Analysis and stability of bent-core liquid crystal fibers

Patricia Bauman; Daniel Phillips

doi:10.3934/dcdsb.2012.17.1707

Article Contents

2012, Volume 17, Issue 6: 1707-1728. Doi: 10.3934/dcdsb.2012.17.1707 open access

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Analysis and stability of bent-core liquid crystal fibers

Patricia Bauman^1, and
Daniel Phillips^2,

1.
Department of Mathematics, Purdue University, West Lafayette, IN 47906
2.
Department of Mathematics, Purdue University, West Lafayette, IN 47907

Received: February 2011

Revised: October 2011

Published: September 2012

Abstract / Introduction Related Papers Cited by

Abstract

In this paper we analyze a free-boundary model for free-standing fibers made from smectic layers of kinked (bent-core) liquid crystal molecules. In [1] a radial model was proposed to explain how fibers form (assuming radially symmetric configurations) based on the distinctive packing and ferroelectric properties of bent--core molecules. We develop this model further to include smectic energy terms so as to allow for non--circular cross--sections with non--radial configurations and fields. We show that the relative size of the energy's elasticity constants can be used to determine the stability (instability) of radially symmetric fibers with respect to non--radial perturbations.

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Mathematics Subject Classification: Primary: 35.

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References

[1]	C. Bailey, E. C. Gartland Jr. and A. Jàkli, Structure and stability of bent core liquid crystal fibers, Physical Review E, 75 (2007), 031701.doi: 10.1103/PhysRevE.75.031701.
[2]	J. Chen and T. C. Lubensky, Landau-Ginzburg mean-field theory for the nematic to smectic-C and nematic to smectic-A phase transitions, Phys. Rev. A, 14 (1976), 1202-1207.doi: 10.1103/PhysRevA.14.1202.
[3]	D. A. Coleman, J. Fernsler, N. Chattham, M. Nakata, Y. Takanishi, E. Körblova, D. R. Link, R.-F. Shao, W. G. Jang, J. E. Maclennan, O. Mondainn-Monval, C. Boyer, W. Weissflog, G. Pelzl, L.-C. Chien, J. Zasadzinski, J. Watanabe, D. M. Walba, H. Takezoe and N. A. Clark, Polarization-modulated smectic liquid crystal phases, Science, 301 (2003), 1204-1211.doi: 10.1126/science.1084956.
[4]	I. Dahl, Interaction between electric field and liquid crystals with spontaneous polarization: Derivation of suitable free energy expression for a cell with an applied voltage, Ferroelectrics, 84 (1988), 327-343.doi: 10.1080/00150198808016231.
[5]	A. Jàkli, Personal correspondence.
[6]	A. Jàkli, D. Krüerke and G. G. Nair, Liquid crystal fibers of Bent-Core molecules, Phys. Rev. E, 67 (2003), 051702.
[7]	A. Jàkli, C. Bailey and J. Harden, Chapter 2: Physical properties of banana liquid crystals, in "Thermotropic Liquid Crystals: Recent Advances'' (ed. A. Ramamoorthy), Springer, 2007.
[8]	F. M. Leslie, I. W. Stewart and M. Nakagawa, A continuum theory for smectic C liquid crystals, Mol. Cryst., 198 (1991), 443-454.doi: 10.1080/00268949108033420.
[9]	A. Nemes, A. Eremin, R. Stannarius, M. Schultz, H. Nàdasi and W. Weissflog, Structure characterization of free-standing filaments drawn in the liquid crystal state, Phys. Chem. Chem. Phys., 8 (2006), 469-476.
[10]	R. Stannarius, A. Nemes and A. Eremin, Plucking a liquid chord: Mechanical response of a liquid crystal filament, Phys. Rev. E, 72 (2005), 020702.doi: 10.1103/PhysRevE.72.020702.