Stability and vibrations of catenoid-shaped smectic films

M. Ben Amar; P. P. da Silva; N. Limodin; A. Langlois; M. Brazovskaia; C. Even; I. V. Chikina; P. Pieranski

doi:10.1007/s100510050303

2021 Impact factor 1.398

Condensed Matter and Complex Systems

Eur. Phys. J. B 3, 197-202 (1998)
https://doi.org/10.1007/s100510050303

Stability and vibrations of catenoid-shaped smectic films

M. Ben Amar¹, P. P. da Silva¹, N. Limodin², A. Langlois², M. Brazovskaia², C. Even², I. V. Chikina³ and P. Pieranski²^a

¹ CNRS-Laboratoire de Physique Statistique de l'ENS, 24 rue Lhomond, 75231 Paris Cedex 05, France
² Laboratoire de Physique des Solides, Université Paris-Sud, Btiment 510, 91405 Orsay Cedex, France
³ Laboratoire Léon Brillouin, CEA Saclay-CNRS, 91191 Gif-sur-Yvette Cedex, France

Corresponding author: ^a pawel@lps.u-psud.fr

Received: 25 November 1997
Revised: 30 January 1998
Accepted: 9 March 1998
Published online: 15 May 1998

Abstract

Catenoid-shaped smectic films are spanned between two coaxial circular frames separated by a distance H. It is shown that there exists a critical height H^* such that below it two shapes of the catenoid are possible. The stability of these two shapes is analysed in terms of their vibrations. The spectrum of eigenfrequencies is calculated as a function of the catenoid height. It is shown that the frequency of the fundamental mode is real for the stable shape and imaginary for the other shape. Experimental study of vibrational eigenmodes performed on stable SCE4 films confirms this theoretical prediction.

PACS: 61.30.-v – Liquid crystals / 62.30.+d – Mechanical and elastic waves; vibrations / 03.40.-t – Classical mechanics of continuous media: general mathematical aspects

© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1998