arXiv subjects

B. Zilbergleyt

Publications and source records attributed to B. Zilbergleyt.

At least 19 recordsLinked to original sources

arXiv2012

Thermodynamic Branch in the Chemical System Response to External Impact

The paper gives an account of a detailed investigation of the thermodynamic branch as a path of the chemical system deviation from its isolated thermodynamic equilibrium under an external impact. For a combination of direct and reverse reactions in the same chemical system, full thermodynamic branch is presented by an S-shaped curve, whose ends asymptotically achieve appropriate initial states, which, in turn, are logistic ends of the opposite reactions. The slope tangents of the steepest parts of the curves, the areas of the maximum rate of the shift growth vs. the external thermodynamic force, occurred to be directly proportional to the force and, simultaneously, linearly proportional to the thermodynamic equivalent of chemical reaction, which is the ratio between the amount in moles of any reaction participant, transformed in an isolated system, along the reaction way from its initial state to thermodynamic equilibrium, to its stoichiometric coefficient. The found linearity is valid for arbitrary combination of the stoichiometric coefficients in a reaction of compound synthesis from chemical elements like aA+bB=AaBb, and confirms the exclusive role of the thermodynamic equivalent of transformation as the chemical system characteristic of robustness and irreversibility. Results of this work allow for quantitative evaluation of the chemical system shift from thermodynamic equilibrium along thermodynamic branch and its rate vs. the shifting force. Such an investigation became possible due to the development of discrete thermodynamics of chemical equilibria.

physics.gen-ph↗

arXiv2011

New Thermodynamic Paradigm of Chemical Equilibria

The paper presents new thermodynamic paradigm of chemical equilibrium, setting forth comprehensive basics of Discrete Thermodynamics of Chemical Equilibria (DTd). Along with previous results by the author during the last decade, this work contains also some new developments of DTd. Based on the Onsager's constitutive equations, reformulated by the author thermodynamic affinity and reaction extent, and Le Chatelier's principle, DTd brings forward a notion of chemical equilibrium as a balance of internal and external thermodynamic forces (TdF), acting against a chemical system. Basic expression of DTd is the chemical system logistic map of thermodynamic states that ties together energetic characteristics of chemical reaction, occurring in the system, the system shift from "true" thermodynamic equilibrium (TdE), and causing that shift external thermodynamic forces. Solutions to the basic map are pitchfork bifurcation diagrams in coordinates "shift from TdE - growth factor (or TdF)"; points, corresponding to the system thermodynamic states, are dwelling on its branches. The diagrams feature three typical areas: true thermodynamic equilibrium and open equilibrium along the thermodynamic branch before the threshold of its stability, i.e. bifurcation point, and bifurcation area with bistability and chaotic oscillations after the point. The set of solutions makes up the chemical system domain of states. The new paradigm complies with the correspondence principle: in isolated chemical system external TdF vanish, and the basic map turns into traditional expression of chemical equilibrium via thermodynamic affinity. The theory binds together classical and contemporary thermodynamics of chemical equilibria on a unique conceptual basis. The paper is essentially reworked and refocused version of the earlier preprint on the DTd basics, supplemented with new results.

physics.gen-ph↗

arXiv2011

General Expression for the Chemical System Response to External Impact

The paper presents amended basic map of states of chemical systems in discrete thermodynamics of chemical equilibria. Uniting two previously found basic map types in one and covering a wider range of situations, it allows us to obtain more detailed pictures and deeper understanding of what is the general chemical system response to the external impact. Amended in this work general expression allows for more flexibility in the response treatment. Graphical solutions to the map, bifurcation diagrams, contain the monostable thermodynamic branch prior to and the bi-stable area after the bifurcation point. On the static diagrams the first consists of two areas - true thermodynamic equilibrium and open equilibrium; the first area is skipped on the dynamic diagrams. In the bi-stable area, the system stresses, caused by further increase of the external impact, discharge themselves through chaotic oscillations, enveloped by two bifurcation sub-branches. Now bifurcation diagrams, corresponding to the amended map, are essentially closer to some experimental graphs, obtained, for instance, in experiments with electrochemical systems.

physics.chem-ph↗

arXiv2010

Variational principles in chemical equilibria: Complex chemical systems with interacting subsystems

