Optically Transparent Conductive Network Formation Induced by

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Langmuir 2007, 23, 7990-7994

Optically Transparent Conductive Network Formation Induced by Solvent Evaporation from Tin-Oxide-Nanoparticle Suspensions Atsumi Wakabayashi,*,† Yuki Sasakawa,† Toshiaki Dobashi,‡ and Takao Yamamoto§ AdVanced Materials DiVision, Sumitomo Osaka Cement Company, Ltd., Funabashi, Chiba 274-8601, and Departments of Biological and Chemical Engineering and of Physics, Faculty of Engineering, Gunma UniVersity, Kiryu, Gunma 376-8515, Japan ReceiVed February 13, 2007. In Final Form: April 22, 2007 This investigation describes an optically transparent antistatic film composed of antimony-doped tin oxide (ATO) nanoparticles dispersed in a polymer matrix, with remarkably improved electrical and optical properties. The film is fabricated on the basis of a synergistic interaction between self-assembling nanoparticles and self-organizing matrix materials. The antistatic property of the film is obtained at ATO concentrations above a threshold value. A scaling analysis of the data yields an extremely low critical concentration (0.0020 volume fraction), which is considerably lower than the value predicted by percolation theory. Microscopic observations of the film have revealed a characteristic microstructure: “single-stranded” chainlike (linear form or fibrous) aggregates consisting of ATO nanoparticles and large ATO-depleted areas. The experiment results suggest that the high optical transparency and the low critical concentration are derived from the characteristic microstructures of the film.

Introduction Colloidal particles are assembled into ordered and disordered microstructures which lead to the creation of advanced materials with novel properties.1 Several years ago, Texter and Lelental2 fabricated antimony-doped tin oxide (ATO)-gelatin films from colloidal suspensions containing metal oxide particles which were used as antistatic coatings for imaging, electronic, and packaging materials. ATO was used as the filler material due to its remarkable combination of electrical and optical properties based on the properly wide band gap. They noted that the obtained ATO-gelatin layers provide robust electronic conductivity that survives aqueous and thermal processing, and the resistivity (F) of the layers follows a power law of the form:3

F ∝ (φ - φc)-t

(1)

where t is the critical exponent and φc is the critical concentration. Wang and Anderson4 compared the resistivity behavior of composite films fabricated from aqueous colloidal suspensions containing ATO particles and different matrix materials. With a gelatin matrix, the yielded critical concentration (0.14-0.16 volume fraction) was found to be comparable to the “basic” value5 predicted by percolation theory for conducting hard spheres placed at random on a space randomly packed with equally sized insulating spheres. However, they found that φc was about 0.04 or lower when latex particles were used as the film former. The microscopic examination of the films indicated that the reduction * To whom correspondence should be addressed. Phone: +81-474-570979. E-mail: [email protected]. † Sumitomo Osaka Cement Co., Ltd. ‡ Department of Biological and Chemical Engineering, Gunma University. § Department of Physics, Gunma University. (1) (a) Wang, X.; Naka, K.; Zhu, M.; Itoh, H.; Chujo, Y. Langmuir 2005, 21, 12395. (b) Dai, L. L.; Sharma, R.; Wu, C. Y. Langmuir 2005, 21, 2641. (c) Goubault, C.; Leal-Calderon, F.; Viovy, J.-L.; Bibette, J. Langmuir 2005, 21, 3725. (d) Wang, C.; Flynn, N. T.; Langer, R. AdV. Mater. 2004, 16, 1074. (e) Tang, Z.; Kotov, N. A. AdV. Mater. 2005, 17, 951. (2) Texter, J.; Lelental, M. Langmuir 1999, 15, 654. (3) (a) Kirkpatrick, S. ReV. Mod. Phys. 1973, 45, 574. (b) Zallen, R. The Physics of Amorphous Solids; John Wiley & Sons: New York, 1983. (4) Wang, Y.; Anderson, C. Macromolecules 1999, 32, 6172. (5) McLachlan, D. S.; Blaszkiewicz, M.; Newnham, R. E. J. Am. Ceram. Soc. 1990, 73, 2187.

