Please use this identifier to cite or link to this item:
http://elar.urfu.ru/handle/10995/101803
Title: | Phase transformations in metastable liquids combined with polymerization |
Authors: | Ivanov, A. A. Alexandrova, I. V. Alexandrov, D. V. |
Issue Date: | 2019 |
Publisher: | Royal Society Publishing |
Citation: | Ivanov A. A. Phase transformations in metastable liquids combined with polymerization / A. A. Ivanov, I. V. Alexandrova, D. V. Alexandrov. — DOI 10.1098/rsta.2018.0215 // Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. — 2019. — Vol. 377. — Iss. 2143. — 20180215. |
Abstract: | This paper is concerned with the theory of nucleation and growth of crystals in a metastable polymer melt with allowance for the polymerization of a monomer. A mathematical model consisting of the heat balance equation, equations governing the particle-radius distribution function and the polymerization degree is formulated. The exact steady-state analytical solutions are found. In the case of unsteady-state crystallization with polymerization, the particle-size distribution function is determined analytically for different space-time regions by means of the Laplace transform. Two functional integrodifferential equations governing the dimensionless temperature and polymerization degree are deduced. These equations are solved by means of the saddlepoint technique for the evaluation of a Laplace-type integral. The time-dependent distribution function, temperature and polymerization degree at different polymerization rates and nucleation kinetics are derived with allowance for the main contribution to the Laplace-type integral. In addition, the general analytical solution by means of the saddle-point technique and an example showing how to construct the analytical solutions in particular cases are given in the appendices. The analytical method developed in the present paper can be used to describe the similar phase transition phenomena in the presence of chemical reactions. This article is part of the theme issue 'Heterogeneous materials: Metastable and nonergodic internal structures'. ©2019 The Author(s)Published by the Royal Society. |
Keywords: | CRYSTALLIZATION METASTABLE LIQUID NUCLEATION POLYMERIZATION CHEMICAL ANALYSIS CRYSTALLIZATION DISTRIBUTION FUNCTIONS FUNCTIONS INTEGRODIFFERENTIAL EQUATIONS LAPLACE TRANSFORMS NUCLEATION PARTICLE SIZE PARTICLE SIZE ANALYSIS POLYMER MELTS DIMENSIONLESS TEMPERATURES GENERAL ANALYTICAL SOLUTION HEAT BALANCE EQUATIONS HETEROGENEOUS MATERIALS LAPLACE-TYPE INTEGRALS METASTABLE LIQUID PHASE TRANSITION PHENOMENON POLYMERIZATION DEGREE POLYMERIZATION |
URI: | http://elar.urfu.ru/handle/10995/101803 |
Access: | info:eu-repo/semantics/openAccess |
SCOPUS ID: | 85062412773 |
WOS ID: | 000465497000013 |
PURE ID: | 9963a66b-bfab-48dc-9b9f-897a5b62aad8 9063482 |
ISSN: | 1364503X |
DOI: | 10.1098/rsta.2018.0215 |
Appears in Collections: | Научные публикации ученых УрФУ, проиндексированные в SCOPUS и WoS CC |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
2-s2.0-85062412773.pdf | 598,32 kB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.