Distortions of the structure by external fields

Detailed analytical and numerical calculations have been presented by Kini. i When a is smalF  

It is seen that for pitch values of the order of the sample thickness, t/ pp should exhibit oscillatory behaviour with varying pitch because of the term sin qh/qh in (4.5.30). A representative theoretical curve is presented in Fig. 4.5.5. This prediction has been verified qualitatively. Measurements of the apparent viscosity on the cholesteryl chloride-cholesteryl myristate mixture, whose pitch, as we have seen earlier, is sensitive to temperature (fig. 4.1.16), showed evidence of oscillations as the temperature was varied (fig. 4.5.6). 

in practical cases, qh is so large that sm qh/qh is negligibly small and / pp approaches a maximum limiting value which is independent of the pitch or gap width. This value is several orders of magnitude less than that for flow along the helical axis and is comparable to that for a nematic. 

1 Magnetic field normal to the helical axis the cholesteric-nematic 

The variation of pitch with magnetic field strength predicted by (4.6.1) has been verified experimentally (fig. 4.6.2). It has also been confirmed that //(, is inversely proportional to the pitch of the undistorted structure. It turns out that with the usually available magnetic field strengths, the experiment is conveniently performed only with cholesterics of relatively large pitch. For example, in a typical measurement using nematic PAA doped with a small amount of cholesteryl acetate was 8.3 kG for Pj = 26 nm. 

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In many applications involving nonequilibrium instabilities and dissipative structures, the sharp transitions corresponding to bifurcation rarely occur. Small impurities, imperfections, or external fields tend to distort these transitions. Many experiments, particularly in fluid dynamics, illustrate this fact and demonstrate, in addition, that small imperfections may have large or even qualitative effects. This very general phenomenon is at the basis of the enhanced sensitivity of systems operating near a bifurcation point discussed in the chapter by I. Prigogine. 

In the previous sections, theories were reviewed where the optical properties of polymer liquids were cast in terms of the microscopic properties of the constituent chains. The dynamics of polymer chains subject to external fields that orient and distort these complex liquids are considered in this section for a variety of systems ranging from dilute solutions to melts. Detailed descriptions of theories for the dynamics and structure of polymer fluids subject to flow are found in a number of books, including those by Bird et al. [62], Doi and Edwards [63], and Larson [64],... 

It is essential to know that for the internal excitation, as well as for the external one, every harmonic of the primary field passing the shell is reduced but that its structure has not been changed. Therefore, the shell, characterized by coordinate a = const, does not distort the structure of any harmonic, regardless of the location of the primary source with respect to the shell. 

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