Prediction of disclinations in nematic elastomers.

We present a theory for uniaxial nematic elastomers with variable asphericity. As an application of the theory, we consider the time-independent, isochoric extension of a right circular cylinder. Numerical solutions to the resulting differential equation are obtained for a range of extensions. For sufficiently large extensions, there exists an isotropic core of material surrounding the cylinder axis where the asphericity vanishes and in which the polymeric molecules are shaped as spherical coils. This region, corresponding to a disclination of strength +1 manifesting itself along the axis, is bounded by a narrow transition layer across which the asphericity drops rapidly and attains a nontrivial negative value. Away from the disclination, the material is anisotropic, and the polymeric molecules are shaped as ellipsoidal coils of revolution oblate about the radial direction. Along with the area of steeply changing asphericity between isotropic and anisotropic regimes, a marked drop in the free-energy density is observed. The boundary of the disclination core is associated with the location of this energy drop. For realistic choices of material parameters, this criterion yields a core on the order of 10(-2) microm, which coincides with observations in conventional liquid crystal melts. Finally, we find that the total energy definitively shows a preference for disclinated states.