Measurement of the Helical Pitch

In further temperature and concentration-dependent measurements of the helical pitch, only mixtures with formamide were chosen as the lengthy evolution time necessary for mixtures with water together with the ever present threat of solvent evaporation make such investigations of mixtures with water much more complicated. In Fig. 5.33 the helical pitch p is plotted versus the reduced temperature T - Tq for a sample with 18 wt% of formamide. The pitch shows the typical temperature dependence known from thermotropic SmC phases [30]. Right after the phase transition into the lyotropic SmC analog phase, the pitch increases rapidly to a value of about 5.5 pm and decreases more slowly towards a low temperature value of about 2.5 pm. However, by repeating the measurement with other concentrations of formamide, no significant difference in the value of p could be detected. 

The reason for this behavior can be found in the measuring conditions. The temperature-dependent measurement of the helical pitch was performed with the direct method cf. Sect. 4.5.1) in a sample of 30 pm thickness. Apparently, in such rather thin samples compared to the value of the helical pitch, the formation of the helical director configuration cannot take place undisturbed, but is influenced significantly by interactions with the surfaces of the liquid crystal cell. Consequently, the observed value of p depends rather on the cell gap than on the intrinsic pitch of the lyotropic SmC analog phase. Nonetheless, the measurement in Fig. 5.33 indicate that the helical pitch of the lyotropic SmC analog phase varies with temperarnre and that the temperature dependence is comparable to the one of thermotropic SmC phases. 

To avoid the influence of surface interactions on the measurement of the helical pitch length, two alterations of the experiment are possible. The first one is to enlarge the thickness of the sample significantly. The second is to measure the helical pitch length under homeotropic boundary conditions which are known to not afifect its value [33]. Both methods, i.e. the direct method cf. Sect. 4.5.1) with samples of 250 pm thickness and the Cano method cf. Sect. 4.5.2), were applied to determine the influence of the solvent concentration on the helical pitch length. 

Fig. 5.33 Temperature dependence of the helical pitch p measured with the direet method in a 30 pm thick sample of C50 with 18 wt% of formamide...

All the above methods give the same error ( 10%) in the determination of the helical pitch, while each of them is suitable for a narrow range of pitches. When measurements are required over a wide interval of change in the pitch, the various methods have to be combined. Figure 6.3 offers an illustration of this. The figure is taken from our own work (see [6] and other references therein). 

Twisting a nematic structure around an axis perpendicular to the average orientation of the preferred molecular axes, one arrives at the molecular arrangement commonly called cholesteric (Kelker and Hatz, 1980). The twisted nematic phase is optically uniaxial, however with the axis perpendicular to the (rotating) director. Such a mesophase combines the basic properties of nematics with the implications of chirality The structure itself is chiral and as a consequence, a non-identical mirror image exists as it is shown schematically in Fig. 4.6-7. Besides the order parameters mentioned before, the essential characteristics of a cholesteric mesophase are the pitch, i.e., the period of the helical structure as measured along the twist axis, and its handedness, i.e., whether the phase is twisted clockwise or anticlockwise. 

A chiral compound, dissolved in a nematic liquid crystal phase, transforms this phase into a chiral phase that is very often a chiral nematic - cholesteric -phase. Under the same condition of concentration and temperature two enantiomers induce helical structures with the same pitch but of opposite sign. The helical pitch p is for low concentrations of the dopant a linear function of mole fraction x. The molecular measure for the chiral induction is the helical twisting power (ITTP) ... 

Thermal optical microscopy also finds extensive use in the analysis of optically active mesophases where the molecules can form macroscopic helical structures. For instance, the pitch length for helical phases can be determined by measuring the distances between the defect lines formed through the interaction of the helical structure and the surface of the preparation. The microscope can also be used as polarimeter to determine helical twist direction for homeotropically aligned helical mesophases. 

The key parameter for the tunability is the helical pitch Po, which can be found from the measurements of... 

Like in the nematic phase, the textures of SmC reveal blurred Schlieren patterns with linear singularities of strength s = 1. The singularities of 5 = 1/2 are not observed due to the reduced symmetry (C2h) of the SmC phase. Chiral smectics C are periodic structures and the helical pitch can be measured under a microscope either from the Grandjean lines or as a distance between the lines indicating periodicity, like in Fig. 8.22 for the cholesteric phase. On the other hand, like in... 

In Eqs. (1) through (3), n and are the extraordinary and ordinary refractive indices of the locally uniaxial system, X is the wavelength of light in vacuum and p is the pitch of the twisted structure defined as the distance measured along the helical axis for the local optic axis to twist around a full 360 . It follows from Eqs. (l)-(3) that the major and minor axes of vibration of both elliptical eigenwaves are either parallel or perpendicular to the local optic axis L. The ellipticities of the eigenwaves, e. and e, are defined by... 

The helical pitch of the SmC phase and its lyotropic analog can be measured by several methods. In this thesis two of them were used to double-check the obtained results. The first applied technique is the so-called direct method [7], which requires an orientation of the layer normal k normal to the direction of observation ( planar alignment ). The second one is the Cano method [7, 8] in which the layer normal k has to be parallel to this direction ( homeotropic ). 

Even in the thermodynamic equilibrium, 0 z) can form a periodic soliton-like structure with a period incommensurate with the helical pitch qo = 2itfPo [41]. When the field is applied the conical distortion can appear, especially for certain values of the twist elastic constants, K22 > Kzz [29, 42]. Such conical distortion can be accompanied by a compression of the hehcal pitch. The results of some earlier controversial observations were discussed in [6] and [1]. Probably, the conical deformation has been observed in a ternary cholesteric mixture by measuring the field-induced changes in the... 

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