in φc was brought about by an efficient electroconductivity resulting from a segregated conductive pathway consisting of coexisting ATO-rich and ATO-poor phases. It was assumed that the segregated conductive pathway was formed through a phase transition of dispersed latex particles. Sun et al.6 prepared composite films from aqueous suspensions containing small ATO particles and large latex particles. They obtained a considerably low value (φc ) 0.05) for the critical concentration and discussed the results in terms of the segregated conductive network formation7,8 derived from differences in particle sizes. The fabricated films maintain optical transparency at ATO concentrations above the critical concentration. Furthermore, they found a considerable reduction in the optical transparency of the films relative to that of the ATO-free film and attributed it to the scattered light from dispersed ATO particles in the transparent matrix. Recently, we described electrical and optical properties of a composite film filled with nanosized (∼8 nm) ATO particles.9 The film was fabricated by using a strategy which was based on the self-assembly (and the self-organization) of colloidal particles at air/liquid10 and liquid/liquid11 interfaces. Microscopic analysis indicated that the ATO nanoparticles were confined into a thin surface layer of the film, resulting in a “quasi-two-dimensional” conductive pathway, and the extremely inhomogeneous and anisotropic distribution of conductor particles could help realize a high efficiency of electroconductivity with low concentrations. (6) (a) Sun, J.; Gerberich, W. W., Francis, L. F. J. Polym. Sci., Part B: Polym. Phys. 2003, 41, 1744. (b) Sun, J.; Velamakanni, B. V.; Gerberich, W. W.; Francis, L. F. J. Colloid Interface Sci. 2004, 280, 387. (7) Malliaris, A.; Turner, D. T. J. Appl. Phys. 1971, 42, 614. (8) Kusy, R. P. J. Appl. Phys. 1977, 48, 5301. (9) Wakabayashi, A.; Sasakawa, Y.; Dobashi, T.; Yamamoto, T. Langmuir 2006, 22, 9260. (10) (a) Cheng, W.; Dong, S.; Wang, E. J. Phys. Chem. B. 2005, 109, 19213. (b) Onoda, G. Y. Phys. ReV. Lett. 1985, 55, 226. (c) Stankiewicz, J.; Vı´lchez, M. A. C.; Alvarez, R. H. Phys. ReV. E 1993, 47, 2663. (d) Pieranski, P. Phys. ReV. Lett. 1980, 45, 569. (e) Earnshaw, J. C. J. Phys. D: Appl. Phys. 1986, 19, 1863. (f) Hurd, A. J.; Schaefer, D. W. Phys. ReV. Lett. 1985, 54, 1043. (g) Paunov, V. N.; Binks, B. P.; Ashby, N. P. Langmuir 2002, 18, 6946. (11) (a) Tarimala, S.; Ranabothu, S. R.; Vernetti, J. P.; Dai, L. L. Langmuir 2004, 20, 5171. (b) Tarimala, S.; Dai, L. L. Langmuir 2004, 20, 3492. (c) Nicolaides, M. G.; Bausch, A. R.; Hsu, M. F.; Dinsmore, A. D.; Brenner, M. P.; Gay, C.; Weitz, D. A. Nature 2002, 420, 299. (d) Aveyard, R.; Clint, J. H.; Nees, D.; Paunov, V. N. Langmuir 2000, 16, 1969. (e) Aveyard, R.; Clint, J. H.; Nees, D.; Quirke, N. Langmuir 2000, 16, 8820. (f) Binks, B. P.; Lumsdon, S. O. Langmuir 2001, 17, 4540.

10.1021/la700433e CCC: $37.00 © 2007 American Chemical Society Published on Web 06/19/2007

