Math @ Duke

Publications [#268308] of John E. Dolbow
Papers Published
 Dolbow, J; Fried, E; Shen, AQ, Point defects in nematic gels: The case for hedgehogs,
Archive for Rational Mechanics and Analysis, vol. 177 no. 1
(2005),
pp. 2151 [s0020500503594], [doi]
(last updated on 2018/05/25)
Abstract: We address the question of whether a nematic gel is capable of sustaining a radiallysymmetric point defect (or, hedgehog). We consider the special case of a gel crosslinked in a state where the mesogens are randomly aligned, and study the behavior of a spherical specimen with boundary subjected to a uniform radial displacement. For simplicity, we allow only for distortions in which the chain conformation is uniaxial with constant chain anisotropy and, thus, is determined by a unit director field. Further, we use the particular freeenergy density function arising from the neoclassical molecularstatistical description of nematic gels. We find that the potential energy of the specimen is a nonconvex function of the boundary displacement and chain anisotropy. In particular, whenever the displacement of the specimen boundary involves a relative radial expansion in excess of 0.35, which is reasonably mild for gellike substances, the theory predicts an energetic preference for states involving a hedgehog at the center of the specimen. Under such conditions, states in which the chain anisotropy is either oblate or prolate have total freeenergy less than that of an isotropic comparison state. However, the oblate alternative always provides the global minimum of the total freeenergy. The Cauchy stress associated with an energeticallypreferred hedgehog is found to vanish in a relatively large region surrounding the hedgehog. The radial component of Cauchy stress is tensile and exhibits a nonmonotonic character with a peak value an order of magnitude less than what would be observed in a specimen consisting of a comparable isotropic gel. The hoop component of Cauchy stress is also nonmonotonic, but, as opposed to being purely tensile, goes between a tensile maximum to a compressive minimum at the specimen boundary. © SpringerVerlag (2005).
Keywords: free energy;internal stresses;point defects;polymer gels;


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