### Abstract

We studied the dynamics of isotropic-nematic transitions in liquid crystalline polymers by integrating time-dependent Ginzburg-Landau equations. In a concentrated solution of rodlike polymers, the rotational diffusion constant D_{r} of the polymer is severely suppressed by the geometrical constraints of the surrounding polymers so that the rodlike molecules diffuse only along their rod directions. In the early stage of phase transition, the rodlike polymers with nearly parallel orientations assemble to form a nematic polydomain. This polydomain pattern, with characteristic length ?, grows with self-similarity in three dimensions over time with an ?~t1^{/}4 scaling law. In the late stage, the rotational diffusion becomes significant, leading to a crossover of the growth exponent from 1/4 to 1/2. This crossover time is estimated to be on the order of t~Dr-1. We also examined the time evolution of a pair of disclinations placed in a confined system by solving the same time-dependent Ginzburg-Landau equations in two dimensions. If the initial distance between the disclinations is shorter than some critical length, they approach and annihilate each other; however, at larger initial separations, they are stabilized.

Original language | English |
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Article number | 061711 |

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

Volume | 83 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jun 28 2011 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

**Polydomain growth at isotropic-nematic transitions in liquid crystalline polymers.** / Yabunaka, Shunsuke; Araki, Takeaki.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Polydomain growth at isotropic-nematic transitions in liquid crystalline polymers

AU - Yabunaka, Shunsuke

AU - Araki, Takeaki

PY - 2011/6/28

Y1 - 2011/6/28

N2 - We studied the dynamics of isotropic-nematic transitions in liquid crystalline polymers by integrating time-dependent Ginzburg-Landau equations. In a concentrated solution of rodlike polymers, the rotational diffusion constant Dr of the polymer is severely suppressed by the geometrical constraints of the surrounding polymers so that the rodlike molecules diffuse only along their rod directions. In the early stage of phase transition, the rodlike polymers with nearly parallel orientations assemble to form a nematic polydomain. This polydomain pattern, with characteristic length ?, grows with self-similarity in three dimensions over time with an ?~t1/4 scaling law. In the late stage, the rotational diffusion becomes significant, leading to a crossover of the growth exponent from 1/4 to 1/2. This crossover time is estimated to be on the order of t~Dr-1. We also examined the time evolution of a pair of disclinations placed in a confined system by solving the same time-dependent Ginzburg-Landau equations in two dimensions. If the initial distance between the disclinations is shorter than some critical length, they approach and annihilate each other; however, at larger initial separations, they are stabilized.

AB - We studied the dynamics of isotropic-nematic transitions in liquid crystalline polymers by integrating time-dependent Ginzburg-Landau equations. In a concentrated solution of rodlike polymers, the rotational diffusion constant Dr of the polymer is severely suppressed by the geometrical constraints of the surrounding polymers so that the rodlike molecules diffuse only along their rod directions. In the early stage of phase transition, the rodlike polymers with nearly parallel orientations assemble to form a nematic polydomain. This polydomain pattern, with characteristic length ?, grows with self-similarity in three dimensions over time with an ?~t1/4 scaling law. In the late stage, the rotational diffusion becomes significant, leading to a crossover of the growth exponent from 1/4 to 1/2. This crossover time is estimated to be on the order of t~Dr-1. We also examined the time evolution of a pair of disclinations placed in a confined system by solving the same time-dependent Ginzburg-Landau equations in two dimensions. If the initial distance between the disclinations is shorter than some critical length, they approach and annihilate each other; however, at larger initial separations, they are stabilized.

UR - http://www.scopus.com/inward/record.url?scp=79961099195&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevE.83.061711

DO - 10.1103/PhysRevE.83.061711

M3 - Article

C2 - 21797391

AN - SCOPUS:79961099195

VL - 83

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 6

M1 - 061711

ER -