Critical fluid density obtained from the theory of generalized charges in accordance with the hypothesis on the first co
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ORIGINAL RESEARCH
Critical fluid density obtained from the theory of generalized charges in accordance with the hypothesis on the first coordination number Anatoly M. Dolgonosov 1 Received: 18 June 2020 / Accepted: 9 November 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this article, a model of hard spheres for critical fluid, based on the hypothesis on the coordination number of molecules in minimally bound infinite clusters, is considered. Variants of homogeneous (quasi-crystalline lattice) and heterogeneous (“Cayley tree forest”) molecular packings at the vertices of a uniform graph of order 3 are described. Using the theory of generalized charges and taking into account the found structures, the dependences of the critical molar volume on electronic structure parameters, which have the character of non-empirical laws, are derived. A priori calculations of molar volumes by the critical state model are in good agreement with the reference data for simple gases and linear hydrocarbons. Keywords Critical molar volume . Critical fluid structure . Coordination number . Lennard-Jones potential . van der Waals interaction . Theory of generalized charges
Introduction The task of describing the thermodynamic properties of substances by their electronic structure is of great importance for theoretical chemistry. The apparatus of thermodynamics allows one to calculate those properties from the equation of state of a substance. Despite its simplicity, the van der Waals theory derives the fundamentally important idea of the law of the corresponding states, expressing the equation of state in a universal form, where critical quantities serve as parameters [1–3]. The law of the corresponding states manifests the independence of the critical state problem from thermodynamics. It is clear that the critical parameters are related to the electronic structure of molecules through the characteristics of intermolecular interaction; however, in modern theoretical approaches, such a relationship is very indirect and does not actually have independent value [4–9]. Attempts to find patterns of the relationship of critical parameters with the structure of the molecule have not given universal solutions and theoretical explanation [10]. An example of an indirect connection—through phase densities in equilibrium—is the Guggenheim empirical formula [3, 11], which was applied
* Anatoly M. Dolgonosov [email protected] 1
Vernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, Kosygin Str., 19, Moscow, Russia
together with the theory of generalized charges (TGC) [12–15] to establish the dependence of the surface tension coefficient and critical temperature on the hydrocarbon structure [16]. In [17], it was shown how to establish such relationships under simple assumptions, using TGC without involving experimental data. The hypothesis on the first coordination number of critical fluid molecules put forward in [17] made possible to find regularities that connect the cr
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