The goal of the paper is to derive a revised condition of global equilibrium in complex chemical systems as variational principle in formalism of recently developed discrete thermodynamics (DTD) of chemical equilibria. In classical approach the problem of complex equilibrium is solved by minimization of the system Gibbs' free energy subject to logistic constraints. DTD demands any isolated system to comprise smaller subentities, which individual equilibria are based on the balance of internal and external thermodynamic forces, acting against them. The internal forces are equal to the subsystems thermodynamic affinities, while external forces originate from subsystems mutual interactions. Those interactions impose additional constraints on the mother system Gibbs' free energy minimum. Basic expression of discrete thermodynamics, being multiplied by subsystems deviations from their "true" thermodynamic equilibria, is naturally identical to d'Alembert's principle. A thermodynamic version of d'Alembert's principle in combination with derived from it thermodynamic version of the principle of virtual work, allowed us to express the interactive constraints as a condition, that the sum of all subsystems thermodynamic affinities, multiplied by their deviations from their "true" equilibria, must be equal to zero. The revised formula of global equilibrium condition in complex chemical systems contains three terms - system Gibbs' free energy, logistic constraints, identical to their classical version, and interactive constraints, originated from the subsystems mutual interactions.

physics.chem-ph↗

arXiv2010

Thermodynamically predicted oscillations in closed chemical systems

All known up to now models of chemical oscillations are based exclusively on kinetic considerations. The chemical gross-process equation is split usually by elementary steps, each step is supplied by an arrow and a differential equation, joint solution to such a construction under certain, often ad hoc chosen conditions and with ad hoc numerical coefficients leads to chemical oscillations. Kinetic perception of chemical oscillations reigns without exclusions. However, as it was recently shown by the author for the laser and for the electrochemical systems, chemical oscillations follow also from solutions to the basic expressions of discrete thermodynamics of chemical equilibria. Graphically those solutions are various fork bifurcation diagrams, and, in certain types of chemical systems, oscillations are well pronounced in the bistable bifurcation areas. In this work we describe a general thermodynamic approach to chemical oscillations as opposite to kinetic models, and depict some of their new features like spontaneity and fractality. The paper doubts exclusivity of the kinetic approach to chemical oscillations, and its aim is to discuss and exemplify thermodynamically predicted chemical oscillations in closed chemical systems.

physics.chem-ph↗

arXiv2009

On Discrete Thermodynamics of Electrochemical Systems and Electrochemical Oscillations

The article presents results of discrete thermodynamics (DTD) basic application to electrochemical systems. Consistent treatment of the electrochemical system as comprising two interacting subsystems - the chemical and the electrical (electrochemical) - leads to ln-logistic map of states of the electrochemical system with non-unity coefficient of the electrical charge transfer. This factor provides for a feedback and causes dynamic behavior of electrochemical systems, including bifurcations and electrochemical oscillations. The latter occur beyond bifurcation point at essential deviation of the chemical subsystem from true thermodynamic equilibrium. If the charge transfer coefficient takes on unity, the map turns into classical equation of electrochemical equilibrium. Spectra of electrochemical oscillations, resulted from the DTD formalism, are multifractals. Graphical solutions of this work are qualitatively compared to some experimental results.

physics.chem-ph↗

arXiv2008

Discrete Thermodynamics of Chemical Equilibria

The paper sets forth comprehensive basics of Discrete Thermodynamics of Chemical Equilibria (DTD), developed by the author during the last decade and spread over series of publications. Based on the linear equations of irreversible thermodynamics, De Donder's definition of the thermodynamic force, and the Le Chatelier principle, DTD brings forward a notion of chemical equilibrium as a balance of internal and external thermodynamic forces, acting against a chemical system. The basic expression of DTD is a logistic map that ties together energetic characteristics of the chemical transformation in the system, its deviation from true thermodynamic equilibrium, and the sum of thermodynamic forces, causing that deviation. System deviation from thermodynamic equilibrium is the major variable of the theory. Solutions to the basic map define the chemical system domain of states comprising bifurcation diagrams with four areas, from true thermodynamic equilibrium to chaos, having specific distinctive meaning for chemical systems. The theory is derived from the currently recognized ideas of chemical thermodynamics and binds classical and contemporary thermodynamics of chemical equilibria into a unique concept. DTD opens new opportunities in understanding and analysis of equilibria in chemical systems. Some new results, included in the paper, have never been published before.

