f f u s i o n a l behaviour r e f l e c t s ( a ) a random-walk motion, i.e.

random a t t h e scale o f a CH u n i t , o r ( b ) a c o l l i s i o n 1 im i t e d b a l i s t i c motion. I n case ( a ) D i s n o t h i n g b u t t h e average hopping f r l q u e n c y ; i n case ( b ) one has

a

⁼ <vX>, where v, and

X

a r e the sol i- td/n v e l o c i t y , and mean f r e e path, respec- t i v e l y . Case ( b ) reduces t o ( a ) i f t h e mean f r e e path tends t o t h e l a t t i c e constant X ⁺

b l .

For case ( a ) , since t h e s o l i t o n motion corresponds t o displace- ments o f l a t t i c e d i s t o r s i o n s , t h e r e e x i s t s an a b s o l u t e l i m i t f o r D

,

namely t h e harmonic o s c i l 1 a t o r frequek/cy

I

^f

- - (K)

uo = ( z K / M ) ~ / ~ , where K i s t h e constant f o r c e , and M t h e CH u n i t mass. The value K = 7 eV/A (Ref. /14/) y i e l d s

wo = 1 x

lo1'

rad/sec, which i s compatible w i t h t h e obtained values f o r D even a t

// '

room temperature. On t h e o t h e r hand,

w i t h y 2 0.33 f o r t h e case of a box-shape sol i t o n , and y 2 0.36 f o r an a1 t e r n a t e d sol i t o n . From Eq. (8) one o b t a i n s % 0 . 9 6 ~ D /L2. D i r e c t use o f t h i s expression can be made w i t h t h e TT1 data a t 4?lak because a! t h i s temperature t h e n u c l e a r r e l a x a t i o n i s unambiguously o n l y induced by t h e UN c o n t r i b u t i o n o f t h e spectrum.

From t h e i n t e r c e p t % a x 1 2 ~ = 120 MHz and t h e value D (4.2) 2 6 x 101° rad/sec d e t e r - mined as above e x p l a ~ n e d one o b t a i n s a sol i t o n f u l l - { i d t h 2L a 17, which compares v e r y w e l l w i t h t h e t h e o r e t i c a l p r e d i c t i o n /9/ : 2e = 14. T h i s i s a l s o c o n s i s t e n t w i t h another determination of t h e s p i n d e l o c a l i z a t i o n t h a t we have made by analyzing t h e zero temperature l i m i t of t h e second moment o f t h e ESR l i n e f o r protonated and deutered samples. T h i s method gives

2%

2 10. N o t i c e t h a t t h e determination from T1 data r e f e r s t o s o l i t o n s i n t h e d i f f u s i v e s t a t e , w h i l e t h e one based upon ESR second moments i s concerned w i t h s o l i t o n s i n t h e trapped s t a t e .

I n conclusion, we p o i n t o u t t h e appropriateness o f magnetic resonance f o r studying t h e behaviour o f n e u t r a l s o l i t i o n s , t a k i n g advantage o f t h e i r spins. By ESR, they a r e d i r e c t l y observed. The ESR l i n e - w i d t h predominantly r e f l e c t s t h e s o l i t o n s i n t h e trapped s t a t e , i n which they a r e s t a y i n g l o n g e r and l o n g e r as t h e temperature i s decreased. We suggest t h a t a t low temperature t h e average t i m e spent by s o l i t o n s i n t h e trapped s t a t e i s t i g h t l y r e l a t e d t o t h e phase memory t i m e TM measured by s p i n echo experiments /21/. As concerns t h e NMR p r o p e r t i e s , n u c l e a r r e l a x a t i o n and dyna- mic p o l a r i z a t i o n , they can be considered as i n d i r e c t observations o f t h e s o l i t o n spins. I n t h i s respect, i t i s noteworthy t h a t f o r r e l a t i n g spin-dynamics t o NMR data we have made t h e assumption o f a unique n u c l e a r spin temperature, which i s v a l i d f o r protons and provided t h a t a t l e a s t a few percent of t h e chains have spins.

