Synthetic Metals, 16 (1986) 17 - 30 17

ELECTRICAL CONDUCTIVITY OF c~-QUINQUETHIOPHENE/STEARIC ACID LANGMUIR-BLODGETT FILMS DOPED WITH IODINE

s. TASAKA*, H. E. KATZ, R. S. HUTTON, J. ORENSTEIN, G. H. FREDRICKSON and T. T. WANG

A T & T Bell Laboratories, Murray Hill, NJ 07974 (U.S.A.)

(Received February 18, 1986; accepted March 12, 1986)

Abstract

Langmuir-Blodgett multilayer films consisting of 0 - 62 mol% purified (~-quinquethiophene (QT) in cadmium stearate-stearic acid (ST) were deposited on glass substrates and characterized by a variety of methods. Exposure of these films to iodine vapor rendered them electrically conduc- tive, the conductivities being strongly dependent on QT concentrat ion and the number of layers deposited. The most conductive samples (>~35 mol% QT, ~10 layers) had o = 0.2 S cm -l . The concentrat ion dependence of the conductivi ty can be broadly described by the two-site percolation models that take into account the specific chain arrangement and the finite con- ductivities of both the QT and ST aggregates in the films. Finally, the relevance of the QT-ST system to other conducting materials is discussed.

Introduct ion

Polyaromatics and polyheterocycles are among the most widely studied organic materials that can be made to conduct electricity. Recent work has focussed on the synthesis and doping of polyphenylene [ 1], polypyrrole [2] and polythiophene [2a, 3], the conductivities of doped polyenes and theo- retical studies [4] of the conduct ion process. The mechanism of conduct ion is still controversial, especially the relative importance of intrachain versus

interchain electron transfer [3a]. Very few experiments have dealt with the relationship between supramolecular organization [5] and the electrical properties of conducting organic materials.

The Langmuir-Blodget t (LB) film technique [6] provides a means of assembling photo- and electroactive organic molecules in ordered arrays of precise dimensions. Functional groups on such molecules have included polyenes [7], amphiphilic dyes [8] and phthalocyanines [9]. Only in rare

*Present address: Tokyo University of Agriculture and Technology, Koganei, Tokyo 184, Japan.

0379-6779/86/$3.50 © Elsevier Sequoia/Printed in The Netherlands

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cases are highly conducting systems obtained, either in the originally deposited films or by subsequent doping [ 10].

Embedding an oligomeric heterocycle in an LB film would provide an oppor tuni ty to s tudy a potentially dopable, non-polymeric organic material in an ordered arrangement. Thus, aspects of the conduct ion process that are no t dependent on intrachain electron movement may be observed. In 1974, it was reported [11] that ~-quinquethienyl (QT) can be deposited in a LB monolayer as a 25 mol% mixture with cadmium arachidate. Photocurrents were detected perpendicular to the plane of the substrate, but simple con- ductivity measurements or doping experiments were not a t tempted. In the present study, we report the characterization of LB films containing 0 - 62 mol% QT in cadmium stearate-stearic acid (ST) multilayers. Conductivities parallel to the plane of the films after I2 doping as a function of number of layers and mol% QT were determined. Finally, possible mechanisms of conductivi ty are considered.

Experimental

The pressure-area isotherms were determined and multilayer films of the QT/ST mixtures were prepared using a J o y c e - L o e b l Trough 4. Mono- layers were spread from chloroform solutions of the mixtures on an aqueous subphase (purified using a Millipore Milli-Q system) containing 2.5 X 10 -4 M CdCl2 and 2.0 X 10 -4 M KHCO3. The pH of the subphase was adjusted using dilute HC1; typically the pH was 6.2. The substrates on which the films were deposited, glass microscope slides and indium-tin-oxide (ITO) coated glass, were washed with detergent, thoroughly rinsed several times with Milli-Q treated water and cleaned in an argon plasma for about one minute. Stearic acid (Alpha) was recrystallized from MeOH. The films were deposited at a surface pressure of 25 mN/m.

