Smectic order

Wlren a nematic phase is cooled towards a smectic A phase, fluctuations of smectic order build up. These fluctuations were called cybotactic clusters in tire early literature. Regardless of tire physical picture of such fluctuations. 

Here A, C and E are phenomenological coefficients in the Landau expansion in tenns of the smectic ordering ... 

C and I account for gradients of the smectic order parameter the fifth tenn also allows for director fluctuations, n. The tenn is the elastic free-energy density of the nematic phase, given by equation (02.2.9). In the smectic... 

Stroobants A, Lekkerkerker FI N W and Frenkel D 1986 Evidence for smectic order in a fluid of hard parallel spherocylinders Phys.Rev.Lett 57 1452-5 Erratum 57 2331... 

Other more exotic types of calamitic liquid crystal molecules include those having chiral components. This molecular modification leads to the formation of chiral nematic phases in which the director adopts a natural helical twist which may range from sub-micron to macroscopic length scales. Chirality coupled with smectic ordering may also lead to the formation of ferroelectric phases [20]. 

The frustration effects are implicit in many physical systems, as different as spin glass magnets, adsorbed monomolecular films and liquid crystals [32, 54, 55], In the case of polar mesogens the dipolar frustrations may be modelled by a spin system on a triangular lattice (Fig, 5), The corresponding Hamiltonian consists of a two particle dipolar potential that has competing parallel dipole and antiparallel dipole interactions [321, The system is analyzed in terms of dimers and trimers of dipoles. When the dipolar forces between two of them cancel, the third dipole experiences no overall interaction. It is free to permeate out of the layer, thus frustrating smectic order. 

A spin-gas microscopic theory has been pursued by Berker et al. [32] to explain the multiplicity of smectic ordering and the re-entrance phenomenon in strongly polar mesogens. They have used a model Hamiltonian of the form... 

Mesophase with a helicoidal supramolecular structure of blocks of molecules with a local smectic C structure. The layer normal to the blocks rotates on a cone to create a helix-like director in the smectic C. The blocks are separated by plane boundaries perpendicular to the helical axis. At the boundary, the smectic order disappears but the nematic order is maintained. In the blocks the director rotates from one boundary to the other to allow the rotation of the blocks without any discontinuity in the thermomolecular orientation. 

X-ray patterns of smectic polymers are characterized by a series of distinct equatorial layer reflexes at small scattering angles, as is seen from Figs. 8 and 9. The presence of small angle reflexes indicates smectic order in packing of side branches, which are stacked perpendicularly or inclinely to the planes of the smectic layers formed by the backbones of macromolecules. 

The smectic order parameter / which describes the spatial variation of density due to the layered structure... 

Salditt, T., Koltover, L, Radler, J.O. and Safinya, C.R. (1997) Two-dimensional smectic ordering of linear DNA chains in self-assembled DNA-cationic liposome mixtures. Phys. Rev. Lett., 79, 2582-2585. 

In our model the moduli of the nematic and smectic order parameters play similar roles, so we will deal with both. Since we consider a situation beyond the phase transition regime, the equilibrium value of the order parameter is non-zero (S s for both nematic and smectic) and only its variations s(n,s can enter the energy density (S = S(q s) + s ) ... 

We write the solution as the vector X = (6,(j),u,vx,vy,i ,P,) consisting of the angular variables of the director, the layer displacement, the velocity field, the pressure, and the modulus of the (nematic or smectic) order parameter. For a spatially homogeneous situation the equations simplify significantly and the desired solution Xo can directly be found (see Sect. 3.1). To determine the region of stability of Xq we perform a linear stability analysis, i.e., we add a small perturbation Xi to... 

Equation (39) shows that nematic degrees of freedom couple to simple shear, but not the smectic degrees of freedom the modulus of the nematic order parameter has a non-vanishing spatially homogeneous correction (see (39)), whereas the smectic order parameter stays unchanged. The reason for this difference lies in the fact that J3 and /3 include h and p, respectively, which coupled differently to the flow field (see (22) and (23)). Equation (38) gives a well defined relation between the shear rate y and the director tilt angle 9o, which we will use to eliminate y from our further calculations. To lowest order 0O depends linearly on y ... 

To implement this intuitive physical picture, we take into account the smectic order dependence (84) of Z i in (63), add the energy of smectic order variations (5) to our collection of energy contributions, and regard as another dynamic variable... 

Polymers with methyl substitution on the central linkage in the stilbene mesogenic group have been prepared, Polymers 4 and 5, and show strictly nematic mesophases . The methyl group seems to act mostly to inhibit the existence of smectic order, but otherwise does not influence the mesophase formation or thermal stability very much. 

The chiral side chain polymers derived from asymmetric esters of terephthalic acid and hydroquinone can form (in a broad temperature range, including ambient temperature) an unusual mesophase (the isotropic smectic phase, IsoSm ) characterized by high transparency and optical isotropy within the visible wavelength range, combined with a hidden layered smectic ordering and some elements of helical superstructure at shorter dimensions of 10 to 250 nm. The short-pitch TGB A model seems to be the most adequate for the mesophase structure. 

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