physics.chem-ph↗

arXiv2008

Equilibrium Constant as Solution to the Open Chemical Systems

According to contemporary views, equilibrium constant is relevant only to true thermodynamic equilibria in isolated systems with one chemical reaction. The paper presents a novel formula that ties-up equilibrium constant and chemical system composition at any state, isolated or open as well. Extending the logarithmic logistic map of the Discrete Thermodynamics of Chemical Equilibria, this formula maps the system population at isolated equilibrium into the population at any open equilibrium at p,T=const, using equilibrium constant as a measure. Real chemical systems comprise multiple subsystems; given the resources are limited, joint solution to the set of such expressions, each relevant to a specific subsystem, gives equilibrium composition for each of them. This result means a fundamental break through in the open systems thermodynamics and leads to formerly unknown opportunities in the analysis of real chemical objects.

physics.chem-ph↗

arXiv2007

Chemical System Complexity and Bifurcation Point: a New Relationship

The article introduces a new relationship between the chemical system complexity and deviation of its bifurcation point from thermodynamic equilibrium. In the formalism of discrete thermodynamics of chemical equilibria, simulation of numerous equilibrium cases with regards to complexity of the reaction hosting systems has lead to a conclusion that the system deviation from thermodynamic equilibrium at the bifurcation point is directly proportional to logarithm of the system complexity parameter. With this relationship one can predict the efforts that are sufficient to destabilize the system thermodynamic branch and achieve the bifurcations area.

physics.chem-ph↗

arXiv2007

Discrete Thermodynamics of Lasers

The paper offers a discrete thermodynamic model of lasers. Laser is an open system; its equilibrium is based on a balance of two thermodynamic forces, one related to the incoming pumping power and another to the emitted light. The basic expression for such equilibrium is a logistic map, graphical solutions to which are pitchfork bifurcation diagrams. As pumping force increases, the relative populations on the ground and lasing branches tend to zero and unity correspondingly. An interesting feature of this model is the line spectrum of the up and down transitions between the branches beyond bifurcation point. Even in a simple case of 2-level laser with only 2 possible transition types (up and down), the spectra look like sets of the line packets, starting well before the population inversion. This effect is an independent confirmation of the Einstein's prohibition on practical realization of 2-level laser. Multilevel lasers may be approached by employing the idea of thermodynamic activity for the emitting atoms. Considering coefficient of thermodynamic activity of the lasing level atoms to be proportional to the ratio of life times on the upper and lasing (the 3d) levels, one can derive a new basic map for the multilevel laser system. For a modest ratio only of 0.01, spontaneous transitions between levels are pushed to the area beyond population inversion, opening a space for the functioning of laser.

physics.optics↗

arXiv2006

Discrete Thermodynamics And Emergence Of Bifurcations In The Chemical Systems

The paper investigates emergence of pitchfork bifurcations in the chemical systems. The systems may be split conditionally by two groups, the strong and the weak, depending upon system complexity and its potential response to the external impact. This work investigates birth and development of bifurcations in the systems of both types. As a special case of a weak system with high degree of the equilibrium transformation, emergence of bifurcations was studied in the discrete thermodynamic model of 2-level laser.

physics.chem-ph↗

arXiv2006

Discrete Thermodynamics of 2-level Laser - Why Not and When Yes

The paper explores a possible application of the discrete thermodynamics to a 2-level laser. The model accounts for the laser openness to incoming pumping power and coming out energy with the emitted light. As an open system, a laser should be in open equilibrium with thermodynamic forces, related to both energy flows. Conditions of equilibria are expressed by a logistic map with specially developed dynamic inverse pitchfork bifurcation diagrams for graphical presentation of the solutions. The graphs explicitly confirm the triggering nature of a laser where bistability is manifested by pitchfork ground and laser branches, with the relative population equilibrium values close to 1 and 0 correspondingly. Simulation was run for a 2-level laser emitting light from far infrared to short wave UV. A newly discovered feature of such a laser is the line spectrum of up and down transitions of the laser excitable dwellers, occurring between the laser and the ground pitchfork branches beyond bifurcation point. The density of the spectra lines tangibly increases as the branches approach their limits. Transitions of both types are overlapping in opposite phases. This effect is a new confirmation of the Einstein's prohibition on practical realization of a 2-level laser. Wide enough gaps between the lines of the spectra were also discovered in this research. The gaps are shielding the light irradiation and may be considered as potential areas of control over the 2-level laser emissions.

physics.chem-ph↗

arXiv2005

Domains of States of Chemical Systems: Le Chatelier Response, Structure of the Domains and Evolution

