Morphological memory of polymers and their use in developing new materials technology

Мелихов, И. В.; Рудин, В. Н.; Алексеева, О. В.; Kozlovskaya, E. D.; Adzhiev, S. Z.

doi:10.1134/s0040579516030088

Cited by 5 publications

(7 citation statements)

References 33 publications

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“…In the present paper, we continue the line of works [5][6][7][8] and others, devoted to mathematical modeling of emerging and growth of hierarchical structures of a dispersed substance, using the kinetic approach.…”

Section: Statement Of the Problemmentioning

confidence: 82%

“…In order to create a nanostructure (and, generally speaking, some kind of structure) with the desired properties, the phenomena of the emerging and the disruption of the original subnanoparticles, the growth and the dissolution, the appearance and the elimination of growth defects, the capture and the release of the captured impurities, the coalescence and the destruction of agglomerates, recrystallization and the topochemical reactions of sintering and the ceramization are used [5][6][7][8][9]. For describing these phenomena we take into account the properties X ≡ {X 1 , X 2 } of each particle:…”

Section: Statement Of the Problemmentioning

confidence: 99%

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Approaches to determining the kinetics for the formation of a nano-dispersed substance from the experimental distribution functions of its nanoparticle properties

Adzhiev¹,

Мелихов²,

Vedenyapin³

2019

Nanosystems: Phys. Chem. Math.

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In the present paper, we discuss the kinetic equations for the evolution of particles of a nanodispersed substance, distinguishing by properties (sizes, velocities, positions, etc.). The aim of the present investigation is to determine the coefficients for the equations by the distribution functions, which are obtained experimentally. The experiment is characterized by the time interval, which is needed for the measurement of the distribution function. However, the nanodispersed substance is obtained from a highly supersaturated solution or vapor and this time interval is large, thus, one is able to measure distribution functions only when the processes of the integration and the fragmentation of the particles become rather slow. So it is advisable to reconstruct the kinetics for the formation of a nanodispersed substance by the experimental distribution functions measured when the processes are rather slow. The first problem that arises is the obtaining of correct equations, and, hence, the derivation of the equations from each other. From the discrete system of equations for the evolution of discrete distribution functions of particles of a nanodispersed substance, we obtain the continuum equation of the Fokker-Planck type, or of the Einstein-Kolmogorov type, or of the diffuse approximation on the distribution function of nanoparticles distinguishing by the numbers of molecules forming them. We consider the distribution functions, which approximate the experimental data. We determine the coefficients for the equation of the Fokker-Planck type by the stationary and non-stationary distribution functions of a nanodispersed substance. Due to unity of the kinetic approach, the present work may be useful for specialists of various areas, who study the evolution of structures (not only with nanosize) with differing properties.

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Section: Statement Of the Problemmentioning

confidence: 82%

Section: Statement Of the Problemmentioning

confidence: 99%

Approaches to determining the kinetics for the formation of a nano-dispersed substance from the experimental distribution functions of its nanoparticle properties

Adzhiev¹,

Мелихов²,

Vedenyapin³

2019

Nanosystems: Phys. Chem. Math.

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“…From (30), we obtain that, for the equilibrium, the following relations for the reaction rate constants hold true:…”

Section: The Condition Of Detailed Balance the Arrhenius Law And Thementioning

confidence: 99%

“…Note that (31) is a more general condition than (30) in cases, where the rate constants of all reactions are given.…”

Section: The Condition Of Detailed Balance the Arrhenius Law And Thementioning

confidence: 99%

“…The microscopic background for the semidetailed balance was found by Ernst Stueckelberg [29] in the Markov microkinetics of the intermediate compounds present in small amounts and whose concentrations are in quasiequilibrium with the main components. Under these microscopic assumptions, the semidetailed balance condition is just the balance equation for the Markov microkinetics according to the Michaelis-Menten-Stueckelberg theorem formulated by Gorban [30]. For chemical kinetics, this condition (known as the complex balance condition) was introduced by Horn and Jackson in 1972 [11].…”

mentioning

confidence: 99%

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Kinetic Equations for Particle Clusters Differing in Shape and the H-theorem

Adzhiev

Batishcheva

Мелихов

et al. 2019

Physics

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The question of constructing models for the evolution of clusters that differ in shape based on the Boltzmann’s H-theorem is investigated. The first, simplest kinetic equations are proposed and their properties are studied: the conditions for fulfilling the H-theorem (the conditions for detailed and semidetailed balance). These equations are to generalize the classical coagulation–fragmentation type equations for cases when not only mass but also particle shape is taken into account. To construct correct (physically grounded) kinetic models, the fulfillment of the condition of detailed balance is shown to be necessary to monitor, since it is proved that for accepted frequency functions, the condition of detailed balance is fulfilled and the H-theorem is valid. It is shown that for particular and very important cases, the H-theorem holds: the fulfillment of the Arrhenius law and the additivity of the activation energy for interacting particles are found to be essential. In addition, based on the connection of the principle of detailed balance with the Boltzmann equation for the probability of state, the expressions for the reaction rate coefficients are obtained.

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Structure and Properties of the Shell of Elementary Aluminum Oxide Yarns

Медведев¹

2021

Fibre Chem

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Morphological memory of polymers and their use in developing new materials technology

Cited by 5 publications

References 33 publications

Approaches to determining the kinetics for the formation of a nano-dispersed substance from the experimental distribution functions of its nanoparticle properties

Approaches to determining the kinetics for the formation of a nano-dispersed substance from the experimental distribution functions of its nanoparticle properties

Kinetic Equations for Particle Clusters Differing in Shape and the H-theorem

Structure and Properties of the Shell of Elementary Aluminum Oxide Yarns

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