Smectic layer thickness

It has been shown that the AFM in the force spectroscopy mode is a very simple, accurate and straightforward method to measure the smectic layer thickness with a precision of 0.1 nm using a very small drop of a liquid crystal material. The method is less accurate in measuring the smectic compressibility modulus, which is due to the surface tension on a partially immersed AFM tip and the small, not very well defined radius of the AFM tip. 

The smectic C phase formed by chiral molecules (SmC phase) has also a helical superstructure having a pitch incommensurate with the smectic layer thickness. Theoretically chiral phases can also be formed by achiral molecules due to very specific packing [16]. For instance, three achiral rod-Uke molecules of dijfer-ent length may form a chiral trimer or a tripod due to Van der Waals interactions between their fragments, see Fig. 4.25a, and such trimers, in their turn, may form a kind of helical structure. Another example is bent-core or banana like-molecules [17]... 

Smectic A S. Smectic A has a structure in which the molecules are arranged in layers, as shown in Figure 3.2a, but the molecules are disordered within the layers. In thermotropic liquid crystals, the smectic layer thickness way vary from a value that is closer to the length of the molecule to a value that is almost twice this value" and is typically in the range 20-80 A. The lyotropic smectic A phase can have layer thicknesses up to several thousand angstroms. The director n represents the average molecular orientation of the molecules. 

In this equation Zi, describes the position of a mesogen i with respect to the z-axis of Cartesian coordinate system in which z is parallel to the layer normal k and d is the smectic layer thickness. For a hypothetical mesophase with a perfect smectic order, 2 would take a value of 2 = 1. For real SmA phases, typical values are 2 0.7 [19, 20]. 

In the course of the tilting of the mesogens, the smectic layer thickness d shrinks with respect to the SmA phase. This can already be seen by simply comparing... 

Let us finally look back to Fig. 61 and consider the material parameters 0, P, and d, i.e., tilt angle, polarization, and smectic layer thickness. They all depend on temperature d T), P T), and d(T). The temperature variations of 6 and P, if not desirable, at least turned out to be harmless. On the other hand, the much smaller temperature dependence of d (T) turned out to be significantly harmful. 

Figure 92. The shrinkage in smectic layer thickness due to the molecular tilt 0(T) in the SmC phase results in a folding instablity of the layer structure ( chevrons ). Even if the fold can he made to go everywhere in the same direction (in the figure to the right) to avoid invasive zigzag defect structures, the switching angle is now less than 2 9, which lowers brightness and contrast.

Figure 116. Two possible mechanisms for having a tilted smectic phase with a temperature-independent smectic layer thickness below the SmA - SmC transition. In (a) the end chains are first disordered but get more straight as the temperature is lowered in (b) each individual molecule keeps its tilt constant relative to the layer normal, but the azimuthal direction of the tilt is unbiased in the SmA phase. At the SmA - SmC transition the average direction of the molecules begins to get biased.

There is a clear odd-even effect the smectic layer thickness d increases with increasing n, but with an odd-even oscillation in which d for even n is relatively larger than that for odd n. 

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