### Abstract

We study the effect of an externally imposed oscillatory shear on the motion of a grain boundary that separates differently oriented domains of the lamellar phase of a diblock copolymer. A direct numerical solution of the Swift-Hohenberg equation in shear flow is used for the case of a transverse/parallel grain boundary in the limits of weak nonlinearity and low shear frequency. We focus on the region of parameters in which both transverse and parallel lamellae are linearly stable. Shearing leads to excess free energy in the transverse region relative to the parallel region, which is in turn dissipated by net motion of the boundary toward the transverse region. The observed boundary motion is a combination of rigid advection by the flow and order parameter diffusion. The latter includes break up and reconnection of lamellae, as well as a weak Eckhaus instability in the boundary region for sufficiently large strain amplitude that leads to slow wave number readjustment. The net average velocity is seen to increase with frequency and strain amplitude, and can be obtained by a multiple scale expansion of the governing equations.

Original language | English (US) |
---|---|

Article number | 041504 |

Number of pages | 1 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 69 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1 2004 |

### Fingerprint

### Cite this

**Shear-induced grain boundary motion for lamellar phases in the weakly nonlinear regime.** / Huang, Zhi Feng; Viñals, Jorge.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Shear-induced grain boundary motion for lamellar phases in the weakly nonlinear regime

AU - Huang, Zhi Feng

AU - Viñals, Jorge

PY - 2004/4/1

Y1 - 2004/4/1

N2 - We study the effect of an externally imposed oscillatory shear on the motion of a grain boundary that separates differently oriented domains of the lamellar phase of a diblock copolymer. A direct numerical solution of the Swift-Hohenberg equation in shear flow is used for the case of a transverse/parallel grain boundary in the limits of weak nonlinearity and low shear frequency. We focus on the region of parameters in which both transverse and parallel lamellae are linearly stable. Shearing leads to excess free energy in the transverse region relative to the parallel region, which is in turn dissipated by net motion of the boundary toward the transverse region. The observed boundary motion is a combination of rigid advection by the flow and order parameter diffusion. The latter includes break up and reconnection of lamellae, as well as a weak Eckhaus instability in the boundary region for sufficiently large strain amplitude that leads to slow wave number readjustment. The net average velocity is seen to increase with frequency and strain amplitude, and can be obtained by a multiple scale expansion of the governing equations.

AB - We study the effect of an externally imposed oscillatory shear on the motion of a grain boundary that separates differently oriented domains of the lamellar phase of a diblock copolymer. A direct numerical solution of the Swift-Hohenberg equation in shear flow is used for the case of a transverse/parallel grain boundary in the limits of weak nonlinearity and low shear frequency. We focus on the region of parameters in which both transverse and parallel lamellae are linearly stable. Shearing leads to excess free energy in the transverse region relative to the parallel region, which is in turn dissipated by net motion of the boundary toward the transverse region. The observed boundary motion is a combination of rigid advection by the flow and order parameter diffusion. The latter includes break up and reconnection of lamellae, as well as a weak Eckhaus instability in the boundary region for sufficiently large strain amplitude that leads to slow wave number readjustment. The net average velocity is seen to increase with frequency and strain amplitude, and can be obtained by a multiple scale expansion of the governing equations.

UR - http://www.scopus.com/inward/record.url?scp=85036326841&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85036326841&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.69.041504

DO - 10.1103/PhysRevE.69.041504

M3 - Article

C2 - 15169022

AN - SCOPUS:33646200200

VL - 69

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 4

M1 - 041504

ER -