Electrical conductivities in the plane of the film (olt) were measured by means of the standard four-probe technique (films were deposited on glass microscope slides for these measurements). Conductivity data were taken one minute after the samples had been exposed to an N2 atmosphere. All conductivities were ohmic. Conductivities normal to the film surface (o±) were measured for films deposited on ITO glass using an Hg drop electrode on top of the film. Gel permeation chromatography (GPC) was performed on a Beckman HPLC using CH2CI 2 as eluant, a 100 A 'p-spherogel' column, and u.v. detection.

~-Quinquethiophene (Method 1) Bis(bithienyl)-l ,4-butadiyne (5) was prepared [12] as illustrated in

Scheme 1. The first step (formation of 2) was more exothermic than ex- pected [13] and required cooling from the start of the reaction. The butadiyne was obtained only in 46% yield from dibromide 3 (literature value [12] 73%) and was isolated by extraction into CHC13 since the suggested

19

I 2

(~ S / ' ~ S ~,~' CH ----- CBr 2 ~ (~ S / ' ~ S ~ -~- -- H

5 4

5 QT

Scheme 1.

solvent, ether, did not dissolve useful quantities of 5. The sample of 5 ob- tained had m.p. 165 °C (dec) (lit. 167 °C (dec)) and was pure by 13C n.m.r. (CDC13 versus Me4Si) ~ 77.2, 78.6, 119 .9 ,123 .2 , 124.4, 125 .1 ,127 .6 , 135.0, 135.8, 140.2).

A suspension of 5 (104 mg, 0.28 mmol) and powdered Na2S'9H20 (270 mg, 1.1 mmol) in 50 ml dioxane was stirred at reflux for 20 h under Ar. The mixture was cooled, concentrated and triturated with 10 ml of H20 and 2 ml of CH2C12. The residual solids, which could not be crystallized directly, were washed with 2 ml of CH2C12 and extracted with 30 ml of hot dioxane. The hot extract was filtered, concentrated to 7 ml, and diluted to 11 ml with H20. After cooling to ambient temperature, a precipitate had formed and was collected by centrifugation, washed with H20, and dried at 110 °C under vacuum. The yield of QT was 53 mg (47%), m.p. 250 - 52 °C (prior darkening) (lit. [12] 256 - 8 °C), 90 - 95% pure by GPC. When 100 ml of CH2C12 and 50 ml of H20 were used in the trituration step, analytically pure material was obtained as an orange solid in only 15% yield, m.p. 253 - 5 °C, 1H n.m.r. (CDC3 versus Me4Si) 5 6.9 - 7.3 (complex multiplet), mass spectrum: m / e = 412 (M ÷, base peak), GPC: 1 band. Anal. talc. for C20H]28 s : C, 58.22; H, 2.93; S, 38.85. Pound: C, 58.03; H, 2.94; S, 39.06.

o~-Quinquethiophene ( M e t h o d 2) A solution of ~-terthiophene [14] (6, 2.0 g, 8.1 mmol) in 100 ml of

(CH2)40 was cooled to - -78 *C and butyl-lithium (17.7 mmol) was added. After stirring 1 h at - -78 °C, Br2 (0.91 ml, 18 mmol) was added slowly, fol- lowed by stirring 1 h at - -78 °C, then 15 rain at ambient temperature. Ether and H20 were added to form two layers. The organic suspension was separated and concentrated and crystallized from EtOH-PhCH3 to give 2.2 g (61%) of 7 [15] (Scheme 2).

To a solution of 7 (201 mg, 0.50 mmol) and (Ph2PCH2CH2PPh2)NiC12 (10 mg) in 15 ml each of Et20 and (CH2)40 was added a solution of thiophene-2-magnesium bromide (prepared from 320 mg of 2-bromo- thiophene and 48 mg of Mg powder in 5 - 10 ml of EtzO ). The combined solutions were stirred and heated for 16 h at reflux. The reaction was

2O

6 7

7 + ~( S "7/~ MgBr ~, QT

Scheme 2.

quenched with aqueous NH4C1, and the solids were separated, washed with H20 and Et20, and triturated with hot aqueous dioxane. The yield was 170 mg (83%) of orange powder, m.p. 250 - 2 °C (no prior darkening), pure by GPC, n.m.r, and u.v.

