Abstract
This paper explores the evolution of a sharp interface model for phase separation of copolymers in the limit of low volume fraction. Particles both exchange material as in usual Ostwald ripening, and migrate because of an effectively repulsive nonlocal energetic term. Coarsening via mass diffusion only occurs while particle radii are small, and they eventually approach a finite equilibrium size. Migration, on the other hand, is responsible for producing self-organized patterns. We construct approximations based upon an ansatz of spherical particles similar to the classical LSW theory to derive finite dimensional dynamics for particle positions and radii. For large systems, kinetic-type equations which describe the evolution of a probability density are constructed. For systems larger than the screening length, we obtain an analog of the homogenization result of Niethammer & Otto [B. Niethammer, F. Otto, Ostwald ripening: The screening length revisited, Calc. Var. Partial Differential Equations 13-1 (2001) 33-68]. A separation of timescales between particle growth and migration allows for a variational characterization of spatially inhomogeneous quasi-equilibrium states.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1241-1255 |
| Number of pages | 15 |
| Journal | Physica D: Nonlinear Phenomena |
| Volume | 238 |
| Issue number | 14 |
| DOIs | |
| State | Published - Jul 1 2009 |
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Keywords
- Coarsening
- Diblock copolymers
- Ostwald ripening
- Self-organization
ASJC Scopus subject areas
- Condensed Matter Physics
- Statistical and Nonlinear Physics
Cite this
Coarsening and self-organization in dilute diblock copolymer melts and mixtures. / Glasner, Karl B; Choksi, Rustum.
In: Physica D: Nonlinear Phenomena, Vol. 238, No. 14, 01.07.2009, p. 1241-1255.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Coarsening and self-organization in dilute diblock copolymer melts and mixtures
AU - Glasner, Karl B
AU - Choksi, Rustum
PY - 2009/7/1
Y1 - 2009/7/1
N2 - This paper explores the evolution of a sharp interface model for phase separation of copolymers in the limit of low volume fraction. Particles both exchange material as in usual Ostwald ripening, and migrate because of an effectively repulsive nonlocal energetic term. Coarsening via mass diffusion only occurs while particle radii are small, and they eventually approach a finite equilibrium size. Migration, on the other hand, is responsible for producing self-organized patterns. We construct approximations based upon an ansatz of spherical particles similar to the classical LSW theory to derive finite dimensional dynamics for particle positions and radii. For large systems, kinetic-type equations which describe the evolution of a probability density are constructed. For systems larger than the screening length, we obtain an analog of the homogenization result of Niethammer & Otto [B. Niethammer, F. Otto, Ostwald ripening: The screening length revisited, Calc. Var. Partial Differential Equations 13-1 (2001) 33-68]. A separation of timescales between particle growth and migration allows for a variational characterization of spatially inhomogeneous quasi-equilibrium states.
AB - This paper explores the evolution of a sharp interface model for phase separation of copolymers in the limit of low volume fraction. Particles both exchange material as in usual Ostwald ripening, and migrate because of an effectively repulsive nonlocal energetic term. Coarsening via mass diffusion only occurs while particle radii are small, and they eventually approach a finite equilibrium size. Migration, on the other hand, is responsible for producing self-organized patterns. We construct approximations based upon an ansatz of spherical particles similar to the classical LSW theory to derive finite dimensional dynamics for particle positions and radii. For large systems, kinetic-type equations which describe the evolution of a probability density are constructed. For systems larger than the screening length, we obtain an analog of the homogenization result of Niethammer & Otto [B. Niethammer, F. Otto, Ostwald ripening: The screening length revisited, Calc. Var. Partial Differential Equations 13-1 (2001) 33-68]. A separation of timescales between particle growth and migration allows for a variational characterization of spatially inhomogeneous quasi-equilibrium states.
KW - Coarsening
KW - Diblock copolymers
KW - Ostwald ripening
KW - Self-organization
UR - http://www.scopus.com/inward/record.url?scp=66049136610&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=66049136610&partnerID=8YFLogxK
U2 - 10.1016/j.physd.2009.04.006
DO - 10.1016/j.physd.2009.04.006
M3 - Article
AN - SCOPUS:66049136610
VL - 238
SP - 1241
EP - 1255
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
IS - 14
ER -