The commensurate and incommensurate TGBC*liquid crystal phases
Yves Galerne
Institut de Physique et Chimie des Matériaux de
Strasbourg, Groupe des Matériaux Organiques, 23 rue du L
ss,
F-67037 Strasbourg, France
Yves.Galerne@ipcms.u-strasbg.fr
Received 30 November 1999 and Received in final form 5 May 2000
Abstract
We propose complements to the Renn model of the liquid crystal
TGBC* phase. We argue that the rotation angle per helislab is
spontaneously in the radian range, not too small to limit the
energy cost of the twist grain boundaries between the helislabs,
not too large to preserve the double twisting efficiency. Taking
the elastic interactions between the helislabs into account, we
show that the structure may undergo two different lock-ins,
provided that the uncontrolled interactions at the sample surfaces
are small enough. First, for appropriate values of the elastic
constants, an angular lock-in may fix the rotation angle per
helislab at values exactly commensurate to 
.
Three
characteristic lengths of the TGBC* phase, the TGB period and
the thicknesses of both the smectic blocks and of the helislabs are
then commensurate to one another, with moreover, integer ratios at
the most efficient commensurabilities. The TGBC* phase could
thus exist in several versions, incommensurate and commensurate,
according to the steps of a restricted Devil's staircase. A second
elastic lock-in should then arise in the commensurate TGBC*phases, to set the arrays of disclination lines between the
helislabs in simple rectangular lattices, arranged in a helical
manner. Being placed right behind one another, the disclination
lines then coincide when observed along the TGB axis. This could
explain the typical textures with square or hexagonal grids,
observed in oriented samples. The commensurability of the TGBC*phases could be analyzed with X-ray scattering experiments in the
same manner as already reported for the TGBC phase.
PACS
61.30.Cz Theory and models of liquid crystal structure -
61.30.Jf Defects in liquid
crystals - 64.70.Rh Commensurate-incommensurate transitions
Copyright EDP Sciences, Società Italiana di Fisica, Springer-Verlag
