In-silico simulation of porous media: Conception and development of a greedy algorithm G. Román-Alonso a , F. Rojas-González b,⇑ , M. Aguilar-Cornejo a , S. Cordero-Sánchez b , M.A. Castro-García a a Departamento de Ingeniería Eléctrica, Universidad Autonóma Metropolitana – Iztapalapa, P.O. Box 55-534, México DF, Mexico b Departamento de Química, Universidad Autonóma Metropolitana – Iztapalapa, P.O. Box 55-534, México DF, Mexico article info Article history: Received 27 May 2010 Received in revised form 23 August 2010 Accepted 24 August 2010 Available online 31 August 2010 Keywords: Interconnected void network Dual Site-Bond Model Optimization algorithms Monte Carlo method Computational complexity abstract Cubic porous networks consisting of several millions of voids of different sizes are efficiently simulated through a greedy algorithm. The porous network is built on the basis of the Dual Site-Bond Model in which a cavity (site) is always larger than any of its delimiting throats (bonds). When the initial config- uration of the cubic network is established by means of a random (Monte Carlo) seeding on a lattice of sites and bonds, the proper allocation of more pore elements becomes troublesome and time-consuming, and there even exists the chance of not achieving a valid pore network. The complexity of this pioneering Monte Carlo algorithm, in the best case, increases according to the third power of the number of pore ele- ments and, in the worst case is asymptotic to infinity. Here, we have succeeded in the development of an smart non-mistake initial seeding situation of sites and bonds that behaves in the way of a greedy algo- rithm. An initial ordering of sites according to their sizes allows a proper assemblage of these hollows throughout the cubic lattice. From this configuration, the pore network evolves toward the most probable one by a series of legitimate random swappings between sites and bonds. The complexity of the greedy algorithm remained proportional to the cubic power of the total number of sites. In general the execution time of the greedy algorithm results to be faster than that employed with the previous Monte Carlo algorithm. Ó 2010 Elsevier Inc. All rights reserved. 1. Introduction: the conception of a porous network from the concepts of sites and bonds Porous media are complex systems in which a huge amount of pore entities (usually millions, billions and even trillions of them per unit mass of solid) are dispersed within the interior of a solid ma- trix. The term complex applies due to the complicated morphology that the voids can display and the intricate topological way in which they can be distributed and interconnected. The dimensions of the voids in a mesoporous solid range within the nanometric scale, i.e. from 1 nm to 50 nm. These pores are generally interconnected to each other to conform sinuous 3-D (and only occasionally simple) pathways; nevertheless, with the progress of synthetic chemical routes for the nanoscale preparation of mesoporous materials or- dered 2- or 1-D porous networks have also been synthesized [1]. The importance of porous solids rests on the extensive surface area and large pore volume that these substrates can reach. Depending on the pore size and density of the solid phase, surface areas can be as high as 2600 m 2 g 1 and porosities as large as 99%. Obviously, in the case of catalytic or sorption applications, the val- ues of these two parameters are strategic for reaching good perfor- mances in these processes. An ancient classification [2] of porous media involves two specimen classes: corpuscular and spongy. The corpuscular term applies when individual nanoparticles can be discerned; conversely, the spongy term refers to those systems in which it is not obvious to isolate individual nanoparticles from the solid matrix. As examples, xerogels usually correspond to cor- puscular bodies while zeolites can be classified as spongy materi- als. A characteristic, which is definitely the basic feature that a real porous network displays (see Fig. 1(a)), is the fact that cavities or chambers (named as sites) are surrounded by a number of throats, windows or necks (named as bonds) through which the former voids connect to each other. An intuitive property of such a porous network is that cavities always possess larger sizes than their surrounding throats. This idea constitutes the basic Construc- tion Principle (CP) that was employed to develop the Dual Site-Bond Model (DSBM) of porous structures [3]. In order to advance theoretically in the visualization of porous networks, sites can be simply assumed as spherical voids which are connected to homologous elements by a number of cylindrical throats (see Fig. 1(b)). In this way, the probability, SðR S Þ, to choose a site of size R S or smaller from a certain distribution F S ðR S Þ of site sizes expressed on a number-of-elements basis is given by: 1387-1811/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.micromeso.2010.08.016 ⇑ Corresponding author.Tel.: +52 5558044672; fax: +52 5558044666. E-mail addresses: grac@xanum.uam.mx (G. Román-Alonso), fernando@xanum. uam.mx (F. Rojas-González), mac@xanum.uam.mx (M. Aguilar-Cornejo), scs@ xanum.uam.mx (S. Cordero-Sánchez), mcas@xanum.uam.mx (M.A. Castro-García). Microporous and Mesoporous Materials 137 (2011) 18–31 Contents lists available at ScienceDirect Microporous and Mesoporous Materials journal homepage: www.elsevier.com/locate/micromeso