Results

Preparation and characterization of LB films Figure 1 shows a set of four pressure-area isotherms for monolayers

containing 0, 20, 46, and 62 tool% QT in ST (curves a, b, c, and d respec- tively) at pH 6.2. Extrapolation of the linear portion of curve a to zero pressure gave a value of 22 A 2 as the effective molecular cross-sectional area of the stearate moiety. By plotting the areas per molecule obtained in a similar manner from the mixed monolayer data (curves b -d ) versus mole fraction of QT and extrapolating to 100 ml% QT, a value of 26 A 2 is ob- tained as the effective area per molecule of QT.

6O

5O

E z 4 0 E uJ n-

30

W

20

t 0

0 I I ~ L O. 1 0.2 0.3 0 .4

AREA, nmZ/MOLECULE

Fig. 1. Pressure-area isotherms for monolayers of QT/ST mixtures containing 0 (curve a ) , 20 ( b ) , 4 6 (c ) a n d 6 2 m o l % ( d ) of QT.

21

The u.v. absorbance of the films measured with the incident beam normal to the substrate is featureless. When the sample is tilted at an angle to the incident beam, a maximum at 350 nm, corresponding to aggregated QT, is observed [11]. This suggests that QT molecules in the LB film are aligned with their long axes, and consequently their transition dipole moments, normal to the plane of the film. (Anisotropic absorption is also observed in the u.v. absorbance of the doped films, indicating that at least some of the alignment of the QT is preserved after I: incorporation.) X-ray diffraction due to the Cd 2÷ ions was consistent with a 49.6 A spacing of ion layers, and therefore a monolayer thickness of 24 .8 /k , because the chain arrangement in the LB films is of the y-type. The QT could be recovered from the LB films by extraction of the films for several hours with CHaCN. The extracted QT was identical to authentic QT by GPC.

A monolayer containing 33 mol% QT in ST deposited on four layers of pure ST was observed by fluorescence microscopy at 1 #m resolution. The QT was homogeneously distributed (+ 15% at 95% confidence limits), except for widely scattered defects due to microcrystallites or scratches. Similar results were obtained on samples consisting of 10, 20 and 40 layers of 25 mol% QT, microcrystallites being the only obvious inhomogeneities.

Conductivities of the undoped films containing QT were < 10-12 S cm-1 (perpendicular to the plane of the films) and <10 -9 S cm 1 (parallel to the plane). These values are at the limits of detection for the two kinds of mea- surements.

Doping of LB films with I2 Storage of Q T - S T LB films in an evacuated, I2-saturated chamber led to

doping, evidenced by two new broad maxima in the optical absorption spectra at 450 and 750 nm (Fig. 2). The conductivi ty of a maximally doped film containing 30 mol% QT is plot ted as a function of the number of layers (n) in Fig. 3. The conductivity increases rapidly with n for n ~< 7, then saturates at ~10 -1 S cm -1. The dependence of o on mole fraction of QT is

o lo

~_ 12- DOPED z

< QT(57%)+ ST> 15L, 21L

(3£

~ 0 . 0 5

< z / / " 21L ".,. . . . .

I 1 L I L L 500 400 500 600 700 800 900 lO00

WAVELENGTH, nm

Fig. 2. Optical absorp t ion spectra of iodine-doped LB films comprising 13 (solid line) and 21 (dashed line) monolayers of QT (57 mol%)/ST mixture .

22

0

-2

- 4

_o

- 6

30 rnol % QT.

- 8

- I0 I L i L 0 t0 20 25

NUMBER OF LAYERS Fig. 3. Semi log plot o f in-plane conduct iv i ty , 011, as a func t ion of n u m b e r o f monolayers containing 30 mol% of QT in ST.

