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

Abstract

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.

Authors:

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

^[1]

Ural Federal Univ. (Russian Federation)

Publication Date:: 2019-03-04

Research Org.:: SLAC National Accelerator Lab., Menlo Park, CA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1547036

Grant/Contract Number:: AC02-76SF00515

Resource Type:: Accepted Manuscript

Journal Name:: Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences

Additional Journal Information:: Journal Volume: 377; Journal Issue: 2143; Journal ID: ISSN 1364-503X

Publisher:: The Royal Society Publishing

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; polymerization; crystallization; nucleation; metastable liquid

Citation Formats


                    Ivanov, Alexander A., Alexandrova, Irina V., and Alexandrov, Dmitri V. Phase transformations in metastable liquids combined with polymerization.  United States: N. p., 2019. 
Web.  doi:10.1098/rsta.2018.0215.

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                    Ivanov, Alexander A., Alexandrova, Irina V., & Alexandrov, Dmitri V. Phase transformations in metastable liquids combined with polymerization.  United States.  https://doi.org/10.1098/rsta.2018.0215

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                    Ivanov, Alexander A., Alexandrova, Irina V., and Alexandrov, Dmitri V. Mon .  
"Phase transformations in metastable liquids combined with polymerization".  United States.  https://doi.org/10.1098/rsta.2018.0215.  https://www.osti.gov/servlets/purl/1547036.

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@article{osti_1547036,

  title        = {Phase transformations in metastable liquids combined with polymerization},

  author       = {Ivanov, Alexander A. and Alexandrova, Irina V. and Alexandrov, Dmitri V.},

  abstractNote = {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.},

  doi          = {10.1098/rsta.2018.0215},

  journal      = {Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences},

  number       = 2143,

  volume       = 377,

  place        = {United States},

  year         = {2019},

  month        = {3}

}

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Works referencing / citing this record:

Effects of nonlinear growth rates of spherical crystals and their withdrawal rate from a crystallizer on the particle-size distribution function
journal, March 2019

Makoveeva, Eugenya V.; Alexandrov, Dmitri V.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 377, Issue 2143
DOI: 10.1098/rsta.2018.0210

Heterogeneous materials: metastable and non-ergodic internal structures
journal, March 2019

Alexandrov, Dmitri V.; Zubarev, Andrey Yu.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 377, Issue 2143
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Dynamics of particulate assemblages in metastable liquids: a test of theory with nucleation and growth kinetics
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Alexandrova, Irina V.; Alexandrov, Dmitri V.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 378, Issue 2171
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Effects of external heat/mass sources and withdrawal rates of crystals from a metastable liquid on the evolution of particulate assemblages
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Makoveeva, Eugenya V.; Alexandrov, Dmitri V.
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Alexandrov, Dmitri V.
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Ivanov, Alexander A.; Alexandrova, Irina V.; Alexandrov, Dmitri V.
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Modeling and simulation of heat/mass transport, nucleation and growth kinetics in phase transformations
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Title: Phase transformations in metastable liquids combined with polymerization

Abstract

Citation Formats

Continuous emulsion polymerization. Modeling oscillations in vinyl acetate polymerization journal, January 1979

Transient nucleation kinetics of crystal growth at the intermediate stage of bulk phase transitions journal, October 2013

Non-linear evolution of a system of elongated droplike aggregates in a metastable magnetic fluid journal, March 1998

Instability and unsteady processes of the bulk continuous crystallization—I. Linear stability analysis journal, January 1991

Nucleation and particle growth with fluctuating rates at the intermediate stage of phase transitions in metastable systems journal, February 2014

Nucleation kinetics and crystal growth with fluctuating rates at the intermediate stage of phase transitions journal, November 2013

Modelling of unsteady combustion regimes for polydisperse fuels—II. Parametrically controlled combustion journal, January 1993

Computer simulation of viscoelasticity in polymer melts journal, July 1992

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Nucleation and evolution of spherical crystals with allowance for their unsteady-state growth rates journal, January 2018

A complete analytical solution of the Fokker–Planck and balance equations for nucleation and growth of crystals journal, January 2018

Influence of thermal effects on hydrodynamic stability of a polymerization front journal, January 1992

Polymerization and Crystallization of Polyethylene on a Flat Model Catalyst journal, December 1999

Self-similar solidification: morphological stability of the regime journal, March 2004

On the theory of transient nucleation at the intermediate stage of phase transitions journal, April 2014

H∞-Control of a continuous crystallizer journal, August 2001

Kinetics of the intermediate stage of phase transition in batch crystallization journal, September 1990

Dynamic stability analysis of the solidification of binary melts in the presence of a mushy region: changeover of instability journal, March 2000

Nucleation and crystal growth in binary systems journal, March 2014

Thin-film behavior of poly(methyl methacrylates). 9. Crystallization of isotactic poly(methyl methacrylate) in mixed monolayers journal, October 1992

On the theory of nucleation and nonstationary evolution of a polydisperse ensemble of crystals journal, January 2019

Dynamic modelling of the continuous emulsion polymerization of vinyl chloride journal, December 1984

Theory of Crystallization under Equilibrium Polymerization in a Solution and the Investigation of Its Melting Properties journal, October 2005

Modelling of unsteady combustion regimes for polydisperse fuels—I. Instability and auto-oscillations journal, January 1993

H ∞ Control of a Continuous Crystallizer journal, June 2000

Effects of nonlinear growth rates of spherical crystals and their withdrawal rate from a crystallizer on the particle-size distribution function journal, March 2019

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Dynamics of particulate assemblages in metastable liquids: a test of theory with nucleation and growth kinetics journal, April 2020

Effects of external heat/mass sources and withdrawal rates of crystals from a metastable liquid on the evolution of particulate assemblages journal, May 2019

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Continuous emulsion polymerization. Modeling oscillations in vinyl acetate polymerization
journal, January 1979

Transient nucleation kinetics of crystal growth at the intermediate stage of bulk phase transitions
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Non-linear evolution of a system of elongated droplike aggregates in a metastable magnetic fluid
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Instability and unsteady processes of the bulk continuous crystallization—I. Linear stability analysis
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Nucleation and particle growth with fluctuating rates at the intermediate stage of phase transitions in metastable systems
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Nucleation kinetics and crystal growth with fluctuating rates at the intermediate stage of phase transitions
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Modelling of unsteady combustion regimes for polydisperse fuels—II. Parametrically controlled combustion
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Computer simulation of viscoelasticity in polymer melts
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On the theory of the unsteady-state growth of spherical crystals in metastable liquids
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Nucleation and evolution of spherical crystals with allowance for their unsteady-state growth rates
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A complete analytical solution of the Fokker–Planck and balance equations for nucleation and growth of crystals
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Influence of thermal effects on hydrodynamic stability of a polymerization front
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Polymerization and Crystallization of Polyethylene on a Flat Model Catalyst
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Self-similar solidification: morphological stability of the regime
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On the theory of transient nucleation at the intermediate stage of phase transitions
journal, April 2014

H∞-Control of a continuous crystallizer
journal, August 2001

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Effects of nonlinear growth rates of spherical crystals and their withdrawal rate from a crystallizer on the particle-size distribution function
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Heterogeneous materials: metastable and non-ergodic internal structures
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