The paper investigates influence of the Le Chatelier response on the chemical system behavior under stress, the shape of its domains of states in terms of static and dynamic bifurcation diagrams, and the system proneness to evolution. The usage of maps in thermodynamics of chemical systems is discussed. Thermodynamics of chemical triggers, designed in similarity with laser, is described. Results of this work are important in context of new model of chemical equilibrium.

physics.chem-ph↗

arXiv2005

Le Chatelier Response

The article investigates a possible influence of the open chemical system reaction to the external impact on the system transition to a new equilibrium. Potential system response is taken as a combination of various powers of the reaction shift from thermodynamic equilibrium, leading to different equations for the system Gibbs' free energy change. The investigation is focused on two types of the constraints which are put on the system - the "soluble", disappearing when the stressed system achieves its new equilibrium, as it happens in result of a temperature change, and "insoluble", still remaining active in the new equilibrium. It was assumed that the "soluble" constraints activate a wider selection of the reaction shift powers as the system Le Chatelier response, providing for a smooth transition between two equilibrium states. The "insoluble" constraints may suppress some higher powers in the response set, and transition may be accompanied by bifurcations.

physics.chem-ph↗

arXiv2005

Forecast of the Chemical Aging and Relevant Color Changes in Painting

The article describes the potential application of thermodynamic simulation to forecast chemical aging and relevant color changes in painting. Qualitative and numerical results were obtained by applying the method to various mixtures of pigments without and with atmospheric components. The results were compared to the legendary recommendations on incompatible pigment mixtures with about an 80 percent match regarding potential color changes in the aged mixtures. Results for the cadmium yellow-lead white and cadmium lemon-emerald green mixtures are illustrated by pictures, gradually showing color changes caused by the aging. The method of thermodynamic simulation can be a powerful tool to investigate old masterpieces, in developing new materials, and to forecast some aspects of the aging of real masterpieces.

physics.chem-ph↗

arXiv2004

Peculiarities of Thermodynamic Simulation with the Method of Bound Affinity

Thermodynamic simulation of chemical and metallurgical systems is the only method to predict their equilibrium composition and is the most important application of chemical thermodynamics. The conventional strategy of simulation is always to find the most probable composition of the system, corresponding to thermodynamic equilibrium. Traditional simulation methods do not account for interactions within the chemical system. The Method of Bound Affinity (MBA) is based on the theory that explicitly takes into account interactions between subsystems of a complex chemical system and leads sometimes to essential differences in simulation results. This article discusses peculiarities of MBA application, exemplified by results for a complex system with a set of subsystems.

physics.chem-ph↗

arXiv2004

Chemical Equilibrium as Balance of the Thermodynamic Forces

The article sets forth comprehensive basics of thermodynamics of chemical equilibrium as balance of the thermodynamic forces. Based on the linear equations of irreversible thermodynamics, De Donder definition of the thermodynamic force, and Le Chatelier's principle, new thermodynamics of chemical equilibrium offers an explicit account for multiple chemical interactions within the system. Basic relations between energetic characteristics of chemical transformations and reaction extents are based on the idea of chemical equilibrium as balance between internal and external thermodynamic forces, which is presented in the form of a logistic equation, containing only one new parameter. Solutions to the basic equation define the domain of states of the chemical system, from true equilibrium to true chaos. The new theory is derived exclusively from the currently recognized ideas and covers equilibrium thermodynamics as well as non-equilibrium thermodynamics in a unique concept.

physics.chem-ph↗

arXiv2002

Equation of State of Chemical System: From True Equilibrium to True Chaos

The article presents results of preliminary study of solutions to recently offered basic thermodynamic equation for equilibrium in chemical systems with focus on chaotic behavior. Classical part of that equation was investigated earlier in a series of papers. In this work a similarity between one-dimensional logistic map and non-classical (chaotic) term of the equation was discussed to introduce the problem. Results of this work allow us to evaluate the region where open equilibrium belongs to the basin of regular attractor and leads to trivial solutions with zero deviation from true thermodynamic equilibrium, and then to find first bifurcation threshold as a limit of open equilibrium and a limit of the classical region as well. Features of the basic equation are discussed with regard to relative values of the chaotic and thermodynamic temperatures. Obtained results prompt us to consider the basic equation of new theory to be the general equation of state of chemical systems.

physics.chem-ph↗