Abstract
The study of topological invariants of phase diagrams allows for the development of a qualitative theory of the processes being researched. Studies of the properties of objects in the same equivalence class may be carried out with the aim of predicting the properties of unexplored objects from this class, or predicting the behavior of a whole system. This paper describes a number of topological invariants in vapor–liquid, vapor–liquid–liquid and liquid–liquid equilibrium diagrams. The properties of some invariants are studied and illustrated. It is shown that the invariant of a diagram with a miscibility gap can be used to distinguish equivalence classes of phase diagrams, and that the balance equation of the singular-point indices, based on the Euler characteristic, may be used to analyze the binodal-surface structure of a quaternary system.
Highlights
In chemistry and chemical technology, both numerical and qualitative methods are actively used to study different phenomena and systems
Universal singular-points-indices balance equation, based on use of the Euler characteristic, was singular-points-indices balance equation, based on use of the Euler characteristic, was shown to be possible for various object types. It was confirmed by applying the balance equation to analysis of liquid–solid-equilibrium diagrams [20,21,22]
The difference of liquid–solid-equilibrium diagrams from VLE diagrams was in the greater variety of singular points in the latter
Summary
In chemistry and chemical technology, both numerical and qualitative methods are actively used to study different phenomena and systems. The solution to a problem using numerical methods is a fixed result. The use of qualitative methods (dynamical systems theory, group theory, topology, set theory, etc.) allows for the study of the properties of models or objects in general and creates various theories with predictive capabilities. The theory of equilibrium in heterogeneous systems, based on the invariant representation of the Gibbs zero potential, was created using this approach. It has been successfully developed in the research of A.V. Storonkin [1] and his successors. The application of basic concepts of topology and a series of invariants made it possible for thermodynamic–
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