0 ~L

A~.A

-2

3L

b"

E ~

-6

-8

-~o , I ~ i ~ ~ ~ ~ ,

0 0.2 0.4 0.6 0.8 4.0

VOLUME FRACTION OF QT

Fig. 4. Semi log plots o f in-plane conduetivi t ies , Oli , for 1-, 3- and l l - l a y e r e d LB f i lms as funct ions o f vo lume f rac t ion of QT in the QT/ST mixtures.

plotted in Fig. 4 for n = 1, 3 and 11. Again, the functions are monotonic , leveling at a mole fraction of ~ 35%.

The doping process was partially reversible upon removal of the more loosely bound I2, leaving behind a film displaying residual absorbance at 460 nm and higher conductivity than the undoped films. This residual

23

conductivity was anisotropic and stable, with ol = 1.5 × 10 -7 S cm -1 and ou = 3 × 10 -3 S cm -1 for a film having 21 layers of the 50/50 mixture. It was not possible to measure the conductivity of highly doped films in the per- pendicular direction because the Hg drop electrodes reacted with the I2 on the surface of these films.

Recovery of the extractable organics from a doped film followed by GPC analysis showed that most of the extract was QT, but a small amount (<5%) was a higher molecular weight compound, probably decathiophene. Most of the oligomeric thiophene was dissolved from the films after several hours' immersion in CH3CN, but a small portion required Me2SO treatment before it was separated from the substrate.

Discussion

Physical properties o f LB films Except for the single monolayer composition reported [11] by Kuhn

et al., the QT-containing films reported here are without precedent in the literature. Just as Kuhn found for his monolayer, our multilayers showed greatly decreased u.v. absorption with the electric field vector polarized in the plane of the film (incident beam normal to the plane). The ~max at 350 nm that we observe when the incident beam is not normal to the film plane, indicating that the QT molecules are aggregated, is also in agreement with Kuhn [ 11 ]. Ultraviolet spectroscopy, however, provides no information as to the degree of aggregation. The u.v. and X-ray data, obtained on samples containing 48 mol% QT, show that the order in the films is preserved even at a significantly higher proportion of QT than previously employed.

The cross-sectional area that we calculated (26 A 2) for QT in stearate films is significantly higher than previously reported [11] (19 A 2) for QT in arachidate. This may be due to the higher pH at which our films were prepared or the better fit between the length of cadmium stearate (25.8 A) [16] and QT (22 A based on CPK models) versus cadmium arachidate (28 A) [16] and QT. Using CPK models, 28 A 2 is the cross-sectional area of a cylinder defined by rotating the five atoms in thiophene about an axis that bisects the molecule and is parallel to the C3C4 bond. A QT molecule oriented perpendicular to the plane of the film with dihedral angles of 90 ° might also be expected to occupy a 28 A 2 cross section. The value 26 A 2 is reasonable for a moderately twisted QT molecule, with dihedral angles in the 20 ° to 50 ° range.

Doping o f the LB films The iodine-doping experiments described here are among the first

at tempts [7] at forming a conductive complex of a neutral organic com- pound in an LB matrix. The doping procedure seems to cause two separate changes. The first is the formation of a charge transfer (CT) complex, evidenced by the 750 nm feature in the near i.r. and the greatly increased

24

conductivities. The peak absorbance wavelength of 750 nm is in the range of the CT band reported [3a] for poly(methylthiophene)-I2. The second is probably a chemical reaction on a small fraction of the QT, leading to C--I or C--C bond-forming reactions. The residual absorbance at 460 nm of a doped film from which I2 and QT were both removed is probably due to products of these reactions [ 17].