Optically Transparent ConductiVe Network Formation

We obtained a very low value (φc ) 0.004) for the apparent critical concentration and attributed it to this microstructure. The findings of these previous studies indicate that controlled packed conductor particles result in segregated conductive pathways, which again results in a low critical concentration and a better combination of conductivity and transparency of the films. Here, we propose a novel idea to reach even more reduction in the critical concentration by forming a highly segregated conductive pathway derived from the voluminous nature of fractal12 structures. It is suggested that the segregated conductive pathways result in a low percolation threshold when the pathways are made up of large agglomerates and the fractal dimension of the agglomerates is low.13 The strategic points of our idea are to use the voluminous nature of the chainlike cluster structure and a synergistic interaction between different types of the fractal structures. (A) We deposit a composite film from water-based coating solutions containing well-dispersed ATO nanoparticles with hydrophilic surfaces. Colloidal interactions between the nanoparticles can produce aggregates (and agglomerates) of voluminous chainlike fractal structures. (B) The coating solutions contain self-emulsified micelles consisting of ultraviolet (UV) curable resins as matrix materials. In the course of film formation, the self-assembling ATO nanoparticles and the self-organizing matrix materials can interact with each other to result in a highly segregated conductive pathway. The interaction potential between colloidal particles is mainly composed of the van der Waals potential and the electrostatic repulsive potential, and colloid particles whose interaction potential has the second nearest minimum can aggregate diffusionlimited.14 Aggregates of chainlike structures (with low fractal dimensions) can result from aqueous colloidal dispersions of well-dispersed particles through diffusion-limited aggregations,15 which can be realized by the competition between the potentials. The above discussion suggests that aggregates (or agglomerates) of chainlike structure can be obtained by diffusion-limited aggregations from well-dispersed aqueous colloidal dispersions, which leads to strategy A. Additionally, as a method to control particle arrangements in the films, we propose to let the ATO nanoparticles form aggregates in a wet layer containing self-emulsified matrix materials as shown in Scheme 1. The wet layer contains the ATO nanoparticles and the emulsified matrix materials immediately after the layer deposition (Scheme 1a). During the layer drying process, the ATO nanoparticles coalesce to form aggregates and the emulsified matrix materials undergo a phase transition from a spherical phase to a connected phase, which prohibits uniform diffusion of the ATO nanoparticles (Scheme 1b). The ATO nanoparticles can be trapped11 at the liquid/liquid interfaces formed by the matrix materials and aqueous medium to form disordered fractal aggregates. The resulting connected phases of matrix materials can have a fractal structure, and a synergistic interaction between the two types of fractal structures results in a highly segregated conductive pathway (Scheme 1c). To obtain highly segregated conductive pathways, the connected phases uniformly and sparsely distributed in the threedimensional spaces should be suitable. Such a spatial distribution of the matrix materials can be obtained by the sponge structure14,16 (12) Stauffer, D.; Aharony, A. Introduction to Percolation Theory; Taylor & Francis: London, 1992. (13) Schueler, R.; Petermann, J.; Schulte, K.; Wentzel, H.-P. J. Appl. Polym. Sci. 1997, 63, 1741. (14) Safran, S. A. Statistical Thermodynamics of Surfaces, Interfaces, and Membranes; Addison-Wesley: Reading, MA, 1994. (15) (a) Witten, T. A., Jr.; Sander, L. M. Phys. ReV. Lett. 1981, 47, 1400. (b) Meakin, P. Phys. ReV. Lett. 1983, 51, 1119. (16) Holyst, R. Nat. Mater. 2005, 4, 510.

Langmuir, Vol. 23, No. 15, 2007 7991 Scheme 1. Assumed Particle Distributions in Deposited Layersa

a Key: (a) ATO nanoparticles (dots) and self-emulsified matrix materials (large circles) are dispersed in an aqueous medium immediately after layer depositions. (b) In the course of the layer drying process, the nanoparticles are self-assembled into chainlike clusters adhering to interfaces of the matrix materials and the aqueous medium. Sponge structures are assumed as connected phases of the matrix materials. (c) A conductive pathway consisting of the nanoparticles is formed in the polymer matrix.

