Book contents
- Frontmatter
- Contents
- preface
- 1 Self-organized and self-assembled structures
- 2 Order parameter, free energy, and phase transitions
- 3 Free energy functional
- 4 Phase separation kinetics
- 5 Langevin model for nonconserved order parameter systems
- 6 Langevin model for conserved order parameter systems
- 7 Interface dynamics at late times
- 8 Domain growth and structure factor for model B
- 9 Order parameter correlation function
- 10 Vector order parameter and topological defects
- 11 Liquid crystals
- 12 Lifshitz–Slyozov–Wagner theory
- 13 Systems with long-range repulsive interactions
- 14 Kinetics of systems with competing interactions
- 15 Competing interactions and defect dynamics
- 16 Diffusively rough interfaces
- 17 Morphological instability in solid films
- 18 Propagating chemical fronts
- 19 Transverse front instabilities
- 20 Cubic autocatalytic fronts
- 21 Competing interactions and front repulsion
- 22 Labyrinthine patterns in chemical systems
- 23 Turing patterns
- 24 Excitable media
- 25 Oscillatory media and complex Ginzburg–Landau equation
- 26 Spiral waves and defect turbulence
- 27 Complex oscillatory and chaotic media
- 28 Resonantly forced oscillatory media
- 29 Nonequilibrium patterns in laser-induced melting
- 30 Reaction dynamics and phase segregation
- 31 Active materials
- References
- Index
15 - Competing interactions and defect dynamics
Published online by Cambridge University Press: 10 February 2010
- Frontmatter
- Contents
- preface
- 1 Self-organized and self-assembled structures
- 2 Order parameter, free energy, and phase transitions
- 3 Free energy functional
- 4 Phase separation kinetics
- 5 Langevin model for nonconserved order parameter systems
- 6 Langevin model for conserved order parameter systems
- 7 Interface dynamics at late times
- 8 Domain growth and structure factor for model B
- 9 Order parameter correlation function
- 10 Vector order parameter and topological defects
- 11 Liquid crystals
- 12 Lifshitz–Slyozov–Wagner theory
- 13 Systems with long-range repulsive interactions
- 14 Kinetics of systems with competing interactions
- 15 Competing interactions and defect dynamics
- 16 Diffusively rough interfaces
- 17 Morphological instability in solid films
- 18 Propagating chemical fronts
- 19 Transverse front instabilities
- 20 Cubic autocatalytic fronts
- 21 Competing interactions and front repulsion
- 22 Labyrinthine patterns in chemical systems
- 23 Turing patterns
- 24 Excitable media
- 25 Oscillatory media and complex Ginzburg–Landau equation
- 26 Spiral waves and defect turbulence
- 27 Complex oscillatory and chaotic media
- 28 Resonantly forced oscillatory media
- 29 Nonequilibrium patterns in laser-induced melting
- 30 Reaction dynamics and phase segregation
- 31 Active materials
- References
- Index
Summary
Phase separation in systems with competing interactions involves two dynamic phenomena: segregation into two phases, and the creation of supercrystal (modulated phase) ordering. These two processes occur on very different time scales. The early and intermediate-time regimes were discussed in Chapter 14. In these regimes, all important information about the system may be obtained from the scalar order parameter ψ. During the intermediate-time regime, the domain size reaches its saturation value and the time evolution is ultimately governed by this time independent length scale. Systems with a scalar order parameter form domains of the ordered phase separated by domain walls, the relevant topological defect, and evolve so as to decrease the domain-wall energy.
In the presence of long-range repulsive interactions, the late stage of phase ordering involves the evolution from a disordered liquid of minority phase droplets towards the crystalline (hexagonal) ground state through the gain of orientational and positional order. As discussed in Chapter 9, systems with continuous order parameters have point, line, and other more complex defect structures. The late stages of the phase separation processes are dominated by the motion of these defects and, as time evolves, both their density and energy decrease. This is in contrast to model B in the absence of long-range repulsive interactions, where the late-stage kinetics is curvature driven and the conservation law plays an important role.As long-range repulsive interactions become important, qualitatively different late-stage effects emerge, since dipolar forces compete with forces arising from line tension.
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- Chapter
- Information
- Dynamics of Self-Organized and Self-Assembled Structures , pp. 120 - 127Publisher: Cambridge University PressPrint publication year: 2009