8
ELSEVIER Synthetic Metals 65 (1994) 159-166 SYlIIITHETU( InUI|TRLS Spin dynamics study in polyaniline: macroscopic and microscopic transport property relationship J.P. Travers a'*, P. Le Guyadec% P.N. Adams b, P.J. Laughlin b, A.P. Monkman u aCEAIDdpartement de Recherche Fondamentale sur la Mati~re Condensde/SESAM/Laboratoirc de Physique des M~taux Synthdtiques, 17 rue des Martyrs, 38054 Grenoble Cedex 9, France bApplied Physics Group, Department of Physics, University of Durham, South Road, Durham DH1 3LE, UK Received 28 December 1993; accepted 27 January 1994 Abstract Proton spin lattice relaxation times Ta have been measured in the frequency range 7-95 MHz on a set of unstretched and stretched polyaniline films, together with d.c. conductivity. A highly anisotropic quasi 1D spin diffusion is evidenced in all the samples. It is shown that while stretching increases parallel d.c. conductivity, it favours interchain hoppings at the microscopic scale. These results are interpreted in a coherent picture that links the macroscopic transport properties to the microscopic ones. In particular, d.c. conductivity anisotropy is shown to be of geometrical nature when the microscopic transport anisotropy is very high. It is also concluded that the carrier mean free path is not consistent with metallic conductivity. Keywords: Polyaniline; Transport; Spin dynamics I. Introduction One of the basic questions in the field of conducting polymers is to know if we are dealing with a metallic state or not in these materials. Actually, the answer is not straightforward since the situation may differ from one polymer to another, as well as from one sample to another according to the preparation method. Moreover, the situation may be somewhat confused owing to the fact that different arguments have been used in the literature to conclude in favour of a metallic state. Among them, let us mention: (i) the observation of a temperature-independent contribution to the mag- netic susceptibility which is generally assumed to be of Pauli type; (ii) the existence of a temperature range in which the derivative of the conductivity with respect to the temperature is negative; and (iii) a finite value for the extrapolated conductivity towards T=0 K. In fact, the first argument implies only statistical consid- erations about the electronic states, in particular, the existence of a finite density of states at Fermi level. In this connection, it has been recently shown that disorder can give rise to a so-called Pauli susceptibility in a system of localized states [1]. On the other hand, *Corresponding author. the last two arguments are related to the localized or extended character of these states and, therefore, to the very nature of the metallic state in the framework of the localization transition [2]. This aspect is crucial in conducting polymers owing to their microscopic one- dimensional (1D) character. It is well known that even a vanishingly small disorder formally results in the localization of all electronic states in a pure 1D system [3], then leading to an insulator (at T=0) in which conduction proceeds through hopping at finite tem- perature. However, the metallic state may be stabilized by three-dimensional (3D) couplings [4]. From this point of view, conductivity measurements appear to be a priori the most appropriate way to discriminate be- tween the two states. Experimentally, the situation is more complicated. The macroscopic d.c. conductivity is so strongly affected by the disorder which is present at every scale of the structure and the morphology that it is practically no longer related to the microscopic state. This point is well illustrated by the fact that while the models which are generally invoked to account for the thermal variation of conductivity are based on totally different microscopic pictures, they all lead to the same macroscopic behaviour [5]. Thus, it turns out that the study of the intrinsic nature of the conducting state of conducting polymers would greatly benefit from 0379-6779/94/$07.00 © 1994 Elsevier Science S.A. All rights reserved SSDI 0379-6779(94)02151-N

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ELSEVIER Synthetic Metals 65 (1994) 159-166

SYlIIITHETU( InUI|TRLS

Spin dynamics study in polyaniline: macroscopic and microscopic transport property relationship

J.P. Travers a'*, P. Le Guyadec% P.N. Adams b, P.J. Laughlin b, A.P. Monkman u aCEAIDdpartement de Recherche Fondamentale sur la Mati~re Condensde/SESAM/Laboratoirc de Physique des M~taux Synthdtiques, 17 rue des