Two days' doping is required before CT absorbance and conductivities reach their maximum values, probably due to the slowness of the penetra- tion of I2 into the quasi-crystalline LB array. Since we observe o± >> 10 -12 S cm -1 for doped films after the labile I2 has been removed, some significant amount of I2 must penetrate during doping to the layers near the substrate, even if the bulk of the I2 resides near the surface of the film. Although poly- thiophene can accept as much as 3 equiv. I2 for every 5 thiophene units [18], the otl values of our I2-saturated QT films are probably reasonable assuming a less than stoichiometric incorporation of I2 [3b] , even in the surface layers. It was not possible to determine directly the I2 uptake in our systems.

Conductivity of doped films The conductivi ty of I2-saturated films, when plot ted as a function of

QT concentrat ion as in Fig. 4, shows two regimes. Focussing first on the multi layer films, we observe that the conductivi ty reaches a plateau for QT concentrat ion ~35 mol%. This ult imate conductivi ty (0.2 S cm -1) is similar to that in I2<ioped polythiophene (10 -2 to 10 -1 S cm -1) [3b] , and slightly higher than we determined in an I2<loped evaporated film of pure QT. Thus neither the large chain lengths achieved by polymerizat ion nor the additional ordering achieved by the LB process greatly increases the conductivi ty of I2- doped thiophene oligomers. It appears that for polymers as well as molecular assemblies, the ult imate conductivi ty is limited by the rate of intermolecular electron transfer [19].

In order to s tudy whether the conductivi ty behavior shown in Fig. 4 is a manifestation of classical percolation, we have investigated two-site percolation models that are relevant to the present system. The first model, which will be referred to as the monolayer model, consists of an infinite two-dimensional array of space-filling hexagons and is depicted in Fig. 5(a). Each hexagonal cell is assumed to be occupied by a phase that is highly con- ductive, with probabil i ty ¢, and by a phase that has a low conductivity, with probabil i ty 1 - - ¢ . If the I2-complexed QT molecules were distributed com- pletely at random in the LB films, then the highly conductive phase could be taken as a single molecule and the phase with low conductivi ty could be assumed to be an undoped molecule. However, the above u.v. absorption measurements suggest that the complexed molecules are not randomly dis- tr ibuted, bu t are clustered in small aggregates. Because it is likely that such aggregates have an approximately random distribution, the model can still be applied, bu t with a cell size that corresponds to the average size of a cluster. The cell can then be considered to contain the high conductivity

25

... ~ ' ° " (a)

(b)

Fig. 5. The monolayer and bulk percolation models. (a) The monolayer model consists of an infinite array of space-filling hexagons. (b) The bulk model consists of commensurate layers, each layer having the structure of the monolayer model.

phase if it is occupied by a cluster of doped molecules and to contain the low conductivity phase if it is occupied by undoped molecules. Regardless of the interpretation of a cell and its phase, ~ is assumed to correspond to the volume fraction of doped molecules in the film. We expect that the monolayer model is applicable to the single layer I:-doped films.

The second model, which will be referred to as the bulk model, consists of a macroscopic stack of commensurate layers, each layer containing an infinite two-dimensional array of hexagonally close-packed cells. The bulk model is depicted in Fig. 5(b) and is expected to be applicable to the LB films with 11 or more layers. Note that conductivity is higher in the bulk systems than in the monolayers because zig-zag paths of conduction that traverse several layers are available in the former, but obviously are not possible in the latter cases.

In both models the highly conductive phase is distributed, with volume fraction ~b, at random among the cells, but in the monolayer model electrical conduction is confined to a single layer. For simplicity, we assume that there is no anisotropy in the conductivity of a particular cell, but we do allow a non-zero conductivity for a cell that contains the low conductivity phase. The intrinsic conductivity of a cell that is occupied by the low conductivity phase will be denoted aa, while the conductivity of a highly conductive cell will be denoted ab (with a a ~ Ob).