formed by the soft matters; the surface of the resin aggregation in the sponge phase is expected to have a multiconnected surface and “permeates” all the space. However, at the same time, the multiconnected surface structure in the sponge phase may prohibit the uniform diffusion of the ATO nanoparticles to disturb a formation of the conductive pathway that extends within the system. Avoiding this difficulty, we use the phase transition from the spherical phase to the sponge phase of the resin-water system. The ATO nanoparticles are expected to develop a conductive pathway adhering to the sponge phase surface during the phase transition, which is caused by evaporation of water from the deposited wet layers. Note that it is not necessary that the sponge structures appear in equilibrium. Various types of organic materials are expected to form the sponge structure in nonequilibrium conditions, and choosing an adequate evaporation rate of the medium could quench the sponge structure to result in a highly segregated conductive pathway. The above discussion leads to strategy B. In this study, we prepare antistatic layers by using the proposed strategy and examine the electrical and optical properties as well as microscopic structures of them. The obtained extremely low critical concentration (φc ) 0.0020) shown below is consistent with electromicroscopic observation of a branched chain network consisting of ATO nanoparticles. Because the nanoparticle distribution in the polymer matrix is three-dimensionally isotropic in contrast to that reported in our previous study,9 the critical concentration of the present film can be much lower than that of the previous one. Experimental Section Preparation and Characterization of Nanoparticles. Electrically conductive ATO nanoparticles (Sumitomo Osaka Cement, Sumice Fine ATO WF103) were used in this study. The nanoparticles were prepared hydrothermally by treating precursor colloids in an autoclave. Briefly, 570 g of SnCl4‚5H2O (Merck) and 45 g of SbCl3 (Merck) were dissolved in 3000 g of fuming HCl (6 N). The obtained solution was stirred for 30 min in an ice bath, and 2000 g of aqueous ammonia (25%) was added until a pH value of 3-4 was reached. The resulting precipitates were washed with deionized water until no trace of chloride ions could be detected. An 8000 g portion of an aqueous dispersion containing the obtained precipitate (5%) was put into a stainless steel autoclave, heated at 350 °C for 5 h in static conditions, and cooled to room temperature. The colloidal dispersion shows a blue color. The shape of the obtained particles was observed directly using a Hitachi H800 transmission electron microscope. Samples for the transmission electron microscopy (TEM) observation were prepared

7992 Langmuir, Vol. 23, No. 15, 2007 by spotting grids with the colloidal dispersion containing the particles and letting the spots dry. The particle size was determined through an analysis of X-ray powder diffraction (XRD) line broadening. Samples for the XRD measurements were prepared by removing water from the colloidal dispersion of ATO nanoparticles with a rotary evaporator (bath temperature 50 °C). After being dried at 100 °C, the residue was ground in a mortar. The analysis was performed using a PANalytical X’pert RPO MPD system with Ni-filtered Cu KR radiation at 45 kV and 40 mA. Particle Size Distribution Analysis of Colloidal Dispersions. The particle size distribution of the dispersed ATO nanoparticles and matrix materials was determined by dynamic light scattering (DLS; Leeds Northrup Microtrac UPA instrument). Samples for the analysis were prepared by diluting the dispersions to total solids of 1 wt % before the measurements. Preparation of Antistatic Layers. Acrylate monomer (hydroxypropyl acrylate, Nippon Shokubai) and photoinitiators (benzophenone and 1-hydroxycyclohexyl phenyl ketone in a 50:50 weight ratio, Chiba Speciality Chemicals) were used as-received. Urethane acrylate oligomer (Nippon Gohsei, UV-W101B) was dissolved in warm water (60 °C) at a concentration of 20 wt %. The self-emulsified matrix material was prepared by mixing the urethane acrylate oligomer and the acrylate monomer in a 40:60 weight ratio. The photoinitiators were also added to the mixtures at 5% compared to the total solids. The water-based coating solutions were prepared by dispersing the required amount of ATO nanoparticles with the self-emulsified matrix material and photoinitiators into water at a total solids content of 35%. All aqueous solutions were prepared using deionized water. The formulated coating solutions were applied onto poly(methyl methacrylate) (PMMA) panels (thickness of 2 mm) using a wirewound rod to yield wet layers (thickness of 32 µm) at 25 °C and 60% relative humidity. The resulting wet layers were dried at 60 °C for 10 min and irradiated by a high-pressure mercury lamp with a 700 mJ/cm2 UV dose in air conditions to yield completed antistatic layers. Characterization of Deposited Layers. The surface electrical resistivity Fs (Ω/square) of the layers was determined by applying a 500 V potential according to American Society for Testing and Materials (ASTM) standard test method D257 using a resistivity meter (Mitsubishi Chemical, HIRESTA-IP with a concentric ring URS probe). The bulk resistivity F was calculated from the measured surface resistivity value and film thickness, where surface resistivity is related to the bulk resistivity by F ) Fs × layer thickness. The layer thickness (ca. 2 µm) was determined using a Tencor P10 stylus profilometer (Tencor Instruments). Optical clarity of the layers was determined according to American Society for Testing and Materials (ASTM) standard test method D1003 using a haze meter (Tokyo Densyoku, TC-HIIIDP). The haze value H (%) is defined as H ) Td/Tt × 100, where Tt is the total luminous transmittance and Td is the diffuse luminous transmittance. Spectral transmittance T of the layers was measured using a UV-vis-NIR spectrophotometer (JASCO, V750). The distribution of ATO nanoparticles in the crosssectional layer samples was observed using the above-mentioned TEM instrument. For the TEM observation, cross-sectional samples were prepared using a Seiko SMI2050 focused ion beam (FIB) system. The distribution of ATO nanoparticles on the layer surfaces was observed using a Hitachi S-4000 field emission scanning electron microscope operated at an acceleration voltage of 15 kV.