Martyrs, 38054 Grenoble Cedex 9, France bApplied Physics Group, Department of Physics, University of Durham, South Road, Durham DH1 3LE, UK

Received 28 December 1993; accepted 27 January 1994

Abstract

Proton spin lattice relaxation times T a have been measured in the frequency range 7-95 MHz on a set of unstretched and stretched polyaniline films, together with d.c. conductivity. A highly anisotropic quasi 1D spin diffusion is evidenced in all the samples. It is shown that while stretching increases parallel d.c. conductivity, it favours interchain hoppings at the microscopic scale. These results are interpreted in a coherent picture that links the macroscopic transport properties to the microscopic ones. In particular, d.c. conductivity anisotropy is shown to be of geometrical nature when the microscopic transport anisotropy is very high. It is also concluded that the carrier mean free path is not consistent with metallic conductivity.

Keywords: Polyaniline; Transport; Spin dynamics

I. Introduction

One of the basic questions in the field of conducting polymers is to know if we are dealing with a metallic state or not in these materials. Actually, the answer is not straightforward since the situation may differ from one polymer to another, as well as from one sample to another according to the preparation method. Moreover, the situation may be somewhat confused owing to the fact that different arguments have been used in the literature to conclude in favour of a metallic state. Among them, let us mention: (i) the observation of a temperature-independent contribution to the mag- netic susceptibility which is generally assumed to be of Pauli type; (ii) the existence of a temperature range in which the derivative of the conductivity with respect to the temperature is negative; and (iii) a finite value for the extrapolated conductivity towards T=0 K. In fact, the first argument implies only statistical consid- erations about the electronic states, in particular, the existence of a finite density of states at Fermi level. In this connection, it has been recently shown that disorder can give rise to a so-called Pauli susceptibility in a system of localized states [1]. On the other hand,

*Corresponding author.

the last two arguments are related to the localized or extended character of these states and, therefore, to the very nature of the metallic state in the framework of the localization transition [2]. This aspect is crucial in conducting polymers owing to their microscopic one- dimensional (1D) character. It is well known that even a vanishingly small disorder formally results in the localization of all electronic states in a pure 1D system [3], then leading to an insulator (at T=0) in which conduction proceeds through hopping at finite tem- perature. However, the metallic state may be stabilized by three-dimensional (3D) couplings [4]. From this point of view, conductivity measurements appear to be a priori the most appropriate way to discriminate be- tween the two states. Experimentally, the situation is more complicated. The macroscopic d.c. conductivity is so strongly affected by the disorder which is present at every scale of the structure and the morphology that it is practically no longer related to the microscopic state. This point is well illustrated by the fact that while the models which are generally invoked to account for the thermal variation of conductivity are based on totally different microscopic pictures, they all lead to the same macroscopic behaviour [5]. Thus, it turns out that the study of the intrinsic nature of the conducting state of conducting polymers would greatly benefit from

0379-6779/94/$07.00 © 1994 Elsevier Science S.A. All rights reserved SSDI 0379-6779(94)02151-N

160 J.P. Travers et al. / Synthetic Metals 65 (1994) 159-166

the possibility of probing the charge carrier motion at the microscopic scale.

Also of interest is the question of the anisotropy of conductivity. At the molecular level, anisotropy is ob- viously expected for topological reasons, but very little is known about its order of magnitude. How does it compare with what is observed in 1D organic con- ductors? At the macroscopic level, anisotropy is obtained on films either upon stretching or by direct orientation during polymerization. The anisotropy is attributed to the average orientation of the chains induced by stretch- ing. However, several questions are still open concerning this point. Does the stretching modify the stacking of chains at the microscopic level, or only induce a geo- metrical rearrangement at the level of the grain or the fibrilla? What is the relationship between the macro- scopic anisotropy and the microscopic one? In most of the cases, it has been observed that the anisotropy of conductivity is almost temperature independent [6]. To our knowledge none of the hypotheses which have been proposed to account for this result has been definitively proved.

