TY - JOUR

T1 - Shapes and singularities in triatic liquid-crystal vesicles

AU - Bowick, Mark J.

AU - Manyuhina, O. V.

AU - Serafin, F.

N1 - Funding Information:
This research was supported in part by the National Science Foundation under Grant No. NSF PHY-1125915. FS acknowledges the hospitality and stimulating discussions at the Kavli Institute for Theoretical Physics, University of California, Santa Barbara. The authors acknowledge financial support from the Soft Matter Program of Syracuse University.
Publisher Copyright:
© EPLA, 2017.

PY - 2017/1

Y1 - 2017/1

N2 - Determining the equilibrium configuration and shape of curved two-dimensional films with (generalized) liquid-crystalline order is a difficult infinite-dimensional problem of direct relevance to the study of generalized polymersomes, soft matter and the fascinating problem of understanding the origin and formation of shape (morphogenesis). The symmetry of the free energy of the LC film being considered and the topology of the surface to be determined often requires that the equilibrium configuration possesses singular structures in the form of topological defects such as disclinations for nematic films. The precise number and type of defect plays a fundamental role in restricting the space of possible equilibrium shapes. Flexible closed vesicles with spherical topology and nematic or smectic order, for example, inevitably possess four elementary strength +1/2 disclination defects positioned at the four vertices of a tetrahedral shell. Here we address the problem of determining the equilibrium shape of flexible vesicles with generalized liquid-crystalline order. The order parameter in these cases is an element of S1/Zp, for any positive integer p. We will focus on the case p = 3, known as triatic liquid crystals (LCs). We construct the appropriate order parameter for triatics and find the associated free energy. We then describe the structure of the elementary defects of strength +1/3 in flat space. Finally, we prove that sufficiently floppy triatic vesicles with the topology of the 2-sphere equilibrate to octahedral shells with strength +1/3 defects at each of the six vertices, independently of the scale.

AB - Determining the equilibrium configuration and shape of curved two-dimensional films with (generalized) liquid-crystalline order is a difficult infinite-dimensional problem of direct relevance to the study of generalized polymersomes, soft matter and the fascinating problem of understanding the origin and formation of shape (morphogenesis). The symmetry of the free energy of the LC film being considered and the topology of the surface to be determined often requires that the equilibrium configuration possesses singular structures in the form of topological defects such as disclinations for nematic films. The precise number and type of defect plays a fundamental role in restricting the space of possible equilibrium shapes. Flexible closed vesicles with spherical topology and nematic or smectic order, for example, inevitably possess four elementary strength +1/2 disclination defects positioned at the four vertices of a tetrahedral shell. Here we address the problem of determining the equilibrium shape of flexible vesicles with generalized liquid-crystalline order. The order parameter in these cases is an element of S1/Zp, for any positive integer p. We will focus on the case p = 3, known as triatic liquid crystals (LCs). We construct the appropriate order parameter for triatics and find the associated free energy. We then describe the structure of the elementary defects of strength +1/3 in flat space. Finally, we prove that sufficiently floppy triatic vesicles with the topology of the 2-sphere equilibrate to octahedral shells with strength +1/3 defects at each of the six vertices, independently of the scale.

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U2 - 10.1209/0295-5075/117/26001

DO - 10.1209/0295-5075/117/26001

M3 - Article

AN - SCOPUS:85015723397

VL - 117

JO - EPL

JF - EPL

SN - 0295-5075

IS - 2

M1 - 26001

ER -