Skip to main content
Journal cover image

Point defects in nematic gels: The case for hedgehogs

Publication ,  Journal Article
Dolbow, J; Fried, E; Shen, AQ
Published in: Archive for Rational Mechanics and Analysis
July 1, 2005

We address the question of whether a nematic gel is capable of sustaining a radially-symmetric point defect (or, hedgehog). We consider the special case of a gel cross-linked 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 free-energy density function arising from the neo-classical molecular-statistical 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 gel-like 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 free-energy less than that of an isotropic comparison state. However, the oblate alternative always provides the global minimum of the total free-energy. The Cauchy stress associated with an energetically-preferred hedgehog is found to vanish in a relatively large region surrounding the hedgehog. The radial component of Cauchy stress is tensile and exhibits a non-monotonic 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 non-monotonic, but, as opposed to being purely tensile, goes between a tensile maximum to a compressive minimum at the specimen boundary. © Springer-Verlag (2005).

Duke Scholars

Published In

Archive for Rational Mechanics and Analysis

DOI

ISSN

0003-9527

Publication Date

July 1, 2005

Volume

177

Issue

1

Start / End Page

21 / 51

Related Subject Headings

  • General Physics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Dolbow, J., Fried, E., & Shen, A. Q. (2005). Point defects in nematic gels: The case for hedgehogs. Archive for Rational Mechanics and Analysis, 177(1), 21–51. https://doi.org/10.1007/s00205-005-0359-4
Dolbow, J., E. Fried, and A. Q. Shen. “Point defects in nematic gels: The case for hedgehogs.” Archive for Rational Mechanics and Analysis 177, no. 1 (July 1, 2005): 21–51. https://doi.org/10.1007/s00205-005-0359-4.
Dolbow J, Fried E, Shen AQ. Point defects in nematic gels: The case for hedgehogs. Archive for Rational Mechanics and Analysis. 2005 Jul 1;177(1):21–51.
Dolbow, J., et al. “Point defects in nematic gels: The case for hedgehogs.” Archive for Rational Mechanics and Analysis, vol. 177, no. 1, July 2005, pp. 21–51. Scopus, doi:10.1007/s00205-005-0359-4.
Dolbow J, Fried E, Shen AQ. Point defects in nematic gels: The case for hedgehogs. Archive for Rational Mechanics and Analysis. 2005 Jul 1;177(1):21–51.
Journal cover image

Published In

Archive for Rational Mechanics and Analysis

DOI

ISSN

0003-9527

Publication Date

July 1, 2005

Volume

177

Issue

1

Start / End Page

21 / 51

Related Subject Headings

  • General Physics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics