### 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 |

### Fingerprint

### Keywords

- Coarsening
- Diblock copolymers
- Ostwald ripening
- Self-organization

### ASJC Scopus subject areas

- Condensed Matter Physics
- Statistical and Nonlinear Physics

### Cite this

*Physica D: Nonlinear Phenomena*,

*238*(14), 1241-1255. https://doi.org/10.1016/j.physd.2009.04.006

**Coarsening and self-organization in dilute diblock copolymer melts and mixtures.** / Glasner, Karl B; Choksi, Rustum.

Research output: Contribution to journal › Article

*Physica D: Nonlinear Phenomena*, vol. 238, no. 14, pp. 1241-1255. https://doi.org/10.1016/j.physd.2009.04.006

}

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 -