Multistability in the mixtures of smectic-$C^{*}$ materials with compensated twisting power

The effect of multistability in the mixtures of smectic-$C^{*}$ materials with compensated twisting power, i.e., the existence of a large number of almost equiprobable states in the same mixture under the same conditions, is analyzed in the framework of elastic continuum theory. A simple molecular model is also considered. It is shown that multistability can follow from the bulk properties of the smectic-$C^{*}$ materials with compensated twisting power, but with high spontaneous polarization. Multistability leads to the formation of ferroelectric domains, in which the director oscillates in space. The length and amplitude of this oscillation is tunable smoothly by an electric field. Theoretical results for the domain length agree completely with the experimental data. A suggestion is made as to why each domain structure is remembered without the energy consumption, when the electric field is abruptly switched off. The structural dependence on material parameters, such as the spontaneous polarization, the elastic constant, and the equilibrium wave number, is predicted.

Figure 1

Photograph of the planar cell with multistable smectic material FLC-346 placed between crossed polarizers: (a) before application of an electric field; (b) after the application and removal of the field. The image area in the photographs is $45\times 45\mu {\text{m}}^2$. Reproduced with permission from Ref. [25]. Copyright Pleiades Publishing, Inc., 2006.

Figure 2

Textures of multistable smectic material FLC-497 placed between crossed polarizers after application and switching off of the driving pulses with amplitudes (a) $\pm 3.3$ V, (b) $\pm 4.7$ V, (c) $\pm 6.5$ V, and (d) $\pm 15\text{V}$. The image area in the photographs is $350\times 400\mu {\text{m}}^2$. Reproduced with permission from Ref. [25]. Copyright Pleiades Publishing, Inc., 2006.

Figure 3

Flexoelectric polarization causes opposite-handedness of the helical rotation in (a) and (b) because of the opposite signs of flexoelectric constants. Molecules are supposed to be chiral (not shown); their handedness can be the same in (a) and (b).

Figure 4

Azimuthal orientation of the tilt plane normal with respect to the electric-field direction as a function of coordinate $z$ along the smectic layer normal in the oscillating regime.

Figure 5

Local minima free energies as functions of parameter ${\tau }^2=3P_{s}E/\left(K{q}_0^4\right)$, in correspondence with Eq. (12). Here ${\gamma }^{*}=0.01$. For each minimum $n$, the amplitude of oscillation ${\phi }_m$ belongs to the interval from $2\pi (n-1)$ to $2\pi n$.

Figure 6

Reduced period of multistable smectic structure as a function of parameter ${\tau }^2=3P_{s}E/\left(K{q}_0^4\right)$. Here ${\gamma }^{*}=0.01$. The right scale represents the corresponding values of amplitude ${\phi }_m$. An inset represents the smaller scale, at which the weakly first-order phase transition from the uniform rotation to the oscillation in space happens. The square bars reproduce the experimental variation of period calculated from Fig. 2 at substitution $p_0=28.3\mu \text{m}$ and $K{q}_0^4/P_s=17.8\text{V}/\mu \text{m}$.