Metastability in Fluctuation Driven First-order Transitions: Nucleation of Lamellar Phases

Details Metastability in Fluctuation Driven First-order Transitions: Nucleation of Lamellar Phases Metastability in Fluctuation Driven First-order Transitions: Nucleation of Lamellar Phases

1995-01-26

arxiv.org/abs/patt-sol/9501004v2

Physics

Condensed Matter

32 pages, plus post-script uuencoded file of figures appended. Requires use of auxiliary files subeqn.sty and subeqnarray.sty

Scientific paper

10.1103/PhysRevE.52.1828

The nucleation of a lamellar phase from a supercooled homogeneous phase in a fluctuation driven first-order transition is studied, based on a phenomenological free energy due to Brazovskii. The absence of phase coexistence in the corresponding mean-field approximation makes application of the standard droplet theory of homogeneous nucleation problematic. A self-consistent coarse-graining procedure is introduced to overcome this difficulty, and the barrier height for nucleation of a critical droplet is estimated in the weak-coupling limit. Contrary to earlier estimates the critical droplet shape is shown to be anisotropic in general. Some effects of distortions and defects in the lamellar structure are considered and are shown to affect the critical droplet only very near coexistence where the probability of nucleation vanishes. The coarse-graining procedure introduced here follows from a novel application of the momentum-shell renormalization group method to systems in the Brazovskii class. Possible applications of the theory to the microphase separation transition in diblock copolymers and to Rayleigh-B\'{e}nard convection are briefly discussed.

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