In the present paper, we report spin dynamics and d.c. conductivity data obtained on unstretched and stretched polyaniline (PANI) films which supply new results about both the conducting state and the effect of stretching at the microscopic level, as well as about the connection between the microscopic transport an- isotropy and the macroscopic one. Spin dynamics enables one to probe the electronic spin motion at the chain level, whatever the structure and morphology of the material at intermediate and macroscopic scales. If the spin carriers are also charge carriers (electrons in metals or polarons in conducting polymers) the transport prop- erties can be analysed at the microscopic level. Of particular interest is the case of low dimensional systems in which the method allows one to determine the microscopic anisotropy of the motion. For instance, spin dynamics has been revealed as a powerful tool for investigating the motion of electrons in 1D organic conductors [7] and that of polarons in polypyrrole [8], polyaniline [9] and polythiophenes [10]. We present here the first spin dynamics study devoted to the effect of stretching on conducting polymer films, namely, on polyaniline films. Comparative measurements have been performed on stretched and unstretched samples. The analysis of the data gives new information on the stretching-induced microscopic modifications. A simple model is proposed which accounts for the relationship between microscopic and macroscopic conductivity an- isotropy.

2. Spin dynamics

The basic idea is that the characteristics of the electronic spin motion, i.e., the 'spin dynamics', as

probed at the chain level by magnetic resonance tech- niques, reflect electron interactions which are related to magnetic and transport properties. The spin dynamics is described by the motion spectrum f(oJ) which is the Fourier transform (in the frequency domain) of the two-spin correlation function f(t):

f ( t) = (S~(t)ST'(O) )/kT,~ (1)

where S~(t) is the a component at time t of the spin located at site A, and 2=x/(glzB) 2 is the reduced spin susceptibility.

The spin motion may be, for instance, the time evolution of the spin component of fixed electron spins in magnetic systems or the 'true motion' of conduction electrons in metals, of neutral solitons in trans-poly- acetylene and of polarons in polyaniline. In the case of a 'true motion' f ( t) is nothing but the probability for a given spin to come back to its starting point after time t. If the spin is also a charge carrier then f(t) (andf(oJ)) contains information about microscopic trans- port properties.

For a standard random walk, i.e., a diffusion process, one has

f( t) = (Dt) - a/2 (2)

where D is the diffusion coefficient and d the space dimension in which the diffusion takes place. For top- ological reasons only, f(~o) exhibits different frequency dependences according to d. In particular, in 1D systems f(~o) diverges towards low frequency as (Do))-1~. This divergence comes from the difficulty for a diffusive particle to diffuse away from its starting point in a strictly 1D system. However, for real quasi 1D systems, this divergence is truncated in particular by interchain couplings, thus giving [11]

f(co)~(2OlntraOg) -1/2 for Di, ter<o~<Di,tra

(1D limit) (3)

f(o~)-~(Din,erDi,,ra) -1/2 for oJ<Di,,er (3D limit) (4)

where D~,r, and Dinter a re the intra- and interchain diffusion coefficients, respectively.

For sufficiently high spin concentration, the spin motion and therefore fQo) governs both the electronic and nuclear spin relaxation in a solid. So, several magnetic resonance techniques, such as nuclear mag- netic resonance (NMR), electronic spin resonance (ESR) or dynamic nuclear polarization (DNP) can provide information about spin dynamics. These meth- ods have been revealed to be particularly fruitful in studyingvarious 1D systems: spin diffusion in Heisenberg chains [12], magnetic solitons in antiferromagnetic chains [13], 1D triplet-exciton systems [14], 1D organic conductors [7], neutral solitons in trans-(CH)x [15] and, more recently, polarons in conducting polymers [8-10].

