Nematic phase elasticity moduli

All physical parameters mentioned above are material specific and temperature dependent (for a detailed discussion of the material properties of nematics, see for instance [4]). Nevertheless, some general trends are characteristic for most nematics. With the increase of temperature the absolute values of the anisotropies usually decrease, until they drop to zero at the nematic-isotropic phase transition. The viscosity coefficients decrease with increasing temperature as well, while the electrical conductivities increase. If the substance has a smectic phase at lower temperatures, some pre-transitional effects may be expected already in the nematic phase. One example has already been mentioned when discussing the sign of Ua- Another example is the divergence of the elastic modulus K2 close to the nematic-smecticA transition since the incipient smectic structure with an orientation of the layers perpendicular to n impedes twist deformations. 

Figure 30. Thermal evolution at three frequencies of the dynamic shear elastic modulus G in an elastomer exhibiting a smectic phase and a nematic phase [118],...

In contrast to the extensive experimental investigations of nematic, cholesteric and chiral SmC phases, comparatively little work has been done on tbe characterization of the physical properties of SmA and SmC elastomers. The elongation, A, has been measured as a function of temperature for constant external load for a number of different loads in SmA sidechain elastomers [6]. It was found that A increases monotonically as a function of temperature for a material, which has a SmA-I transition. In addition it was shown that the elasticity modulus, E, decreases monotonically with temperature. X-ray investigations on SmA phases in side-chain LCE have been performed [70]. It was found that for the family of compounds studied, the orientation of the mesogenic groups was always perpendicular to the direction of stretching. 

In conclusion, from the measurements of x the coefficient yi = 0 3 — 012 could be found if the cell thickness and elastic modulus are known. Note that yj coefficient is the most important for applications. Then, using data on the ratio of 0 3/012 we can find 0 3 and ot2 separately. Further, using the known coefficient for the isotropic phase viscosity 0 4 = 2ria, the coefficients 0 5 = 2r[t. — 2ria + 0.2 and ag = 2r]b — 2ria — 0 3 can be calculated and, for the particular nematic liquid crystal, the applicability of the Parodi relationship ag — ag = a2+ 0 3 verified. As to aj it can be found from... 

The oscillations of I (U) are well seen in the experimental plot. Fig. 11.21. The measurements were made at 27°C on 55 nm thick cell filled with a mixture having ta = 22. From the I (U) curve, the field dependence of the phase retardation 8(17) and the Frederiks transition threshold Uc were obtained. In mm, from Ec = UJd and Fq. (11.56) the splay elastic constant Ku was found. The bend modulus "33 was calculated from the derivative dbldU. The same material parameters may be found for the whole temperature range of the nematic phase. 

Here, is an effective elastic modulus for the azimuthal motion of the director in the SmC phase that includes factor sin 9 [11]. Due to this factor, in the one-constant approximation, which will be used below, k 10 dyn is roughly one order of magnitude smaller than for nematics. The third term in the equation for Tch determins the difference in the transition temperatures for a helical and unwound ferroelectric. 

In the smectic A phase the director is always perpendicular to the plane of the smectic layers. Thus, only the splay distortion leaves the interlayer distance unchanged [7], and only the elastic modulus K i is finite while K22 and Kzz diverge when approaching the smectic A phase from the nematic phase. On the other hand, the compressibility of the layered structure and the corresponding elastic modulus B is taken into account when discussing the elastic properties of smectic phases. The free energy density for the smectic A phase, subjected to the action of an external electric field, is... 

So far it has been tacitly assumed that the rod-like particles are completely rigid. Particularly for rod-like polymers this is frequently not the case. For these systems the wormlike chain model, which can be seen as a thin cylinder with an elastic bending modulus provides a better description than the completely rigid rod. This flexibility of the particles has a pronounced effect on the isotropic-nematic phase transition, which has been extensively reviewed by Odijk l. In the following I will limit myself to systems that consist of (almost) perfectly rigid rods. 

In equations (5)-(8), i is the molecule s moment of Inertia, v the flow velocity, K is the appropriate elastic constant, e the dielectric anisotropy, 8 is the angle between the optical field and the nematic liquid crystal director axis y the viscosity coefficient, the tensorial order parameter (for isotropic phase), the optical electric field, T the nematic-isotropic phase transition temperature, S the order parameter (for liquid-crystal phase), the thermal conductivity, a the absorption constant, pj the density, C the specific heat, B the bulk modulus, v, the velocity of sound, y the electrostrictive coefficient. Table 1 summarizes these optical nonlinearities, their magnitudes and typical relaxation time constants. Also included in Table 1 is the extraordinary large optical nonlinearity we recently observed in excited dye-molecules doped liquid... 

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