CMM-2011 – Computer Methods in Mechanics 9–12 May 2011, Warsaw, Poland CMM-2011 – Computer Methods in Mechanics 9–12 May 2011, Warsaw, Poland CMM-2011 – Computer Methods in Mechanics 9–12 May 2011, Warsaw, Poland Computer method for modeling the micro-structure of aerogel Imre Varga 1 and Ferenc Kun 2 1 Department of Informatics Systems and Networks, University of Debrecen P.O.box 10, H-4010 Debrecen, Hungary e-mail: varga.imre@inf.unideb.hu 2 Department of Theoretical Physics, University of Debrecen P.O.box 5, H-4010 Debrecen, Hungary e-mail: feri@dtp.atomki.hu Abstract We present a variant of the recently developed void expansion method (VEM) to generate random heterogeneous materials with a highly porous micro-structure. A polydisperse mixture of structural and void particles is generated by gradually expanding randomly placed initially point-like objects. Computer simulations revealed that varying the volume fraction of void and structural particles a percolation transition occurs where the critical volume fraction can be tuned by the relative volume fraction of the two components. We achieved critical volume fractions down to 0.05 which enables us to model the structure of aerogels. A detailed analysis of the micro-structure of VEM clusters is presented. Keywords: porous media, micro-structures 1. Introduction Aerogels have been in the focus of considerable scientific in- terest in recent years. This interest was mainly stimulated by its special physical properties. Aerogel is a manufactured material, derived from a gel in which the liquid component of the gel has been replaced with a gas. The result is the lowest bulk density of any known porous solid. Except for this, aerogels exhibit several additional extreme features. In spite of its large-scale porosity it has a considerable mechanical strength, it has very low thermal- and electrical conductivity, it has huge surface-to-volume frac- tion, it is transparent with almost the same reflection coefficient as air, etc. Due to these extreme properties aerogels are candidates for a large number of potential applications from space investi- gations through optics, nuclear physics, low-temperature physics and acoustics to microelectronics and electrical engineering [1]. Several experimental techniques have been used to carefully an- alyze the structure of aerogels of different materials from small angle neutron scattering to positron annihilation lifetime spec- troscopy [2, 3]. These investigations revealed that on small length scales aerogels have a fractal structure, where the fractal dimen- sion can be controlled by the fabrication process in the range 1.5 − 2.5. Based on these studies, aerogels can be conceived as aggregates of blobs which have fractal characteristics. It is a grate challenge for theoretical investigation to reproduce the complex micro-structure of aerogels and understand their mechanical and fracture behavior in terms of the structural properties. From computational point of view, in the computer model- ing of aerogels we face similar problems to the investigation of granular materials. In both fields particle packings have to con- structed, however, for granular matter typically high, while for aerogels low packing fraction is desired. The fractal nature of the structure of AG poses additional difficulties. Several differ- ent numerical methods have been worked out in the literature for the construction of particle packing which can be classified into two groups: there are physically based method where during the generation process particles interact with each other and the final structure is obtained by computer simulations of the time evolu- tion of the dynamics of the particle ensemble. Other strategies are more formal relaying on mathematical constructions such as Voronoi tessellation and Delaunay tetrahedrization. Investigation of aerogels in the literature are mostly based on the diffusion- limited cluster-cluster aggregation (DLCCA) process [4], mod- eling the physic-chemical process of gelation. The advantage of the method is that it produces well-controlled fractal structures, however, it does not allow for the tuning of the porosity of the system. In the present paper we propose an alternative approach for the computational investigation of structural features of aerogels, namely, we extend the void expansion method and explore its capabilities for the modeling of fractal porous structures. The method is physically based in the sense that during the genera- tion process particles interact through contact forces and move according to Newton’s law. However, compared to other physical approaches such as DLCCA, our method provides the additional advantage of the flexible control of porosity. 2. Generation process We propose an extension of the so-called void expansion method (VEM) which was recently introduced to generate the micro-structure of random heterogeneous materials with a con- trollable porosity [5]. Our final goal is to work out a computer model of aerogels in the framework of which the mechanical re- sponse of aerogels can be analyzed by computer simulations. In our approach a polydisperse mixture of structural and void particles is generated where the two types of spherical particles have two different roles. The final structure is composed by struc- tural particles while the void ones ensure the porosity of the sys- tem. Our model system is a cubic simulation box of side length L containing NS structural particles with radius RS and NV void-particles with radius RV . Three physically relevant parame- ters characterize the generated structures: the volume fraction of structural particles which can define as φS = 4NS π 3L 3 R 3 S , (1)