FREQUENCY AND TEMPERATURE DEPENDENCE OF IH NMR OF TRANS-(CH)x

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FREQUENCY AND TEMPERATURE DEPENDENCE OF IH NMR OF TRANS-(CH)x

P. Sokol, J. Gaines, S. Cho, D. Tanner, H. Gibson, A. Epstein

To cite this version:

P. Sokol, J. Gaines, S. Cho, D. Tanner, H. Gibson, et al.. FREQUENCY AND TEMPERATURE

DEPENDENCE OF IH NMR OF TRANS-(CH)x. Journal de Physique Colloques, 1983, 44 (C3),

pp.C3-349-C3-352. �10.1051/jphyscol:1983370�. �jpa-00223031�

FREQUENCY AND TEMPERATURE DEPENDENCE OF JH NMR OF T R A N S - < C H )Y ( a )

P.E. Sokol*(1), J.R. Gaines(1), S.I. C h o ^ - , D.B. Tanner"""(X), H.W. Gibson(2)

and A.J. Epstein (2)

(1) The Ohio State University, Columbus, Ohio 43210, U.S.A.

(2) Xerox Webster Research Center, Webster, New York 14580, U.S.A.

Résume - Nous avons étudié" la dépendance en température (0,3K<T <4^2K) et en fréquence (23MHz <"f <35MHz) du temps de relaxation spin-lattice T des protons dans le composé trans-(CH) . A 432K, nos résultats concordent avec ceux obtenus par Nechtschein et al. Quand l'échantillon est refroidi, T s'allonge, et T =Otf -û, ou Of et â sont des fonctions de la température. T peut aussi être exprime par T " A exp(-4/T), où A =« Yll est l'énergie d'activation (et A et ¥ sont des constantes). Nous observons un facteur g égal à 3,3 pour l'énergie d'activation, ce qui suggère que nous sommes dans la limite de basses températures de la diffusion I-D de spins nucléaires tel que Clark et al. l'ont indiqué.

Abstract - We have carried out a study of the temperature (0.3K<T ^4.2K) and frequency (23MHz <f <35MHz) dependence of the proton spin lattice relaxation time, T , of trans-(CH) . The data at 4.2K are in agreement with earlier measurements of Nechtschein et al. As the sample is cooled, T continues to increase, with

-I -h

TT =°ff -/3, where <X and /3 are temperature dependent quantities. Alternately T is expressed as an activated quantity, T = A exp(-A/T), with /I « /*H (A and ^ constant). The observed g factor of 3.3 for the activation energy suggests that we are in the low temperature limit for I-D nuclear spin diffusion as discussed by Clark et al.

Polyacetylene, (CH) , has been the subject of much recent work /l,2/. Many of the studies have concentrated on the question of the existence of domain walls

(solitons) in the trans-(CH) ehain. Earlier experiments that have attempted to measure the motion of the soliton and its coupling to the (CH) chain have been in the temperature range from room temperature to 4.2K, where thexmagnetic spin energy is much less than the thermal energy, kT. We report here measurements that are at lower temperatures where the magnetic spin energy becomes comparable to or larger than kT.

Recent Nuclear Magnetic Resonance (NMR) and Dynamic Nuclear Polarization (DNP) measurements at room temperatures have demonstrated that solitons are mobile and diffuse freely in one dimension (I-D) along the chain. Nechtschein and coworkers 131 have found that

for the I-D diffusing soliton and that Dw, the diffusion constant along the chain, 13 -I

is 6x10 s at room temperature. Their observation of the Overhauser Effect (0E) in DNP experiments supports the I-D soliton diffusion model.

At low temperatures, I00K and below, the interpretation of the results is not as clear. The I-D diffusive behavior for T (T«tt»% is still observed /4/, but the relaxation rate extrapolates to a negative value at infinite frequency.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983370

C3-350 JOURNAL DE PHYSIQUE

D m experiments show a Solid State Effect (SSE) indicating that the soliton is becoming localized. For a localized soliton nuclear relaxation will occur through diffusion of the nuclear magnetization, along the (CH)x chain, to the fixed soliton.

'

H NUCLEAR MIAXATION

When the electron and nuclear Zeeman energies, W e and w, respectively, are much smaller than kT the nuclear relaxation rate is given by /5/

where <A'> and

( 0 ~ 2

are the mean square of the scalar and dipolar parts of the hyperfine coupling and dLand d+are the fourier transforms of spin correlation functions. At high temperatures in the isotropic paramagnetic region one has

adz=&*

For a soliton moving with I-D diffusive behavior the spectral density is given by

where C is a normalization constant. This leads to the I-D diffusive result given by Equation I.

At low temperatures the Zeeman energy of the electron spin becomes comparable to the thermal energy and Equation 2 is no longer valid since dfwill no longer be effective in relaxing the nuclear spins. If the soliton remains freely diffusing at low temperatures then we would observe the behavior predicted by Equation I with a different proportionality constant than the high temperature value.

The DNP experiments at low temperatures indicate that the soliton is becoming localized. In this case we expect that the nuclear relaxation will procede via I-D diffusion of the nuclear magnetization along the chain to the fixed soliton i.e. nuclear spin diffusion. In this case the relaxation rate is given by / 5 /

where C is the soliton concentration, is the nuclear spin diffusion constant, and t i s the electron relaxation time. Because the Zeeman energy for the soliton is on the order of the thermal energy Ccould show a thermally activated behavior of the form

where f o is a constant and A is the activation energy. The magnetic energy of the soliton will determine L\ and we would therefore expect A to depend on the magnetic field.

