Breakup of universality in the generalized spinodal nucleation theory

Cyrill B. Muratov, Eric Vanden Eijnden

Research output: Contribution to journalArticle

Abstract

The problem of nucleation near spinodal is revisited. It is shown that the standard scaling argument due to Unger and Klein [Phys. Rev. B 29:2698-2708 (1984)] based on neglecting all but the first two terms of the Taylor expansion of the potential in the free energy functional is only valid below critical dimension. At critical dimension, the nucleating droplet has a bigger amplitude and a smaller spatial extent than predicted by the standard scaling argument. In this case the structure of the droplet is determined in a nontrivial fashion by the next order term in the expansion of the potential. Above critical dimension, the amplitude of the nucleating droplet turns out to be too big to justify expanding the potential in Taylor series, and no universality is to be expected in the shape and size of the droplet. Both at and above critical dimension, however, the free energy barrier remains finite, which indicates that the nucleation rate does not vanish at spinodal as predicted by the standard scaling argument.

Original languageEnglish (US)
Pages (from-to)605-623
Number of pages19
JournalJournal of Statistical Physics
Volume114
Issue number3-4
StatePublished - Feb 2004

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Breakup
Critical Dimension
Nucleation
Droplet
Universality
nucleation
Scaling
scaling
Free Energy
free energy
expansion
Taylor series
Taylor Expansion
Energy Functional
Term
Justify
Vanish
Valid
Standards

Keywords

  • Critical droplet
  • Matched asymptotics
  • Non-classical nucleation
  • Scaling
  • Spinodal

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Breakup of universality in the generalized spinodal nucleation theory. / Muratov, Cyrill B.; Vanden Eijnden, Eric.

In: Journal of Statistical Physics, Vol. 114, No. 3-4, 02.2004, p. 605-623.

Research output: Contribution to journalArticle

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