We use the position-space renormalization group technique (PSRG) to obtain approximations for the effective conductivity (in the direction

26

parallel to the layers) o f the two pe rco la t ion models . The appl ica t ion o f this t e chn ique to pe rco la t ion p rob lems has been discussed in an exce l len t review art icle by S tan ley and coworke r s [20] . Use o f PSRG m e t h o d s fo r the ca lcula t ion o f ef fec t ive conduct iv i t ies has been discussed by Bernasconi [21] and e x t e n d e d to f inite conduct iv i t ies o f b o t h types o f cells (or bonds in the case o f a b o n d pe rco la t ion mode l ) by various workers [22, 23] . F o r the p resen t mode ls we e m p l o y the m e t h o d o f Shaw and O t t i n o [23] .

RG (a)

RG ~ ~

(b)

Fig. 6. The renormalization cells for the monolayer and bulk models. (a) The lattice of the monolayer model is partitioned into clusters of three cells. Each such cluster is termed a renormalization cell and on application of the renormalization group is replaced by a new effective hexagonal cell as shown on the right. (b) The renormalization cell on the left is replaced by the effective cell on the right when the PSRG is applied to the bulk model.

The m o n o l a y e r mode l descr ibed above is equivalent to a site percola- t ion mode l on a t r iangular la t t ice in two dimensions . This p ro b l em has been s tud ied exhaus t ive ly by a var ie ty o f theore t ica l me thods . We a d o p t the recurs ion re la t ions der ived by Shaw and O t t i n o t h a t are based on the renor- mal iza t ion c lus ter shown in Fig. 6(a). These a p p r o x i m a t e equa t ions are given by

¢(n + 1) = ¢3(n) + 3¢2(n)[1 - - ¢(n)] (1)

[1--¢(n)] ln o,(n) + 3¢(n) ln[oa(n)/2 + oa(n)O'(n)%(n) oh(n) aa(n + 1) = exp

1 + 2¢(n)

(2)

27

[¢(n) ln°b(n)+3[1--cP(n)]ln[ °b(n)/2+ Oa(n )°a(n)°b(n)]+ Ob(n )

Ob(n + 1) = exp 3 -- 2¢(n)

(3)

where Oa(0) = Oa, Ob(0) = Ob and ¢(0) = ¢. For a specified set of Oa, Ob and ~, these recursion relat ions can be i terated to convergence. The unstable f ixed po in t in eqn. (1) is ¢* = 0.5, which is known to be the exact percolat ion threshold in the case t ha t oa = 0. For start ing values of ¢ greater than 0.5 and n large enough to obta in the desired accuracy, Ob(n + 1) is used as an esti- mate of the effective conduct iv i ty , while oa(n + 1) is used if ¢ < 0.5. The above equat ions are believed [23] to yield an accurate approximat ion for the effect ive conduc t iv i ty o f the mono laye r model over the entire range of ¢.

The bulk mode l differs f rom convent ional percolat ion models because its lat t ice is anisotropic and thus has d i f ferent effective conduct ivi t ies in the direct ions perpendicular and parallel to the layers. Note tha t this is the case even though the intrinsic conduct ivi t ies o f the cells are isotropic. However, there is no d i f f icu l ty in ex tending the me thods of ref. 23 to such a s i tuat ion. We shall only be concerned with the parallel conduc t iv i ty in the present paper. Using the renormal iza t ion cell shown in Fig. 6(b), the fol lowing recursion relat ions are obta ined:

¢(n + 1) = [~a(n) + 3¢2(n)(1 -- q~(n))] [2 + 2¢3(n) -- 3¢2(n)] (4)

oa(n + 1) = e x p [ ( [ 1 --q~(n)] 2 In Oa(n) + 611 - - ¢ ( n ) ] ¢ ( n ) ln[(3oa(n) + Oab)/4 ]

+ 9~2(n) ln[(Oa(n) + O~b)/2]}{[1 --~b(n)]2 + 611 --O(n)]O(n)

+ 9¢2(n)} -1] (5)

Ob(n + 1) = exp[{O4(n)In Oh(n) + 6~3(n)[1 - -¢ ( n ) ] ln[(3ob(n) + Oab)/4]

+ 9¢2(n)[1 -- ¢(n)] 2 In [(Ob(n) + Oab)/2]