EXPERINENTAL RESULTS

We have measured t e temperature (0.3K<T<4.2K) and frequency (23~Iiz<f<35 MHz) dependance of the 'H nuclear relaxation rate. At the highest temperatures studied in this work our measurements overlap with previous measurements / 4 / and our results are in good agreement with them. We find a relaxation time that increases monotonically as the sample is cooled. Also, at constant temperature the relax- ation time increases with increasing magnetic field. We will present the data in terms of both the I-D soliton diffusion model and the nuclear spin diffusion model.

Figure I presents the data in a form that shows the I-D soliton diffusion character of the results. Equation I predicts that a straight line passing through the origin should represent the data. We find that the data is represented by a straight line, but that it does not pass through the origin. The data is best represented by the form

f u n c t i o n o f temperature a t d i f f e r e n t of

f-'

^{a t different} magnetic f i e l d s (H = 5.45, 7.15, 8.35 Kg) a t u r e s (T = 4.5, 4.2, 1.0, 0.85, 0.60

where at and a r e temperature dependent. A d i f f u s i o n c o n s t a n t can be o b t a i n e d from o< and we f i n d t h a t t h i s d i f f u s i o n c o n s t a n t i n c r e a s e s w i t h d e c r e a s i n g temper- a t u r e . Below III t h e d i f f u s i o n c o n s t a n t can be f i t t o t h e t h e r m a l l y a c t i v a t e d form

where D i s a c o n s t a n t . Only r e l a t i v e v a l u e s of D,,can be o b t a i n e d s o no v a l u e f o r Do

9s

quoted.

F i g u r e 2 p r e s e n t s t h e d a t a i n a form t h a t shows t h e I-D n u c l e a r s p i n d i f f u - s i o n behavior. The l i n e s a r e f i t s t o t h e t h e r m a l l y a c t i v a t e d form

where A i s a c o n s t a n t and

a

i s t h e a c t i v a t i o n energy. The measured a c t i v a t i o n energy, shown i n F i g u r e 3, depends on t h e magnetic f i e l d a p p l i e d t o t h e sample.

The f i e l d dependance is given by

which h a s been c o n s t r a i n e d t o p a s s through zero. Thus we can e x p r e s s o u r r e s u l t s , i n terms o f t h e composite v a r i a b l e H/T, i n t h e simple form

DISCUSSION

Using t h e I - D s o l i t o n d i f f u s i o n model we f i n d t h a t t h e p r e d i c t e d form (Equation I )

C3-352 JOURNAL DE PHYSIQUE

does not fit the data without the

addition of a temperature dependent

FIELD ( Yj)

negative intercept. It has been

2.5. ^{2.3 4. 20} 9.3

proposed /7/ that if the soliton

diffusion rate is slow enough n

effects due to the finite extent of

x

the soliton need to be considered.

In this case the intercept will

-

_A

^{2.0 -}

decrease as the diffusion constant increases, in agreement with our measurements.

The diffusion constant

obtained from these measurements C

.

0

-

increases in a thermally activated manner as the temperature decreases.

This type of behavior has been pre- c dicted by Maki 181 using a model in

which the solitons propagate ballis-

tically at low temperatures. The

-

activation energy Maki predicts, approximately IOK, is much larger than the experimentally observed activation energy. This model is

also in disagreement with the ob-

0 1 0 20 30 4 0

served SSE at low temperatures.

Alternately, we have presented

Frequency (MHz)

the data using the I-D nuclear spin

diffusion model. Observation of the Fig. 3

-

Activation energy as a function SSE at low temperatures in DNP exper- of magnetic field or frequency.

iments indicates the solitons are

localized and that nuclear relaxation should be due to nuclear spin diffusion.

The observation of thermally activated behavior for the nuclear relaxation time implies that the electron spin relaxation time is also thermally activated. The field dependence of the activation energy gives an observed g factor of 3.3, assumingbSg4H. Clark 191 has proposed that in the high field low temperature limit ( g & ~ / k ~ > > I) the observed g factor should be 2 g e 4 in rough agreement with our results.

In conclusion, we find that both the I-D soliton diffusion model and the I-D nuclear spin diffusion model fit the experimental results, within the limitations discussed in the text. In view of the DNP experiments and experiments on (CD) /2/

it is most likely that relaxation procedes via nuclear spin diffusion to a fixgd soliton. In this case the measurements indicate an electron relaxation time that is thermally activated and depends on the composite variable H/T.

(a) Supported in part by U.S. NSF Grants DMR-8106166 and DMR-8204069

*

Present address, Dept. of Physics, Univ of Illinois, Urbana-Champaign, 111.,61801

+

Present address, Dept. of Physics, Univ of Florida, Gainesville, FL 32611 I

-

Proc. of Int. Conf. on Low-Dimensional Conducters, Boulder, Colorado (1981)

Mol. Cryst. Liq. Cryst. (1981) 2

-

These Procedings

3

-

Nechtschein M., Devreux F., Greene R.L., Clarke T.C. and Street G.B., Phys. Rev. Lett. (1980) 3561

4

-

^{Devreux E.,} Holczer K., Nechtschein M., Clarke T.C. and Greene R.L., C o m u n - ications to the International Conference on Physics in One Dimension, Fribourg, Switzerland (August 1980)

5

-

Devreux F., Phys. Rev. BI3(1976)4651

6

-

Abragam A., The Principles of Nuclear Magnetism (Oxford Univ. Press, Oxford, England, 1961)

7

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Nechtschein M.,Devreux F.,Genoud F.,Gugliemi M.,Holczer K.,Phys. Rev. B z (1983) 61

8

-

^{Maki K.,} Phys. Rev. BZ6(1982)2181 and references therein

9

-

Murayama C.T., Sanny J., Clark W.G., Gtemad S., and Maxfield H., These Proced- ings