### 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 language | English (US) |
---|---|

Pages (from-to) | 605-623 |

Number of pages | 19 |

Journal | Journal of Statistical Physics |

Volume | 114 |

Issue number | 3-4 |

State | Published - Feb 2004 |

### Fingerprint

### 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

*Journal of Statistical Physics*,

*114*(3-4), 605-623.

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

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 114, no. 3-4, pp. 605-623.

}

TY - JOUR

T1 - Breakup of universality in the generalized spinodal nucleation theory

AU - Muratov, Cyrill B.

AU - Vanden Eijnden, Eric

PY - 2004/2

Y1 - 2004/2

N2 - 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.

AB - 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.

KW - Critical droplet

KW - Matched asymptotics

KW - Non-classical nucleation

KW - Scaling

KW - Spinodal

UR - http://www.scopus.com/inward/record.url?scp=3542998723&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3542998723&partnerID=8YFLogxK

M3 - Article

VL - 114

SP - 605

EP - 623

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 3-4

ER -