Disclinations in a homogenously deformed nematic elastomer

We consider a nematic elastomer which has been cross-linked in an isotropic state. As an application, we consider the time-independent, isochoric, homogeneous 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 uniaxial. 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 uniaxial. The material thereby becomes anisotropic away from the disclination. The anisotropic regions show a markedly different distribution for the free energy. This distribution of energy determines the radius of the core to be on the order of 10⁻² μm. This work is a first step toward gaining an understanding of the existence of defective states in homogenous deformed nematic elastomers.