ZP. Travers et aL / Synthetic Metals 65 (1994) 159-166 161

The nuclear spin lattice relaxation time T1 is given by [16]

where a and d are the scalar and dipolar hyperfine couplings; ~oe/2~r and ~On/27r are the electronic and nuclear Larmor frequencies, respectively. At a given temperature, the term kT2 in Eq. (5) can be replaced by c/4 where c is the concentration of equivalent Curie spins per unit cell. Thus, by measuring T1 as a function of frequency, the motion spectrum can be described within two windows corresponding to ~oe and ~on, re- spectively.

3. Experimental

Films of emeraldine base (EB) were synthesized using a modification of the route given by Angelopoulos et al. [17]. The basic synthesis involves a chemical oxidation of aniline hydrochloride by ammonium persulfate. After careful washing of the product, the EB powder is dissolved in NMP and films are cast onto glass substrates. After removal of solvent, the films can be removed from the substrate. A full account of our synthesis and materials characterization can be found elsewhere [18]. To orient the films, we use uniaxial stress. This is applied to the film in a specially constructed stretching rig based on a system used to align precursor poly- acetylene films [19]. Briefly, stress can be applied to the films held between two jaws by a spring and screw arrangement. This alignment can be performed over a range of temperatures (via electrical heating of the stretch rig) and in a controlled environment, e.g., vac- uum, argon, etc. Once the films have been stretched, they can be doped with HCI. In all cases the quoted percentage elongation is given by [(l-lo)/lo]× 100%, where I is the final length of the film and l0 the original length of the film as measured between the jaws of the stretch rig. Two sets of three separate films each were studied: unstretched films and 300% stretched films. They were all issued from the same polymerization batch.

Proton spin lattice relaxation times T1 were measured using a standard 7r-r-rr/2 pulse sequence with a Bruker CXP 100 spectrometer, over the frequency range 7-95 MHz at room temperature. A single exponential was observed for magnetization recovery. Since we have previously shown that nuclear relaxation in PANI is strongly depending upon hydration state [20,21], mea- surements were performed on dried samples. From the evolution of T1 at a given frequency under secondary pumping, we concluded that a 48 h minimum pumping time was required to reach steady state. For instrumental

sensitivity reasons all the films of a set were placed together in the same measuring cell.

Spin concentration, c per aniline unit, was determined using a double ESR cavity by comparison to a calibrated reference.

D.c. conductivity measurements were performed on rectangular-shaped samples of each film, by means of the Montgomery technique [22].

4. Results and discussion

4.1. Experimental results

In Table 1 are reported the average values of the measured d.c. conductivity on each set of samples. Parallel, X ~t, and perpendicular, X ±, conductivities refer to the stretching direction, and AM represents the macroscopic anisotropy E,/E ±. Of course, in the un- stretched films, the values of X~t and X. are equal within the experimental uncertainty, which is about 10%.

The average measured spin concentration was 1.5 × 10 -2 per monomer in the unstretched films and 1.3 × 10 -2 in the stretched films. The rather high spin concentration of these compounds as compared to unprotonated ones and the narrowness of the ESR lines (2 to 4 G) give evidence that most of the spins correspond to polarons associated with the conducting state of PANI. Polarons are obviously existing either in the polaron-bipolaron picture [23] or in the polaron lattice model [24]. In Fig. 1, the normalized relaxation rate T{l/c for unstretched samples have been plotted as a function of f - 1/2 where f is the nuclear Larmor frequency. In Fig. 2, are reported the data for both the unstretched and the 300% stretched films in the same coordinates. Such a type of plot is convenient to show a 1D spin diffusion. Two points can be emphasized: (i) the T~ -1 variations measured on the two sets of samples are both composed of two straight lines in our plot which suggests a quasi 1D diffusion with an in- terchain hopping introducing a crossover frequency ~oc; and (ii) oJc is clearly shifted towards high frequencies in the stretched films.

