Elasticity theory of smectic and canonic mesophases

Abstract

The general theory of elasticity for smectic and canonic mesophases is formulated, starting from the assumption that the equilibrium state is spatially periodic. The various surface terms appearing in the deformation free energy density are considered as well. The efFective description of the elastic behavior of a general nonchiral smectic mesophase involves one positional elastic constant, 16 bulk orientational elastic constants, and six surface orientational elastic constants. One additional bulk orientational elastic constant is required for the description of a general chiral smectic mesophase. The efFective description of the elastic behavior of a general nonchiral canonic mesophase involves six positional elastic constants and three bulk orientational elastic constants. In this case the property of chirality does not introduce additional orientational elastic constants. The elastic constants for some relevant smectic and canonic mesophases are given, including the elastic constants for the antiferroelectric Sm-C& and ferrielectric Sm-C' and Sm-C~phases. PACS number(s): 03.40.Dz

Layer distortions induced by a magnetic field in planar samples of smectic C liquid crystals

“…This setting of a coincides with that of Stallinga and Vertogen [22] up to second order in the first derivatives of u. Notice, by equation (23), that e remains as stated in (28) under the transformation W.{W; also note that u z is unchanged under the simultaneous changes u.…”

“…A comparison with the work of the Orsay Group is made and it is also shown in appendix B that for each of the three usual equivalent nonlinear formulations of the bulk energy w b , the same quadratic energy in terms of u arises for variables separable solutions. The selection of the forms for the perturbations to the vectors a and c are motivated by the work by Stallinga and Vertogen [22] who have given a quite general formulation of these vectors for smectic phases in terms of u and its derivatives. (We note here that u corresponds to the component denoted by u z in [22]: this is because the components u x and u y , also introduced in [22], do not enter the theory.)…”

“…The selection of the forms for the perturbations to the vectors a and c are motivated by the work by Stallinga and Vertogen [22] who have given a quite general formulation of these vectors for smectic phases in terms of u and its derivatives. (We note here that u corresponds to the component denoted by u z in [22]: this is because the components u x and u y , also introduced in [22], do not enter the theory.) The consequent energies are summarized in § 2.5.…”

Simulation of Surface-Enhanced Ordering in Smectic Films

“…We extend the model by adding a nematic elastic term, l 1 , to model smectic defects [14][15][16] in addition to nucleation and growth. An important aspect of the model is the inclusion of a second order derivative term of the complex order parameter.…”

Nonlinear hydrodynamics of strongly deformed smectic C and C liquid crystals

“…An early, not quite satisfactory attempt in that direction has been made by the present au- terms that are not compatible with the layer structure, but would lead to a different ground state with a different symmetry and different broken symmetries. Quite recently the statics of strongly deformed (layered) smectic as well as discotic phases (including strong curvature and compression) has been discussed [8]. A dynamic theory based on continuum mechanics of smectic C and C* phases with strong layer curvature, but with constant layer spacing (no true elasticity, i.e.…”