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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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