The Phase Transitions from Chiral Nematic Toward Smectic Liquid Crystals |
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Authors: | Sookyung Joo Daniel Phillips |
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Institution: | (1) Institute for Mathematics and its Applications, University of Minnesota, 400 Lind Hall, 207 Church Street S.E., Minneapolis, MN 55455, USA;(2) Mathematics Department, Purdue University, West Lafayette, IN 47907, USA |
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Abstract: | A Chen-Lubensky energy is used to investigate phase transitions from chiral nematic to smectic C* and smectic A* liquid crystal phases. We consider a liquid crystalline material Ω confined between two parallel plates, where the dimensions of Ω are assumed to be large relative both to the width of a smectic layer and the material’s chiral pitch. We take boundary conditions so that the smectic phase melts at the plates’ surfaces and prove the existence of energy minimizers in an admissible set consisting of order parameters and molecular directors . Then under the physically observed assumption that the Frank elasticity constants become large near a phase transition, we establish estimates for the transition region separating phases. In particular we derive analytic estimates proving that chirality lowers the transition temperature regime above which minimizers are nematic and below which minimizers are in a smectic phase.Research supported by NSF grants DMS-0306516 and DMS-0456286. |
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