Theory of domain patterns in systems with long-range interactions of Coulomb type

C. B. Muratov
Phys. Rev. E 66, 066108 – Published 10 December 2002
PDFExport Citation

Abstract

We develop a theory of the domain patterns in systems with competing short-range attractive interactions and long-range repulsive Coulomb interactions. We take an energetic approach, in which patterns are considered as critical points of a mean-field free energy functional. Close to the microphase separation transition, this functional takes on a universal form, allowing us to treat a number of diverse physical situations within a unified framework. We use asymptotic analysis to study domain patterns with sharp interfaces. We derive an interfacial representation of the pattern’s free energy which remains valid in the fluctuating system, with a suitable renormalization of the Coulomb interaction’s coupling constant. We also derive integro-differential equations describing stationary domain patterns of arbitrary shapes and their thermodynamic stability, coming from the first and second variations of the interfacial free energy. We show that the length scale of a stable domain pattern must obey a certain scaling law with the strength of the Coulomb interaction. We analyzed the existence and stability of localized (spots, stripes, annuli) and periodic (lamellar, hexagonal) patterns in two dimensions. We show that these patterns are metastable in certain ranges of the parameters and that they can undergo morphological instabilities leading to the formation of more complex patterns. We discuss nucleation of the domain patterns by thermal fluctuations and pattern formation scenarios for various thermal quenches. We argue that self-induced disorder is an intrinsic property of the domain patterns in the systems under consideration.

  • Received 27 March 2002

DOI:https://doi.org/10.1103/PhysRevE.66.066108

©2002 American Physical Society

Authors & Affiliations

C. B. Muratov*

  • Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102

  • *Electronic address: muratov@njit.edu

References (Subscription Required)

Click to Expand
Issue

Vol. 66, Iss. 6 — December 2002

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×