Appl. Phys. A 74 [Suppl.], S954–S956 (2002) / Digital Object Identifier (DOI) 10.1007/s003390101167 Applied Physics A Materials Science & Processing Combination of SANS and 3D stochastic reconstruction techniques for the study of nanostructured materials E.S. Kikkinides 1, ∗ , K.L. Stefanopoulos 2 , T.A. Steriotis 2 , A.C. Mitropoulos 3 , N.K. Kanellopoulos 2 , W. Treimer 4 1 CPERI/CERTH, 6th km. Charilaou-Thermi Rd, 57001 Thermi-Thessaloniki, Greece 2 NCSR “Demokritos”, 15310 Agia Paraskevi Attikis, Greece 3 Department of Petroleum Technology, Cavala Institute of Technology, 65404 Ag. Lucas, Cavala, Greece 4 HMI, Glienicker Straße 100, 14109 Berlin, Germany Received: 13 July 2001/Accepted: 24 October 2001 –  Springer-Verlag 2002 Abstract. Ceramic nanostructured materials have recently re- ceived scientific and industrial interest due to their unique properties. A series of such nanoporous structures were characterised by SANS techniques. The resulting scattering curves were analysed to obtain basic structural information regarding the pore size distribution and autocorrelation func- tion of each material. Furthermore, stochastic reconstruction models were employed to generate 3D images with the same basic structural characteristics obtained from SANS. Finally, simulation results of permeation on the reconstructed images provide very good agreement with experimental data. PACS: 61.12.Ex; 61.43.Bn; 61.43.Gt Studies in the fields of engineering have led to computer- based tools for the representation of the actual pore structure and the acquisition of reliable assessments of several trans- port properties such as permeability, conductivity and diffu- sivity [1–3]. These are mainly statistical methods in terms of a stochastic simulation of porous media in 3D, utilizing information obtained from 2D images of thin sections. The basic principle is that both the real and the model structures should have identical statistical properties, such as the aver- age porosity and the autocorrelation function, which are used as input for the creation of the simulated structures under the assumption of statistical homogeneity [1]. In many cases, information on the aforementioned properties of the materi- als is obtained directly from scanning (SEM) or transmission (TEM) electron microscopy images. Alternatively this infor- mation can be obtained indirectly from small-angle scattering (SAS) data [4–7]. 1 Experiment In this work two membranes representing different classes of porous materials were studied: ∗ Corresponding author. (Fax: +30-31/498-380, E-mail: kikki@cperi.certh.gr) –A γ-Al 2 O 3 mesoporous pellet, prepared by symmetrical compaction of aluminium oxide powder [8]. – A commercial α-Al 2 O 3 macroporous membrane in fiber form. The membranes were characterized by N 2 (γ-Al 2 O 3 ) and Hg (α-Al 2 O 3 ) porosimetry. The porosity measured is reported in Table 1, while the pore size distributions deduced are plot- ted in Fig. 1c and d respectively. The γ-Al 2 O 3 membrane was attached to a permeability rig [9], outgassed under high vac- uum at 200 ◦ C and the differential steady-state permeability of N 2 and He was measured at mean pressures ranging from 1 to 60 bar. The measurements were carried out by keep- ing both sides of the membrane under pressure while main- taining a constant small pressure head (1 bar) on the high- pressure side. The permeability was calculated after monitor- ing the pressure change on the low-pressure side. Following Barrer [10] proper corrections were performed in order to subtract the Knudsen and slip flow contributions and thus extract only the viscous component of the overall permea- bility measured. The validity of corrections was confirmed, since the values calculated for both gases were identical. The permeability of the macroporous α-Al 2 O 3 membrane was measured after attaching the membrane to an air cylinder equipped with a pressure reducer. Air (1–10 bar) was ad- mitted to the high-pressure side of the membrane, and the volume flow was measured by a soap flowmeter attached to the low-pressure side, while the pressure head was monitored by means of a differential manometer. The aforementioned corrections for Knudsen and slip flow contribution were also applied. Table 1. Comparison between calculated permeability ( P sim ) of the recon- structed porous materials and experimental values ( P exp ) Material ε P exp (m 2 ) P sim (m 2 ) Mesoporous γ-Al 2 O 3 0.42 4.0 × 10 -19 3.1 × 10 -19 Macroporous α-Al 2 O 3 0.355 2.5 × 10 -17 2.0 × 10 -17