Phase transformations in metastable liquids combined with polymerization

Ivanov, Alexander A.; Alexandrova, Irina V.; Alexandrov, Dmitri V.

doi:10.1098/rsta.2018.0215

Title: Phase transformations in metastable liquids combined with polymerization

Journal Article · 03 March 2019 · Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences

DOI: https://doi.org/10.1098/rsta.2018.0215 · OSTI ID:1547036

^[1]; Alexandrova, Irina V. ^[1];

^[1]

Ural Federal Univ. (Russian Federation)

Here, we report on 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 integro-differential equations governing the dimensionless temperature and polymerization degree are deduced. These equations are solved by means of the saddle-point 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 this paper can be used to describe the similar phase transition phenomena in the presence of chemical reactions.

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Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-76SF00515

OSTI ID:: 1547036

Journal Information:: Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences, Journal Name: Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences Journal Issue: 2143 Vol. 377; ISSN 1364-503X

Publisher:: The Royal Society PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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Modeling and simulation of heat/mass transport, nucleation and growth kinetics in phase transformations Alexandrov, Dmitri V.; Galenko, Peter K.; Starodumov, Ilya O. The European Physical Journal Special Topics, Vol. 229, Issue 2-3 https://doi.org/10.1140/epjst/e2019-900174-5	journal	February 2020
Dynamics of particulate assemblages in metastable liquids: a test of theory with nucleation and growth kinetics Alexandrova, Irina V.; Alexandrov, Dmitri V. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 378, Issue 2171 https://doi.org/10.1098/rsta.2019.0245	journal	April 2020
Towards the theory of phase transformations in metastable liquids. Analytical solutions and stability analysis Ivanov, Alexander A.; Alexandrova, Irina V.; Alexandrov, Dmitri V. The European Physical Journal Special Topics, Vol. 229, Issue 2-3 https://doi.org/10.1140/epjst/e2019-900081-0	journal	February 2020
Effects of nonlinear growth rates of spherical crystals and their withdrawal rate from a crystallizer on the particle-size distribution function Makoveeva, Eugenya V.; Alexandrov, Dmitri V. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 377, Issue 2143 https://doi.org/10.1098/rsta.2018.0210	journal	March 2019
Nonlinear dynamics of polydisperse assemblages of particles evolving in metastable media Alexandrov, Dmitri V. The European Physical Journal Special Topics, Vol. 229, Issue 2-3 https://doi.org/10.1140/epjst/e2019-900049-4	journal	February 2020
Heterogeneous materials: metastable and non-ergodic internal structures Alexandrov, Dmitri V.; Zubarev, Andrey Yu. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 377, Issue 2143 https://doi.org/10.1098/rsta.2018.0353	journal	March 2019
Effects of external heat/mass sources and withdrawal rates of crystals from a metastable liquid on the evolution of particulate assemblages Makoveeva, Eugenya V.; Alexandrov, Dmitri V. The European Physical Journal Special Topics, Vol. 228, Issue 1 https://doi.org/10.1140/epjst/e2019-800201-3	journal	May 2019

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