Results and Discussion Resistivity Behavior of Deposited Layers. Antistatic layers were deposited from water-based coating solutions containing ATO nanoparticles. Figure 1 shows a variation of the resistivity F of the layers as a function of the ATO volume fraction φ. A steep decrease in resistivity, i.e., the conductor-insulator transition, is observed at a very low ATO concentration. We have found that the resistivity F of the layers follows the power law3 for percolation, and a nonlinear least-squares fit of the data according to eq 1 yields t ) 1.6 ( 0.1 and φc ) 0.0020 ( 0.0003.

Wakabayashi et al.

Figure 1. Resistivity of deposited layers as a function of the ATO volume fraction. Inset: scaling analysis of resistivity data with respect to the ATO volume fraction.

The linear behavior in the log-log plot of the data confirms the validity of the analysis (the inset of Figure 1). The value of the exponent t for composites is most often found to lie in the “universality” range5 of 1.65-2.0. The yielded value also lies in this range. On the other hand, the yielded critical concentration is extremely low compared with the “basic” value5 predicted by percolation theory. It should also be noted that the yielded critical concentration is considerably lower than the values reported in previous studies4,6 (including our preceding study9). Optical Properties of Deposited Layers. The optical clarity of the layers was evaluated by the haze measurement. At the critical concentration (0.0020 volume fraction), a haze value increase of less than 0.1% (Figure 2a) and a total luminous transmittance reduction of less than 0.5% (the inset of Figure 2a) were observed. The negligible cloudiness indicates that the obtained layers are optically very clear. Additionally, it has been found that the amount of nanoparticles to achieve the level of electrical conductivity for the antistatic applications2 does not affect the optical transparency of the deposited layers in the wave length range of 400-800 nm (Figure 2b). These results indicate that the obtained antistatic layers exhibit an improved transparency compared with the values6,9 reported in previous studies. Morphological Features of Aggregated Nanoparticles. Percolation theory3,5 predicts that an “infinite” cluster appears in a system at the percolation threshold. The optical properties of the system should be closely related to the morphological features of the dispersed conductor particles and the infinite cluster consisting of the particles. Figure 3 shows a representative TEM image of an ATO nanoparticle. The analysis shows that the ATO nanoparticle has a typical granular morphology, in which we can determine the unit cell size of 3.35 Å from the reflection of the 110 surface. The observed particle size in the TEM image agrees well with the average crystallite size (8 nm) determined through the analysis of XRD line broadening (data not shown). Figure 4 shows a representative TEM image of a cross-sectional deposited layer sample at an ATO concentration (0.0017 volume fraction) close to the critical concentration, where the cross-sectional sample (thickness about 100 nm) for the TEM analysis was prepared using an FIB system. In the image, nanoparticles are observed as dark zones while matrix regions are observed as bright zones. The analysis shows a two-dimensional projection of a three-

Optically Transparent ConductiVe Network Formation

Langmuir, Vol. 23, No. 15, 2007 7993

Figure 2. Optical properties of deposited layers. (a) Haze value of the layers as a function of the ATO volume fraction. Inset: total luminous transmittance of the layers as a function of the ATO volume fraction. (b) Transmittance spectra of an uncoated PMMA panel and coated PMMA panels (ATO volume fractions 0.0007 and 0.0017).

