Eur. Phys. J. E (2012) 35: 133
https://doi.org/10.1140/epje/i2012-12133-7

Regular Article

Parity of the weak Fréedericksz transition

¹ CNISM and Dipartimento di Fisica, Università di Siena, via Roma 56, 53100, Siena, Italy
² Dipartimento di Ingegneria dell’Innovazione, Università del Salento, via per Monteroni, 73100, Lecce, Italy

^* e-mail: gaetano.napoli@unisalento.it

Received: 12 September 2012
Revised: 14 November 2012
Accepted: 3 December 2012
Published online: 19 December 2012

Abstract

Motivated by the recent experimental findings by Kumar et al. (Phys. Rev. E., 82, 011701 (2010)) in which the inverse Fréedericksz transition is observed, we have theoretically investigated the parity and the stability of the equilibrium configurations of a Fréedericksz cell with weak planar boundary conditions. Within the one-constant approximation of the Frank theory, the bulk equilibrium equation reduces to the nonlinear pendulum equation. Its solutions, when combined with boundary conditions deriving by the energy anchoring, lose uniqueness, exhibiting various symmetries. Thus, at a given anchoring strength and applied field, the cell becomes a system with metastable discrete energy levels. Our analysis proposes an explanation of the experimental results.