Please use this identifier to cite or link to this item: http://hdl.handle.net/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://hdl.handle.net/10995/101803
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85062412773
PURE ID: 9063482
9963a66b-bfab-48dc-9b9f-897a5b62aad8
ISSN: 1364503X
DOI: 10.1098/rsta.2018.0215
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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