dimensional structure embedded in a slice of the layer. The analysis clearly indicates that the nanoparticles form continuous clusters of “single-stranded” chainlike structure. Field emission scanning electron microscopy (FE-SEM) analysis was also performed on the deposited layer samples to determine the nanoparticle distribution on the layer surfaces (Figure 5). In contrast to the TEM image, the nanoparticles are observed as bright zones while matrix regions are observed as dark zones. The analysis also indicates that continuous clusters of singlestranded chainlike structure have been formed (Figure 5a). The morphological feature of the image is consistent with that of the TEM image. These results indicate that the three-dimensional network of single-stranded chainlike (linear or fibrous form) structure is embedded in the polymer matrix. When an incident light ray encounters dispersed particles which form small regions of different refractive indices in a transparent matrix, light scattering takes place. The intensity of scattered light increases drastically when the size of the small region reaches

the visible light wavelength.17 The scattered light from the particles dispersed in the transparent matrix results in the cloudiness of the deposited layers. Because the width of the single-stranded chainlike cluster is regarded as the size (8 nm) of the nanoparticle, the negligible cloudiness of the layer can be attributed to the characteristic cluster structure. Segregated Conductive Pathway Derived from Volume Exclusion Effects. The microscopic analysis suggests that the obtained low critical concentration is derived from the characteristic microstructure, that is, the chainlike clusters of low particle density. Additionally, it should be noted that TEM analysis indicates that large ATO-depleted areas (200-400 nm in width) are formed among the clusters (Figure 4). The FE-SEM analysis clearly indicates that the single-stranded chains are separated by the ATO-depleted areas (Figure 5b). These results suggest that (17) Kerker, M. The Scattering of Light and Other Electromagnetic Radiation; Academic Press: New York, 1969.

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Figure 3. TEM image of a nanoparticle. The sample for the TEM observation was prepared by spotting a grid with a colloidal dispersion containing the nanoparticles and letting the spot dry.

Figure 4. TEM image of a cross-sectional layer sample (ATO volume fraction 0.0017). The sample (thickness about 100 nm) was prepared using an FIB system.

Wakabayashi et al.

Figure 6. Particle size distribution analysis of colloidal suspensions: (a) ATO nanoparticles without matrix materials, (b) matrix materials which contain urethane acrylate oligomer and hydroxypropyl acrylate in a 40:60 weight ratio.

areas (Figure 6). These results may indicate that the ATO-depleted areas are derived from the self-emulsified matrix materials. The reduction in the percolation threshold of systems consisting of small conducting particles and large insulating particles is interpreted in terms of the segregated conductive network formation7,8 derived from differences in the size of the two species of particles. These percolation models were originally proposed to explain the percolation phenomena in a dry premixed and a subsequently sintered mixture of conducting and insulating particles. Although there are fundamental differences between the assumed systems and our system, the theoretical approach of these percolation models could give some insight into the conductive network formation of the present system. Thus, we estimated the threshold value according to these models as about 0.01, which is considerably larger than the experimentally determined value (0.0020). A more accurate estimation is required before further discussion. However, these results seem to suggest that the synergistic interaction between the two types of volume exclusion effects (derived from the single-stranded chainlike cluster structures and the ATO-depleted areas) makes a contribution to the reduction in the percolation threshold: Random percolation theory is not expected to hold in our complex system.

Conclusion

Figure 5. FE-SEM images of a layer sample containing nanoparticles (ATO volume fraction 0.0017) at (a) high and (b) low magnifications.

the volume exclusion effect derived from the ATO-depleted areas also makes a contribution to the low critical concentration. Particle size analysis of the dispersed particles by the DLS method shows a narrow size distribution for the colloidal dispersion of ATO nanoparticles with a mean particle size of about 10 nm and a rather broad size distribution (from 80 to 600 nm) for selfemulsified matrix materials with a mean particle size of about 300 nm, which is comparable to the size of the ATO-depleted

We have demonstrated that antistatic layers with a high conductivity and a high transparency can be fabricated from aqueous coating solutions, which contain ATO nanoparticles and self-emulsified UV-curable matrix materials. The yielded critical concentration (0.0020 volume fraction) was found to be extremely low. The antistatic layers exhibit extremely high optical clarity (less than 0.1% haze) at ATO concentrations above the critical concentration. Microscopic analysis has suggested that a highly segregated conductive network is formed. The network is characterized by aggregated ATO nanoparticles of singlestranded chainlike (linear or fibrous form) structures and large ATO-depleted areas. The excellent optical and electrical properties of the layers have been attributed to the segregated conductive network derived from the characteristic microstructure. It is very interesting and challenging to investigate the relation between the fractal dimension of the ATO aggregates and the critical exponent of the resistivity. Details of the morphological features of the ATO-depleted areas and their fractal analysis will be reported in the near future. LA700433E