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September  2012, 17(6): 1707-1728. doi: 10.3934/dcdsb.2012.17.1707

## Analysis and stability of bent-core liquid crystal fibers

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

Received  February 2011 Revised  October 2011 Published  May 2012

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.
Citation: Patricia Bauman, Daniel Phillips. Analysis and stability of bent-core liquid crystal fibers. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1707-1728. doi: 10.3934/dcdsb.2012.17.1707
##### 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). doi: 10.1103/PhysRevE.75.031701. Google Scholar [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. doi: 10.1103/PhysRevA.14.1202. Google Scholar [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. doi: 10.1126/science.1084956. Google Scholar [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. doi: 10.1080/00150198808016231. Google Scholar [5] , A. Jàkli,, Personal correspondence., (). Google Scholar [6] A. Jàkli, D. Krüerke and G. G. Nair, Liquid crystal fibers of Bent-Core molecules,, Phys. Rev. E, 67 (2003). Google Scholar [7] A. Jàkli, C. Bailey and J. Harden, Chapter 2: Physical properties of banana liquid crystals,, in, (2007). Google Scholar [8] F. M. Leslie, I. W. Stewart and M. Nakagawa, A continuum theory for smectic C liquid crystals,, Mol. Cryst., 198 (1991), 443. doi: 10.1080/00268949108033420. Google Scholar [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. Google Scholar [10] R. Stannarius, A. Nemes and A. Eremin, Plucking a liquid chord: Mechanical response of a liquid crystal filament,, Phys. Rev. E, 72 (2005). doi: 10.1103/PhysRevE.72.020702. Google Scholar

show all references

##### 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). doi: 10.1103/PhysRevE.75.031701. Google Scholar [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. doi: 10.1103/PhysRevA.14.1202. Google Scholar [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. doi: 10.1126/science.1084956. Google Scholar [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. doi: 10.1080/00150198808016231. Google Scholar [5] , A. Jàkli,, Personal correspondence., (). Google Scholar [6] A. Jàkli, D. Krüerke and G. G. Nair, Liquid crystal fibers of Bent-Core molecules,, Phys. Rev. E, 67 (2003). Google Scholar [7] A. Jàkli, C. Bailey and J. Harden, Chapter 2: Physical properties of banana liquid crystals,, in, (2007). Google Scholar [8] F. M. Leslie, I. W. Stewart and M. Nakagawa, A continuum theory for smectic C liquid crystals,, Mol. Cryst., 198 (1991), 443. doi: 10.1080/00268949108033420. Google Scholar [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. Google Scholar [10] R. Stannarius, A. Nemes and A. Eremin, Plucking a liquid chord: Mechanical response of a liquid crystal filament,, Phys. Rev. E, 72 (2005). doi: 10.1103/PhysRevE.72.020702. Google Scholar
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