3. Model

transverse, can be clearly identified. Both set of variables are completely decoupled: there are five in the first and two in the second group. The longitudinal variables in turn can be separated into two mutually independent sets. The first is composed of two variables whose dynamics determine the existence of acoustic propagation modes; while the second, formed by three variables, giving rise to three hydrodynamic modes: one related to the orientation of the director and two more, the socalled visco-heat modes, that result from the coupling of the thermal diffusive and shear modes due by the presence of the gradient thermal and the gravitational field. As will be discussed later on, from the set of transverse variables, two hydrodynamic modes emerge: one due to the orientation of the director and another one due to shearing. Altogether, there are seven nematic hydrodynamic modes: five longitudinal and two transversal. As will be shown below, the applied gradient of temperature and gravitational field produce their greatest effect in the pair of viscoheat modes, which is quantified in them by means of the Rayleigh quotient R=Rc, where R is the number of Rayleigh and Rc the value that it reaches when in the

The liquid crystal phase is a well-defined and specific phase of matter characterized by a remarkable anisotropy in many of their physical properties as solid crystals do, although they are able to flow. Liquid crystal phases that undergo a phase transition as a function of temperature (thermotropics) exist in relatively small intervals of temperature lying between solid crystals and isotropic liquids. Due to this intermediate nature, sometimes, these states are called also mesophases [32]. In general, liquid crystals are synthesized from organic molecules, some of which are elongated and uniaxial, so they can be represented as rigid rods; others are formed by disc-like molecules [35]. This molecular anisotropy is manifested macroscopically through the anisotropy of the mechanical, optical, and transport properties of these substances. The typical dimensions of the lengths of this type of

Liquid crystals are classified by symmetry. As it is well known, isotropic liquids

with spherically symmetric molecules are invariant under rotational, Oð Þ3 , and

Representation of the average orientation of the molecules of a thermotropic NLC by means of the director

nematic initiates the convection.

Non-Equilibrium Particle Dynamics

2. Liquid crystalline phases

structures are some tens of angstroms.

Figure 1.

vector n^.

148

Consider a NLC thin layer of thickness d under the presence of a constant gravitational field g !¼ �g^z, where g denotes its magnitude and ^z the unit vector along the z axis. The initial configuration of the layer is homeotropic with a preferential orientation n^<sup>0</sup> along the z axis, as depicted in Figure 2. The nematic is confined between two parallel flat plates kept at fixed temperatures T<sup>1</sup> and T<sup>2</sup> (T<sup>1</sup> , T2), so that a uniform temperature gradient ∇zT � �α^z is established downward in the layer. The situation where the temperature gradient goes from bottom to top can also be considered, and in this case, ∇zT � α^z. The gravitational force induces a pressure gradient, ∇zp ¼ �ρg^z, where ρ is the mass density.

### Figure 2.

The NLC cell subject to a constant gravitational field g ! and an external uniform temperature gradient ∇T. k ! is the scattering vector.
