Bifurcation and "self-organization" of a system

Abstract

Absrtact. Triangulation of a multicomponent system was shown on example of the CaO-SiO 2 -H 2 O system. "The Gibbs function normalized to the total number of electrons" was applied in order to reflect all the possible transformations of components of the system at non-equilibrium as well as at equilibrium conditions. The bifurcation points of the system are located at the each intersection of the line connected compositions of the interacting components and the stable secant line. It was shown the possibility of the "self-organization" processes which is based on the exchange as well as that reactions. IntroductionNatural and technological objects are represented by multicomponent systems. Chemical and physicochemical interactions of these systems are defined by the substance microstates. Geometric images of the multicomponent systems can be represented by the phase diagram which is based on the continuity and consistency principles [1] which reflects the transformation processes between components of a system. The "structure-property" diagram is the precise geometric model of the complex functions which are establishing the relationship between temperature, volume, concentration and the other physical and chemical factors which are determining the state of the open system. In other words, the "structure-property" diagram merges together chemical transformations of matter and space geometric transformations into one whole. The phase diagram allows to define phase boundaries of the different phases existing in the system as well as to reveal not pronounced chemical processes. Additionally it allows to high light the weak interparticle interactions that do not lead to the formation of new compounds or to the decomposition of existing phases [2]. The phase diagrams enables widely consider problems of physical chemistry and chemical thermodynamics, reflecting modern ideas about the properties of individual substances as well as their mixtures, phase and chemical equilibria, and surface phenomena jointly. They are widely used in search of new intermetallic compounds [3][4][5], the glass-forming systems in the crystalline, glassy and molten states [6][7][8], solid solutions [9,10], predicting of the properties of metastable states [11][12][13] , analysis of phase transitions and critical phenomena [14,15], the fabrication of composite materials [16,17], the processes of separation and purification of substances [18,19], the development of algorithms for constructing phase diagrams [20][21], and others [22][23][24][25] presently.Study of the phase diagrams implies partitioning of the multidimensional figures on individual cells -media of the invariant points which are called triangulation. The topological [1,2], geometric [26,27] and thermodynamic [28,29] triangulation techniques are available at this moment. The main feature of the systems triangulation is the determination of the constituents forming only eutectic composition (single phase units). The constituents of a single phase unit do not form new compounds and ...

Production Entropy and Negentropy

“…The bifurcation points in the CaO-SiO 2 -H 2 O system were determined based on the triangulation of the system [7,8]. Triangulation of the CaO-SiO 2 -H 2 O system (Figure 1) and the method for studying the processes of transformation of components are fully described in [8][9][10][11][12][13].…”

“…The bifurcation points in the CaO-SiO 2 -H 2 O system were determined based on the triangulation of the system [7,8]. Triangulation of the CaO-SiO 2 -H 2 O system (Figure 1) and the method for studying the processes of transformation of components are fully described in [8][9][10][11][12][13]. Thermodynamic parameters of the compounds: "The Gibbs function normalized to the total number of electrons", "Average electron heat capacity", "Average electron entropy" for the initial compounds in the solid state for the examples under consideration are given in Table 1.…”

Bifurcation Sequence

“…This function characterizes accumulation of the Gibbs energy density on molecular bonds. At the formation of bonds, "The Gibbs function normalized to the total number of electrons" adequately responds to all changes in the structure of the compound, allows to judge the reactivity of the compound its stability [8], to determine the value of the chemical potential and affinity, to calculate the production and flow of entropy, thermodynamic force and flow, thermodynamic "probability" of the interaction, the conversion degree of components in the course of a chemical reaction, to describe the processes of "self-organization" [10], to carry out triangulation of multicomponent systems and to determine mechanisms of reactions. "The Gibbs function normalized to the total number of electrons" is interpreted by us as the chemical potential of a substance, that is 298 in chemical reactions can be considered.…”