4.2. Analysis

Two cases can be a priori considered depending on whether the crossover from 1D to 3D behaviour lies

Table 1 D.c. conductivity and anisotropy measured on stretched and un- stretched PANI films using the Montgomery method

Ell (S/cm) ,V.,± (S/cm) AM

Unstretched films 40 40 1 300% stretched films 210 23 9

162 J.P. Travers et aL / Synthetic Metals 65 (1994) 159-166

A "7 U Q;

1.1

"7

k-

10000

8000

6000

4000

2000

• unstretched film I

i

i

t

f = 2 0 . 7 MHz c

i

O i I I , , , i I i , , , I , I 10114 O. 1 0.2 0,3 (F requency ) "l/z ( MHz "'/2)

Fig. 1. Proton spin lattice relaxation rate (normalized to the spin concentration) as a function o f f -1~2 for unstre tched PANI films. The arrow indicates the crossover from 1D to 3D diffusion in the to. range.

in the to, range (case A) or in the toe range (case B). However, the high frequency part of the data extrap- olates towards zero which is a,strong argument in favour of case A. Since the spin concentration c is known, a quantitative fit of the data using Eqs. (3) to (5) requires only the knowledge of the hyperfine couplings. Assuming homogeneous delocalization for the electron spin over the six carbon and nitrogen atoms of a monomer unit, we have taken a/3% = 23.4/7 = 3.3 G, and we have used d = a/2, as usual for aromatic carbons, and experimen- tally confirmed in polyaniline [21]. There are two fitting p a r a m e t e r s : Dintr a and Ointer.

In unstretched films, it appears that case B leads to a set of values which is not consistent with the starting hypothesis. On the contrary, in case A we are dealing

with a coherent picture where Di. t ra = 1.6 + 0.9 × 1012

rad/s, Dinte, = 1.3 X 108 rad/s and the 1D to 3D crossover lies in the to, range: fc = D i n t e r / 2 7 r = 20.7 MHz. The value o f D i n t r a is in good agreement with previous ones obtained on standard powder samples of PANI [9,11]. On the other hand, the interchain spin diffusion coefficient Din,er appears to be much lower in our films than in powder samples. Thus, the polaron motion anisotropy, which we define as the microscopic anisotropy, Am =D~,tr,/D~,ter, is actually very high in our PANI films since Am = 104. Such a high value might be explained by large differences between crystallographic structures of films and powders. It has been shown that standard PANI powder corresponds to the ES-I structural form, while protonated films cast from a solution of EB in

J.P. Travers et al. / Synthetic Metals 65 (1994) 159-166 163

'T U

10000

u 800C

600C

4000

2000

I f " " I I

• unstretched film

o 300% stretched film

H

Ill t t

E - ' l f =40 MHz

¢

&

f =20.7 MHz ¢

I

Q I i I , I , , I I , , , = , , ,

0.1 0,2 0 ,3 0 ,4

(Frequency)"" ( M H z " " )

Fig. 2. Normalized proton spin lattice relaxation rate as a function o f f -1/2 for unstretched and 300% stretched PANI films. The shift of the 1D to 3D crossover towards high frequencies clearly indicates that stretching increases the interchain spin diffusion rate.

NMP correspond to the ES-II form [25,26]. In particular, the compactness of the ES-II form is actually 20% smaller than the ES-I form [26]. Also, in the ES-II form, neighbouring chains are out of phase in the a direction (corresponding to the shortest interchain dis- tance), which could probably decrease the ~--orbital overlap and therefore the interchain transfer integral.

We now address the case of stretched films. The analysis is similar to the previous one. It leads to the following set of values: Ointr a = 3.0 "Jr- 1.6 × 1012 rad/s and Di,,¢, = 2.5 × 10 a rad/s. The crossover frequency is then fc = 40 MHz. These results are summarized in Table 2 together with those obtained for unstretched films.

