Ferroelectric liquid crystals improper ferroelectrics

In solid state all the 10 pyroelectric crystal groups allow in principle for bistable switching behaviour. This is the proper ferroelectricity. Under certain conditions ferroelectricity (improper) can be realized in liquid crystals. This was shown by Meyer and coworkers115 in 1975. Since that time intense activities have been initiated, applying this property for flat-panel devices, switches, light modulators etc. In principle, three effects can be observed and used ... 

Ferroelectrics in which the polarization P is not the primary order parameter are called improper ferroelectrics. The concept was introduced by Dvofak [88] in 1974. As we have seen in the last example, improper ferroelectrics may behave very differently from proper ferroelectrics. The differences are related to the nature of the coupling. If we write the coupling term -Xq P, our first example showed that for n = 1, the behavior may, however, be very similar to that of proper ferroelectrics. This class of improper ferroelectrics for which = 1 is called pseudoproper ferroelectrics. Ferroelectric liquid crystals belong to this class. 

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... 

In the absence of any constraints, the direction of Ps rotates from one smectic layer to the next, with a period equal to the smectic C pitch, and so the average polarization for a sample would be zero. However, surface treatment or application of a field can cause the helix to untwist, resulting in a permanently polarized sample. The spontaneous polarization arises from a preferred alignment of molecular dipole components which are perpendicular to the molecular long axis, but it behaves differently from the ferroelectric and ferromagnetic polarization characterised for crystals. The liquid crystalline ferroelectric phases identified so far are improper ferroelectrics, since the spontaneous polarization results from a symmetry constraint, whereas in proper ferroelectrics the polarization results from dipole -dipole interactions. The Curie-Weiss law for proper ferroelectrics predicts a second order phase transition at the Curie temperature from the high temperature paraelectric state to a permanently polarized ferroelectric state ... 

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