However, t h i s c o n d i t i o n might n o t be f u l f i l l e d i n case o f i s o t o p i c d i l u t i o n o f protons, o r f o r n u c l e i w i t h small magnetic moments,namely t h e 1 3 C .

References

1. NECHTSCHEIN M., these d ' E t a t

,

Grenoble (1967).

2. SHIRAKAWA H., IT0 I., and JKEDA S., D i e Macromol

.

Chim. 179 (1978) 1565.

3. WEINBERGER B.R., CHIANG C.K., GAU S.C., HEEGER A.J., a n d c D I A R M I D A.G., Appl. Phys. L e t t . 35 (1979) 83.

4. GOLDBERG I.B., CROW H.R., NEWMAN P.R., HEEGER A.J., and MacDIARMID A.G., J. Chem. Phys. 70 (1979) 1132.

5. WEINBERGER B.R.,KAUFER I . , PRON A., HEEGER A.J., and MacDIARMID A.G., Phys.

Rev. B 20 (1979) 223.

6. WEINBERER B. R., EHRENFREUND E., PRON A., HEEGER A.J., and MacDIARMID A.G., J. Chem. Phys. 72 (1980) 4749.

7 . NECHTSCHEIN M. ,TEVREUX F., GREENE R.L., CLARKE T.C., and STREET G.B., Phys.

Rev. L e t t . 44 (1980) 356.

8. ABRAGAM A. , T h e P r i n c i p l e s o f Nuclear Magnetism (Oxford Univ. Press, Oxford, England, 1961) Chap. 9.

9. SU W.P., SCHRIEFFER J.R., and HEEGER A.J., Phys. Rev. L e t t . 42 (1979) 1698 ; RICE M.J., Phys. L e t t . 71A (1979) 152 ; SU W.P., SCHRIEFFER X R . , and

HEEGER A.J., Phys. ~ e v . m 2 (1980) 2099.

10. DEVREUX F., BOUCHER J.P., and NECHTSCHEIN M., J. Phys. ( p a r i s ) 35 (1974) 271.

11. DEVREUX F., HOLCZER K., NECHTSCHEIN M., CLARKE T.C., and

GREENET-L.,

Lecture Notes i n Physics, Springer Verlag 23 (1981).

12. HOVER K., and CLARK G., I n t . Conf . o n Low-Dimensional Conductors, Boulder, Colorado ( 1 981 ).

13. HOLCZER K., BOUCHER J.P., DEVREUX F., and NECHTSCHEIN M., Phys. Rev. B

23

(1981) 1051.

14. FINCHER C.R., CHEN C.-E., HEEGER A.J., and MacDIARMID A.G., Phys. Rev,. L e t t . 48 (1982) 100.

15. - VEGA J. e t a l . , t o be published.

16. FRANCOIS B., BERNARD M., and ANDRE J.J., J. Chem. Phys.

75

(1981) 4142.

17. GENOUD F., NECHTSCHEIN M., HOLCZER K., DEVREUX F., and GUGLIELMI M., J. o f Mol

.

and L i q u i d C r y s t a l s , t o appear.

C3-216 JOURNAL DE PHYSIQUE

18. NECHTSCHEIN M., DEVREUX F., GENOUD F., GUGLIELMI M., and HOLCZER K., Phys.

Rev. B 27 (1983) 1 J a n v i e r .

19. MAKI K.,Phys. Rev. B 26 (1982) 2181.

20. DEVREUX F., Phys. Rev.- 2 5 (1982) 6609.

21. SHIREN N.S., TOMKIEWICZ

Y z

KAZYUKA T.G., TARANKO A.R., THOMANN H., DALTON L., and CLARKE T.C., Sol. S t . Corn. 44

-

(1982) 1157.