Disclinations in Homogeneously Deformed Nematic Elastomers
Roy, Bidhan Chandra
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https://hdl.handle.net/2142/87716
Description
Title
Disclinations in Homogeneously Deformed Nematic Elastomers
Author(s)
Roy, Bidhan Chandra
Issue Date
2003
Doctoral Committee Chair(s)
Eliot Fried
Department of Study
Theoretical and Applied Mechanics
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Language
eng
Abstract
A nematic elastomer is a rubber-like solid formed by cross-linking of a polymeric fluid that includes nematic liquid crystalline molecules as side- or main-chain elements. This thesis explores issues concerned with disclinations---which are tubular neighborhoods in which the material is isotropic and, thus, behaves like conventional rubber---in such materials. Following Fried and Todres, we consider a nematic elastomer that has been cross-linked in the isotropic state. As an application, we consider the time-independent, isochoric homogenous deformation of a right circular cylinder wherein each circular cross-section of the specimen is deformed into an ellipse. We explore the possibility of the existence of disclinations when the molecular conformation is (i) uniaxial and (ii) biaxial. In either scenario, numerical solution of the governing boundary-value problem indicates the presence of an isotropic core (the disclination core) of material surrounding the cylinder axis in which the polymeric chains are shaped as spherical coils. The isotropic core is bounded by a narrow transition layer across which the molecular conformation changes from spherical to either uniaxial or biaxial. The material thereby becomes anisotropic away from the disclination. The material shows an energetic preference for biaxial states over uniaxial states. The anisotropic regions show a markedly different distribution for the free energy, deformational stress, and pressure than the isotropic region. This distribution of energy, stress and pressure determines the radius of the core to be on the order of 10-2 mum. The constitutively determined contribution to the orientational stress is completely concentrated at the core boundary.
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