+ 6¢2(n)[1 --~b(n)] 2 ln[(2ob(n) + o, (n) + Oab)/4 ]

+ 2~b(n)[1 -- ¢(n)] a ln[(Oa(n ) + ab(n))/2 ] + 18¢(n)[1 -- ¢(n)] 3

× ln[(o~(n) + Ob(n) + 20,b)/4] + 611 - - ¢ ( n ) ] 4 ln[(2o~(n)

+ Ob(n) + Oab)/4]}{6 -- 4¢(n) -- 9¢2(n) + 12¢3(n) -- 4~4(n)} -1] (6)

where

2(~a(n )ob(n ) O-ab -- Oa(n ) + Ob(n )

28

10 -I ey

lo-2 .g ? 10-3

10-4

~ lo-5

b 10-6

lO -7 o

lo -8 ~ ~._.......~

10-91 I L I I 0.0 0.2 0.4. 0.6 0.8 1.0

Fig. 7. Comparison of the predictions of eqns. (1 ) - (6) for the monolayer and bulk models with the conductivi ty data for the single-layer and 1 l - layer LB films.

Equation (4) has an unstable fixed point at ¢* = 0.203 862. As before, we use ab(n + 1) for the effective conductivi ty when ¢ > ¢* and aa(n + 1) when ¢ < ¢*. Based on our experience with PSRG techniques for related percola- tion problems, we expect that the above equations provide a quantitative approximation for the effective conductivi ty of the bulk model.

In Fig. 7 the numerical solutions of these equations are shown, together with the conductivi ty data for the single- and multiple-layer films. The con- ductivities of the two pure phases for the monolayer model, oa and Ob, were obtained by matching the single-layer data at ¢ = 0 and ¢ = 1. Similarly, the pure phase conductivities for the bulk model were obtained by extrapolating the l l - l aye r data to ~ = 0 and ¢ = 1. The bulk model exhibits an extremely sharp increase in conductivi ty near the percolation threshold at ¢ = 0.2, followed by a plateau region. Comparing this with the conductivi ty of the l l - l aye r sample, we see that o does appear to reach its plateau value at this concentration. Below ¢ = 0.2, however, a decreases exponentially rather than showing the singular behavior predicted by classical percolation. The comparison of the monolayer model with the single-layer data shows analogous features.

The exponential dependence of a on ¢ for the l l - l aye r film starts with a QT concentrat ion as low as 4%. As we have seen, this is well below the concentrat ion required for conduct ion by classical percolation. It is likely that in this low concentrat ion regime, conduct ion takes place by thermally assisted hopping, or tunneling, between classically isolated clusters of doped

29

QT. (In order that the spaces between clusters remain small enough to allow tunneling (25 A), the cluster size is limited to about 100 molecules.) In either case, the conductivity will depend exponentially on the typical separation between doped regions. As the concentration of QT is increased and the inter-cluster separation is reduced, the conductivity is expected to grow as in Fig. 7. In fact, according to this picture, the conductivity should increase exponentially until the percolation threshold, the critical concentra- tion at which inter-cluster transport is no longer the controlling process. This is borne out by the comparison between theory and experiment shown in Fig. 7, which indicates that the exponential growth of o with increasing ¢ stops at the predicted threshold for classical percolation.

Conclusions

It is possible to prepare monolayer and multilayer oriented films con- taining up to 62 mol% QT in ST. These films may be doped with I2 to produce semiconducting materials whose electrical conductivity depends dramatically on the number of layers and the QT concentration. These dependencies can be accounted for by the two-site percolation models that distinguish between monolayer and multilayer phenomena. Thus, the LB technique enables us to observe microscale conductivity phenomena that may be relevant to bulk organic conductors.

Acknowledgement

We are indebted to J. A. Connor for performing the fluorescence microscopy experiments, and to A. M. Mujsce for obtaining mass spectra. Helpful discussion with E. A. Chandross, D. MSbius and G. Wegner are greatly appreciated.

References and notes

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30

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