The isochoric extension of a cylindrical, nematic-elastomeric specimen is studied. Numerical solutions of the resulting boundary-value problem predict that, for sufficiently large extensions, there exists a region surrounding the cylinder axis wherein molecular asphericity vanishes. This regions is bounded by a narrow transition layer across which the asphericity drops rapidly and attains a non-trivial negative value. It is also found that there is a marked drop in the energy density across the transition layer. A state of this type corresponds to a disclination of strength +1 located along the cylinder axis. The disclination core is associated with the region of vanishing asphericity, in which the polymeric molecules are shaped as spherical coils, and the core radius is taken to be the location of the energy drop. At a generic point outside of the core radius, the polymeric molecules are shaped as ellipsoidal coils of revolution oblate about the cylinder radius. For realistic values of the material parameters, the energy criterion yields a core of approximately 0.015 µm, which is consistent with observations in conventional liquid-crystal melts.
Publisher
Department of Theoretical and Applied Mechanics (UIUC)
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