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
2 - Order parameter, free energy, and phase transitions
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
The kinetics of first-order phase transitions involves the separation of an initially one-phase system into two coexisting phases. The formation and coarsening of domains of the coexisting phases as the system evolves are of central interest. The phase segregation process is usually studied by first preparing the system in a region of the phase diagram where the homogeneous state is stable. The system is then suddenly quenched into the two-phase region, and segregation into domains of the two stable phases takes place. Such phase segregation arises in a variety of physical contexts, including binary alloys and fluid mixtures, ferromagnetic systems, superfluids, polymer mixtures, and chemically reacting fluids. The temperature– composition (T, c) phase diagram for a binary mixture composed of constituents A and B is shown in Fig. 2.1. For low enough temperatures, in the region bounded by the coexistence curve the binary mixture will segregate into A-rich and B-rich phases.
A quench that takes the system from a homogeneous to a two-phase region is often performed by changing temperature suddenly at fixed concentration. Such a quench from the one-phase state at high temperatures may be carried out either along the critical isoconcentration line that passes through the critical point (path a), or along off-critical paths (path b). Phase segregation may be monitored by the changes in the local concentration of the binary mixture. In general, the variable that signals the passage from the one-phase to two-phase regions is called the order parameter ø.
- Type
- Chapter
- Information
- Publisher: Cambridge University PressPrint publication year: 2009