Phase transformations in metastable liquids combined with polymerization
- 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.
- 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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