Leslie external fields

Tendencies to instability in nature have been interpreted in various ways in continuum theory. We recall that many substances exhibit several phase transitions as, for example, their temperature is increased. A material initially described as a rigid solid may pass through smectic and nematic liquid crystal phases prior to behaving like an isotropic liquid. In a liquid crystal polymer, the concentration of solvent sometimes has the role of temperature. In the liquid crystal phase, the orientation of the molecules in terms of the optical axis may contribute to the response of this "fluid" to external fields. It is sometimes called an internal variable". The traditional field equations for an isotropic liquid are replaced by a more elaborate collection derived on the basis of continuum theory, (Ericksen [10], Leslie, [16], Hissbrun [H]). 

The values of the rotational viscosity coefflcients obtained for polymers X in the nematic phase (10-10 Pa sec) [37, 40], for polymer vn in the reentrant nematic phase (=5 10 Pa-sec) [42], and finally, the values of the Leslie viscosity coefficients (03, for polymer I (=10 Pa-sec) [43] also indicate the participation of the main chains of the macromolecules in orientational motion. It is evident that the polymeric viscosity of LC melts of comb-shaped polymers also determines all of the basic kinetic features of the orientational processes in external fields. 

The vector Lagrange multiplier j3 has a physical interpretation, as pointed out by Leslie [177]. If we consider planar layers subject to an external body moment, for example via an external field, or, as we shall see below in Section 6.3, perhaps subject to fiow, then equation (6.89) shows that the smectic layers are subject to the moments li = liji/j where i/ is the unit outward surface normal. If the smectic layers are constrained to be planar, for example by boundary plates parallel to the xy-plane with the smectic layer normal a = (0,0,1) coincident with the z axis, then, by (6.90),... 

Liquid crystals are generally characterized by the strong correlation between molecules, which respond cooperatively to external perturbations. That strong molecular reorientation (or director reorientation) can be easily induced by a static electric or magnetic field is a well-known phenomenon. The same effect induced by optical fields was, however, only studied recently. " Unusually large nonlinear optical effects based on the optical-field-induced molecular reorientation have been observed in nematic liquid-crystal films under the illumination of one or more cw laser beams. In these cases, both the static and dynamical properties of this field-induced molecular motion are found to obey the Ericksen-Leslie continuum theory, which describe the collective molecular reorientation by the rotation of a director (average molecular orientation). 

The nematic liquid crystal is orientationally soft, since restoring forces associated with deformation in the director field are very weak. This softness makes alignment of n in bulk samples occur even in very weak external magnetic or electric fields, F s H or E, or by interaction with boundary surfaces and flows in the liquid. This softness also allows for long wavelength thermal fluctuations in the director field. The Leslie viscosity parameters rather than the viscosity coefficients are the more natural quantities of interest for those methods that monitor the viscoelastic response of the nematic to director field modulations. Modulation of n in space and time manifests itself in variations of many bulk properties, e.g. the refractive index [27-37,41-44,48,51,94-106], electric susceptibility [38,39,107-110], or magnetic resonance spectra [40,45-47,111-113]. However, only a limited number of the viscosity parameters/coefficients can be precisely determined by these methods. 

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