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Cholesteric energies

Published online by Cambridge University Press:  29 March 2006

James T. Jenkins
James T. Jenkins
Affiliation:
Department of Mechanics, The Johns Hopkins University
Present address: Faculté des Sciences, Laboratoire de Physique des Solides, 91-Orsay, France.
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Abstract

Repeated observations of a uniformly twisted director field in cholesteric liquid crystals are used to motivate an expression for a free energy which is obtained as an expansion about this state. Terms quadratic in the director perturbation and the gradients of this perturbation are retained. Utilizing invariance arguments, it is possible to obtain significant simplification of the coefficients which appear in the expansion. A properly invariant form of the free energy is produced which agrees with the expansion for small excursions about a twisted state, and which assigns arbitrary values to the non-vanishing coefficients.

The consequences of requiring that a free energy achieve a minimum at a twisted state are explored. A commonly used form of the free energy for cholesteric liquid crystals is seen to be rather severely restricted by this requirement. An alternative to this form is proposed which is a special case of the free energy previously produced. The particular form suggested attains a unique absolute minimum at a characteristic uniform twist.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 45 , Issue 3 , 15 February 1971 , pp. 465 - 475
Copyright
© 1971 Cambridge University Press

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References

de Gennes, P.-G. 1968a Fluctuations d'orientation et diffusion Rayleigh dans un cristal nematique. Comtes Rendus 266 (B), 15–17.Google Scholar
de Gennes, P.-G. 1968b Calcul de la Distorsion d'une Structure Choesterique par un Champ Magnetique Solid State Comm. 6, 163–165.Google Scholar
Durand, G., Leger, L., Rondelez, F. & Veyssie, M. 1969 Magnetically induced cholesteric-to-nematic phase transition in liquid crystals Phys. Rev. Lett. 22, 227–228.Google Scholar
Ericksen, J. L. 1961 Conservation laws for liquid crystals Trans. Soc. Rheol. 5, 23–24.Google Scholar
Ericksen, J. L. 1962a Hydrostatic theory of liquid crystals Arch. Rat. Mech. Anal. 10, 371–378.Google Scholar
Ericksen, J. L. 1962b Nilpotent energies in liquid crystal theory Arch. Rat. Mech. Anal. 10, 189–196.Google Scholar
Ericksen, J. L. 1966a Inequalities in liquid crystal theory Phys. Fluids, 9, 1205–1207.Google Scholar
Ericksen, J. L. 1966b A thermo-kinetic view of elastic stability theory Int. J. Solids Structures, 2, 573–580.Google Scholar
Ericksen, J. L. 1967a Continuum theory of liquid crystals Appl. Mech. Rev. 20, 1029–1032.Google Scholar
Ericksen, J. L. 1967b Twisting of liquid crystals J. Fluid Mech. 27, 59–64.Google Scholar
Frank, F. C. 1958 On the theory of liquid crystals Discuss. Faraday Soc. 25, 19–28.Google Scholar
Leslie, F. M. 1968a Some constitutive equations for liquid crystals Arch. Rat. Mech. Anal. 28, 265–283.Google Scholar
Leslie, F. M. 1968b Some thermal effects in cholesteric liquid crystals. Proc. Roy. Soc A 307, 359–372.Google Scholar
Robinson, C., Ward, J. C. & Beevers, R. B. 1958 Liquid crystalline structure in polypeptide solutions Discuss. Faraday Soc. 25, 29–42.Google Scholar