Considering the raw data, one could conclude that stretching results in an increase of both intra- and

Table 2 Intra- and interchain polaron diffusion coefficients, 1D to 3D crossover frequency and polaron motion anisotropy in PANI films as derived from N M R data

Dintr= Ointer fc AM = (1012 rad/s) (108 rad/s) (MHz) Dimra/

Dinter

Unstretched films 1.6 + 0.9 1.3 20.7 = 104 300% stretched films 3.0+ 1.6 2.5 40 = 104

interchain polaron hopping rates. In fact, there is a large difference of the uncertainty about Din,ra and Din,~r. Din,ra is proportional to the fourth power of hyperfine couplings and to the square of spin concen-

164 J.P. Traverset al. / Synthetic Metals 65 (1994) 159-166

tration so that, owing to uncertainties about these quantities and about data, the precision about Din t r a is rather low and one cannot really conclude about a possible variation. On the other hand, since Dinte r is directly extracted from the position of the knee-shape of the data, regardless of the values of the couplings and the spin concentration, its value is precisely known. Consequently, one is led to conclude only that stretching induces an increase of the interchain polaron diffusion rate. As concerns the microscopic anisotropy, it either remains approximately constant or slightly decreases. How could we explain such a result? The idea which comes to mind is that stretching is generally accompanied by an increase of crystallinity [27], which could rea- sonably increase the average length on which two neighbouring chains are mutually ordered and therefore the interchain hopping probability.

4.3. Macroscopic versus microscopic transport properties

We now consider the way to connect spin dynamics data to conductivity data.

One can first estimate the microscopic conductivity, or, of the material supposing that all charge carriers have the same diffusion coefficient as the one derived for polarons from spin dynamics. This can be carried out in a simple way using the relation tri=ne2DdkT where n is the charge carrier concentration [11]. Ac- cording to the unit cell volume of ES-II [26], a doping level of 0.5 e/ring corresponds to n = 3 . 4 x 102~ cm -3.

Using the values of Din t r a and Din te r for the stretched films, one obtains O ' i n t r a = 2 1 0 _ _ 120 S/cm and t%~er---- 1.8X10 -2 S/cm. While the parallel microscopic con- ductivity satisfactorily compares with the average mea- sured macroscopic d.c. value for the stretched samples, the transverse conductivity does not. It is noteworthy that macroscopic conductivity in stretched films appears not to be limited by interchain charge hopping contrary to what is observed in ES-I powders [9]. This could mean that in NMP-cast stretched films, no more con- tribution to the resistivity appears at scales larger than that scale probed by spin dynamics. In this framework, one can then estimate the mean free path l of the charge carriers with the assumption of a metallic be- haviour: Dintra c2 ~-~'F l, where c, is the lattice constant along the chain and VF is the Fermi velocity. One obtains l/c, = 2 x 10 -2, a value too small to be consistent with a metallic description: charge carrier states are more likely to be localized rather than extended.

The question of anisotropy remains. Is the macro- scopic one, AM~9, related to the microscopic one,

A m -- 104? Let us consider the following picture in which a conducting polymer is composed of small crystalline grains connected together through resistive contacts. For simplicity, we suppose that grains are spherical with 2r as the average diameter. Using ellipsoids or

cylinders instead of spheres leads to the same qualitative results [28]. Inside the grains, the anisotropic conduc- tivity is described by a cylindrical tensor the main axis of which is parallel to the chain direction. In its principal axes, it is only defined with two parameters: the in- trachain (O'intra) and interchain (O'inter) microscopic con- ductivity, respectively. The contact resistance, Re, is assumed to depend on the size of the grains, so that Rc=(po/r)(E/r), where Po is defined as the effective contact resistivity and e the separation between the grains.

In the case of unstretched films, the grain orientation is randomly distributed over the whole space. On the other hand, in stretched films the main axis of the grains, k, is preferentially oriented along the stretching direction z: the probability distribution of the angle q5 between k and z is supposed to be constant inside a cone of vertex half-angle a and zero outside this cone. So, unstretched films (no grain orientation) correspond to a = ~'/2, when better and better oriented films are associated with smaller and smaller t~. The average macroscopic conductivity is then calculated either in the stretching direction or in the perpendicular direction with the following assumptions: - the elementary volume of the material is composed of parallel identical wires the diameter of which is equal to the average grain diameter;

- the wire resistance is that of a grain necklace made of a large number of grains so that we take for every grain an average resistance calculated according to the wire orientation with respect to the stretching direction.

Finally, we end up with the following macroscopic conductivity anisotropy [28]:

AM= ~ l l _ (~),,

1 +/3(e/r)po(tr),, J (6) / 2,3_

where /3 is a constant in the order of unity which depends on shape and arrangement of the grains,

(O') ii ---~ Orintcr + (lTintra -- O'inter)[ 1 + COS 3 + COS20~ ] (7)

is the average grain conductivity along the stretching direction, and

)[2-cos .-cos2~] (O') 3_ = O'inter + (Orintra -- O'inter 6 (8) is the average grain conductivity perpendicular to the stretching direction.

In the limit of very high microscopic anisotropy (Orintra>>0rinter) , and providing that grain orienta- tion upon stretching is not too perfect so that O'intra(2 -- COS O/-- COS20/) >> 60"inter, then Eq. (6) reduces to

J.P. Traverset al. I Synthetic Metals 65 (1994) 159-166 165

2(1 + cos a + cos2a)] AM =l Z-c J

[ ~ + ( #i) 3( dr)poCr,.,.:( 2 - cos, ot - cos2 a) ] x +(tj)/3(dr)pom.,.a(l+cos a + ~ J (9)

the weak temperature dependence of the conductivity anisotropy observed on several stretched conducting polymer films.

The result obtained in Eq. (9) deserves to be em- phasized: the macroscopic anisotropy of conductivity is not related to the microscopic one; it turns out to be mainly a geometrical function depending upon the degree of grain orientation. In other words, perpen- dicular macroscopic conductivity comes only from mis- alignment of the grains. The expression AM (Eq. (9)) is composed of two terms in brackets: while the first one is an increasing function of the orientation that diverges when a goes to zero (perfect orientation), the second one slightly decreases from unity to a finite value when a goes from ~-/2 to zero. Also, we must point out that the macroscopic conductivity anisotropy, as given by Eq. (9), can be only weakly temperature dependent which agrees very well with several exper- imental results [6]. In the opposite limit of low mi- croscopic anisotropy (O'intr a ~ O'inter) , the macroscopic an- isotropy is directly connected to the microscopic one.

Let us now apply this model to the case of PANI films. Taking into account the microscopic anisotropy of the polaron motion, which is about 104, Eq. (9) is clearly valid. Although it is difficult to estimate, the contact resistivity is certainly higher than the average resistivity of a randomly oriented crystalline grain, i.e. Po >> 3/tri,tra- Thus, using reasonable values, i.e. Po-- 30/ O'intra, F ~'~ 50 A for the grain size [29] and e = 5 /~ for the contact thickness, one can account for the observed macroscopic anisotropy, AM = 9, with a = 19 °. This value corresponds to (cos2~b) --- 0.95, which is in good agree- ment with usual experimental values.

5. Conclusions

A correlative study based on spin dynamics and d.c. conductivity measurements has revealed as a fruitful method to obtain new information about the effect of stretching on microscopic and macroscopic transport properties of PANI films. We have found that the polaron motion is highly anisotropic at microscopic scale and that stretching favours the interchain polaron hopping rate. We have demonstrated that the micro- scopic features of the polaron motion derived from the NMR data can account for the macroscopic transport properties and concluded that the behaviour of HCI- doped PANI films is not really metallic. In particular, we have proposed a simple model in which the mac- roscopic conductivity anisotropy of stretch-oriented films is derived from the microscopic properties. This model applies satisfactorily in PANI films. It might explain

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