L.Yu. Ammon - Ph.D. (Eng.), LLC «BIT Intelligent Technology» (Saint-Petersburg). E-mail: luds-a@yandex.ru
V.A. Tupik - Dr.Sc. (Eng.), Associate Professor, Deputy-Rector for International Relations, Saint-Petersburg State Electrotechnical University «LETI» n. a. V. I. Ulyanov (Lenin). E-mail: vatupik@yandex.ru
I.D. Zhabrev - Post-graduate Student, Saint-Petersburg State Electrotechnical University «LETI» n. a. V. I. Ulyanov (Lenin). E-mail: vazabrev2009@rambler.ru

Typically, the sol-gel technology used by hydrolysis of tetraethoxysilane Si (OC2H5)4 + H2O  SiO2 - H2O + C2H5OH or alkaline hydrolysis reaction of silica SiO2 + NaOH  Na4SiO4 + H2O [1]. Structure-forming unit in these reactions is the acid anion orthosilicic [SiO4/2]-4. The spatial structure of this anion is represented as a tetrahedron, in which the silicon atom (from hybridization sp3) is bonded to four oxygen atoms. The average bond length between silicon and oxygen is 0.163 nm, tetrahedral covalent radius of the group is equal to 0.117nm [2]. Regularities of the formation of monomers, dimers, trimers and associates of greater complexity (the effect of temperature, pH, reaction time, etc.) can lead to an understanding of the formation of stable nanoparticles. In this article considers computer model of cluster formation, which consists of silicon-oxygen tetrahedra, similar to the process of polycondensation of the hydrolysis products of tetraethoxysilane. The geometrical structure of the silicon tetrahedron appears to be regular tetrahedron: all of its faces - equilateral triangles, all vertices are equidistant from the center of a tetrahedron. At the vertices of the tetrahedron situated atoms of oxygen, and in the center - the silicon atom. The initial construction of a cluster is a single silicon-oxygen tetrahedron which is located at the origin of a three-dimensional coordinate system. Then initiates an iterative process consisting of formation of regular particles, determining the attachment point, calculation of new coordinates and adding this particle in the sequence representing the cluster in memory. The choice of the attachment point to another particle cluster is random, but each vertex of the tetrahedron has some variational parameter - weight coefficient, which is counted in the determination common point of two tetrahedra. Thus, through the weight coefficients implemented a model representation of the chemical nature and length of the bonds between the atoms of the molecules and their influence on the structuring of the cluster. The second important point simulation is the mechanism of cluster growth, the way in which cluster members are connected to each other. In the natural crystalline silicate systems can be observed band structures when silicon-oxygen tetrahedra are located on some lines, consisting of chains of Si-O?Si and island structures with closed-loop tetrahedral groups. In amorphous silicates, the tetrahedral groups arranged more chaotic. It is believed that in such systems, there are short-range order when the two tetrahedral groups are linked to each other almost on the center line of the silicon atoms or with a slight deviation from linearity at an angle . The accumulation of such variations leads to disruption of the regularity of the structure. These structural representations have been incorporated into the developed model as the angle of deviation from linearity. The physical picture of cluster formation is that the particles, that involved in this formation, are presented of a regular tetrahedron. Connection between two particles occurs through a common vertex (oxygen atom). The orientation of the two connecting particles in the cluster is as follows: first, the silicon atoms and the total (bridging) oxygen atom is located on a straight line, and secondly, the remaining oxygen atoms are most distant from each other. An additional condition of the model is the opportunity to set some deviation from the angle of 180°, when attaching a new particle to an element of the cluster. Thus, in addition to growth rates, there is another parameter of the modeled system - the maximum deflection angle for the docking of two silicon-oxygen tetrahedra. Here are results of simulation, which uses a combination of different values of weights and maximum deflection angles. In this paper was simulated the process of polycondensation of the products of hydrolysis of tetraethoxysilane. The adopted model assumptions suggest that the model adequately describes the process of nanoparticle formation in a real chemical reaction. The developed software allows visually monitor the growth dynamics of the cluster. According to the results of computer simulation determined the dependence of the average number of molecules cluster, which results in a closed structure, on the system parameters: the angle of deflection that occurs when molecules and docking factor that determines the degree of linear growth of the cluster.

 

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