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

摘要

The problem of domain pattern formation in a wide variety of physical, chemical, and biological systems is investigated. The common feature of the systems under consideration is their ability to break up spontaneously into domains--regions with different physical properties separated by sharp interfaces. The formation of such domain patterns is identified as a result of competition between short-range attractive and long-range repulsive interactions. A universal model describing the static and dynamic properties of these domains in systems with a phase transition in the vicinity of the transition point is introduced. It is shown that the stationary domain patterns which form below the transition temperature may be described by a mean-field free energy functional. The stability of these patterns is studied via an asymptotic analysis of the free energy. It is shown that upon varying the control parameters, the system undergoes various morphological instabilities leading to the formation of highly irregular disordered patterns. The kinetics of the destabilization processes is studied through an interfacial model which is derived from the free energy. The nucleation and growth of patterns from the metastable equilibrium phase are also discussed. The theory developed is applicable to microphase separation in block copolymers, charged polyelectrolyte solutions, ceramic compounds, degenerate magnetic semiconductors, and photostimulated ferroelectric semiconductors.