Abstract/Details

Topological defects in nematic and smectic liquid crystals


2012 2012

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Abstract (summary)

Liquid crystals are materials with interesting symmetries and order, and their science and applications are a playground of geometry and elasticity. I discuss various aspects of the study of topology and topological defects in liquid crystalline systems beyond the traditional calculation of homotopy groups. I consider two problems. First, how can we better visualize three dimensional nematic orientation fields given that many experiments and simulations now are creating and manipulating configurations with complicated topology? I show that the Pontryagin-Thom construction leads to a natural set of colored surfaces, generalizing the prototypical dark brushes seen in Schlieren textures between crossed polarizers. If we are interested in properties preserved under smooth deformations, these colored surfaces can stand in for the rest of the configuration, leading to a reduction in dimensionality of the data to be considered, as well as an aesthetically pleasing representation of what's happening. The second problem is the relationship between translational order and orientational order in smectic liquid crystal systems. Smectics are liquid crystals which organize themselves into layers where the naïve generalization of the calculation of homotopy groups leads to results on defects which are incorrect. I show that these difficulties arise from the lack of independence between translational order and orientational order. These considerations are neatly captured by a surface model of two-dimensional smectics. By looking at a smectic configuration as a graph over the sample space, the nature of the rules governing the defects and their relationship to the symmetries of the system are clarified.

Indexing (details)


Subject
Physics;
Condensed matter physics
Classification
0605: Physics
0611: Condensed matter physics
Identifier / keyword
Pure sciences; Configuartions; Liquid crystals; Nematic orientation fields; Topological defects
Title
Topological defects in nematic and smectic liquid crystals
Author
Chen, Bryan Gin-ge
Number of pages
132
Publication year
2012
Degree date
2012
School code
0175
Source
DAI-B 73/09(E), Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9781267351050
Advisor
Kamien, Randall D.
Committee member
Durian, Douglas J.; Liu, Andrea J.; Lubensky, Tom C.; Trodden, Mark
University/institution
University of Pennsylvania
Department
Physics and Astronomy
University location
United States -- Pennsylvania
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3508984
ProQuest document ID
1019056168
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/1019056168
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