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APPLICATION OF LINE GROUP TECHNIQUE FOR DESCRIBING BASIC SYMMETRIES AND MECHANICS OF CHOLESTERIC LIQUID CRYSTALS
Cs. Mészáros
1, I. Farkas
1and Á. Bálint
21Department of Physics and Process Control, Szent István University Gödöllő, Páter K. u. 1., H-2103 Hungary
Tel.:+36 28 522055, Email: Meszaros.Csaba@gek.szie.hu
2Department of Chemistry and Biochemistry, Szent István University Gödöllő, Páter K. u. 1., H-2103 Hungary
Since their discovery and subsequent effective applications in the structural investigation of stereoregular polymers by X-ray scattering, the mathematical formalism of line groups has been playing a role of continuously increasing importance in various branches of the contemporary condensed matter physics.
These symmetry groups represent a uniquely precise mathematical theory for accurate modelling of all kinds of quasi-one dimensional systems.
After their relatively novel use in some direct extensions of the classic crystallographical formalisms and some simple but general treatments of crystals with incommensurately modulated structures, they appeared as the basic formalism for describing of the nowadays extensively investigated carbon nanotubes, too.
In the present work we open a new research direction for applying of the abstract algebraic theory of line groups and their representations via their use for describing of the fundamental properties of cholesteric liquid crystals.
Having described a novel-type symmetry analysis of thermodynamic potentials containing invariants relevant for helical symmetries of such type of liquid crystals, we give some new basic methods for characterizing the mechanics of cholesterics.
It is demonstrated, that this new technique – compared to the earlier ones – gives a much more refined description of the dynamics of cholesteric liquid crystals.
Finally, the existing formalism of light scattering from cholesterics is also refined by taking into account the specific features of line groups, and it is shown, that it is not only in agreement with the relevant existing experimental results, but also allows a more precise interpretation of them.
Acknowledgement: This work was supported/subsidized by TÁMOP-4.2.2.B-10/1-2010-0011
"Development of a complex educational assistance/support system for talented students and prospective researchers at the Szent István University" project.
