SmC Liquid Crystals

Ferroelectricity in liquid crystals is mostly studied in the SmC liquid crystals. These studies resulted in over five thousand patents and thousands of papers. Here we just mention those properties that are in the line of our focus. Much more detailed overviews are given in a number of books and 

Illustration of the local symmetry of the chiral and nonchiral SmC phases of rod-shape molecules. Both SmC and SmC have a two-fold symmetry axis normal to the c-director. In SmC (a) the yz plane is a mirror plane, because the molecules have no handedness in SmC (b) the mirror image would have opposite handedness, so it is not a symmetry operation of the material. For this reason the x component of the molecular dipoles do not average out, allowing the presence of a permanent electric polarization of the material. Note the double-twist representation of the molecules serves only to indicate the chirality, and we do not assume such internal molecular structure. 

In the SmC liquid crystals, the primary order parameter is the director tilt and not the spontaneous polarization. The polarization, therefore, is often called secondary-order parameter, and the SmC materials are called improper ferroelectrics. The main reason for this is the weakness of the dipole-dipole interactions in the molecules. The polar order can be estimated by the ratio of the actual spontaneous polarization and which is the value that would appear when complete polar order is assumed. From its definition, the polarization is the density of the molecular dipoles. Assuming molecular dipoles of 3 Debye ( 10 Cm) and typical molecular weight of 300 g, density of about 1 g/cm = 10 kg/m, we get that in 1 m we have 6 10 molecules, which would give Po 2 W C/m = 2000nC/cm. For a SmC with Pg 100 nC/cnP, this means that less than 5% of the dipoles are ordered in one direction. For this reason, in the first approximation the polarization is proportional to the tilt angle. This relation, indeed, is found to be true for materials with moderate or low polarization. However, for materials with large polarization, like Pg 500 nC/cm, the dipole-dipole interaction becomes considerable, and the proportionality is not true. The deviation is more pronounced at lower temperatures, when the dipole-dipole 

Illustration of the helical ground state (b) and the field-induced unwound state (a and c). The boundary plates are shown so that they are corresponding to the bookshelf alignment. 

Temperature dependence of the spontaneous polarization and of the tilt angle of a material R046-4912 from ROLIC Research LTD. - tilt angle, spontaneous polarization. 

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Oligomers can be regarded as a class of materials combining the reduced viscosity of low molecular weight SmC liquid crystals with the existence of the glassy state at room... 

A proposed explanation of this unusual behavior, which has not yet been observed with the low molecular weight SmC liquid crystals, involves ... 

The phenomenon of sign reversal of P, which has already been demonstrated by Goodby et al. in a low molecular weight SmC liquid crystal [71], can also occur in an SmC polymer [21]. Polymer IX is the first example of an FLCP having such a behavior (Fig. 15). This phenomenon is attributed to a temperature-dependent equilibrium between different conformers of the chiral side chains, which have opposite sign of P. ... 

As shown in Table 6, a and a" are respectively of the same order of magnitude for polymers XII and XIII. It has to be pointed out that in the case of low molecular weight SmC liquid crystals, both o and d ... 

Additional information on ferroelectric and electroclinic switching can be obtained with broadband dielectric spectroscopy. It appears that the molecular dynamics of FLCPs are comparable to those of low molecular weight compounds [67]. However, the experimental observations are made more difficult for FLCPs than for low molecular weight SmC liquid crystals due to the conductivity contribution which takes place at frequencies below 10" Hz and to the difficulty to get a macroscopically well-aligned sample. 

From this ellipsoid we can find y/z for any direction specified by radius-vector r, see the figure. For example such an ellipsoid corresponds to the biaxial phase of the SmC liquid crystal. In this case all the three semi-axes are different i = 2 = ... 

The spontaneous electric polarization Ps of a thermotropic ferroelectric liquid crystal is usually measured with the so-called triangular wave method [16]. For this method, a triangular voltage U is applied to the liquid crystal and the so induced current in the liquid crystal is measured. This current can be divided into several contributions. If measuring a thermotropic SmC liquid crystal, the main contributors to the total current /ei. are the ohmic current, caused by the resistance / ei. of the liquid crystal, the capacitive current, due to the capacity C of the cell, and the polarization reversal current, which originates from the spontaneous electric polarization Ps of the polar liquid crystal. 

Ferroelectricity in SmC liquid crystals is directly observed in the surface-stabilized state in which macroscopic domains of opposite tilt direction are connected to opposite directions of the spontaneous polarization cf. Sect. 1.2). An electric field-induced reversal of the direction of spontaneous polarization also reverses the direction of tilt and thus leads to a polar bistable electro-optic response. In thermotropic SmC liquid crystals this unique combination of a fluid ferroelectric material was and is extensively studied. 

The subject of this thesis is the discovery and characterization of the lyotropic analog of the well-known thermotropic ferroelectric SmC liquid crystal phase. In addition to providing evidence for the existence of this previously unknown phase, the main focus of the work presented is on the investigation of its stmctural properties and chirality effects. In particular, the following results were obtained ... 

The two most common molecular motifs that lead to liquid crystal phase behavior are the rod aud the disk. Clearly rodlike molecules have one unique axis that is longer than the other two, while diskUke molecules have one unique short axis and two longer axes (Figure 1). RodUke molecules organize into nematic or smectic phases, while disklike systems form nematic or colunmar phases. Figure 2 shows schematic diagrams of molecules arranged in a nematic, smectic A (SmA), and smectic C (SmC) liquid crystal phase (= mesophase). There are very many smectic phases of which SmA and SmC are only two. ... 

Ferroelectric SmC liquid crystals have also been used [77], and these give bistable... 

We see from Figure 8.13 that a number of liquid crystal phases, SmC of chiral rod-shape and the tilted columnar phase of chiral disc shape molecules, as well as the SmCP of achiral bent-core, and the tilted bowl-shape molecules all have C2 symmetry with eight independent piezoelectric coefficients. The direct and converse i- piezoelectric effects have been mostly studied in the fluid SmC liquid crystals. 

In addition to the dielectric relaxation modes of anisotropic 3D fluids, just as nematic liquid crystals, helical SmC liquid crystals (see Chapter 1, Figure 1.11) have interesting low-frequency dielectric modes that are related... 

Dierking I, Komitov L, Lagerwall ST, Wittig T, Zentel R (1999) Horizontal chevrrai dmnain formation and smectic layer reorientation in SmC liquid crystals stabilized by polymta-networks. Liq Cryst 26(10) 1511-1519... 

The finite tilt of the director axis from the layer normal (taken as the z axis) introduces a new degree of freedom, namely, a rotation aroimd the z axis, compared to the SmA phase. This rotation preserves the layer spacing and therefore does not require too much energy. Since du/dy and du/dx are equivalent to rotations around the x and y axes, respectively, we may express the free energy in Smectic-C (SmC) liquid crystals in terms of the rotation components ... 

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