Search

The anisotropic physical properties resembling those of fluids and solids of smectic liquid crystals are discussed. Based upon micropolar theory, a set of constitutive equations generalizing the Kelvin‐Voigt model has been derived. Material moduli are restricted by material symmetry and physical considerations. The concepts of reference state fundamental to smectic liquid crystals are discussed. Three types of problems, bending, torsion, and wave propagation, are presented. Future studies and experiments are suggested with the hope of creating further confidence in the theory.

The governing partial differential equation for the distribution of orientations is obtained for nematic liquid crystals. The boundary condition for orientation at the surface of the container depends on the type of surface and the type of liquid crystal. Two extreme cases, orientation either parallel or perpendicular to the surface, have been solved and the orientational effects due to magnetic field is determined.

Two problems in the theory of nematic liquid crystals are formulated. One is concerned with the change of orientation due to magnetic field and the other with shear flow. The solutions of the governing differential equations explain the physical phenomena which have been observed experimentally, namely the alignment of nematic liquid crystals with the magnetic field and with shear flow. In fact, it is shown that these two phenomena are closely related to each other.

The most general solution of micropolar elasticity has been obtained for static plane problems in a circular ring-shaped region. For illustrative purpose, two examples of Volterra's dislocation problem are given to demonstrate the physical meaning of many-valued solutions.

For the thermomechanics of nematic and cholesteric liquid crystals, the Ericksen-Leslie theory and the theory based upon micropolar continuum mechanics are presented. The similarities and differences in basic laws of motion and constitutive equations between these two theories are discussed in detail. For illustrative purpose solutions of some special problems are given in order to illustrate special features of these theories.

Based on the theory of micropolar viscoelasticity a continuum theory of cholesteric liquid crystals is presented. The balance laws of motion are given and a constitutive theory is derived and restricted by the second law of thermodynamics. Material symmetry restrictions are obtained by means of physical considerations. The theory includes thermomechanical effects of dissipation. The axis of ellipse and coefficient of optical activity are defined to characterize the helical structure of cholesteric liquid crystals. Analytically it is shown that in general the coefficient of optical activity depends on the temperature variations, deformation and mechanical stresses. Several special cases of practical importance are studied in detail. A coupling of longitudinal and twist waves along the axis of helix is investigated theoretically and corresponding experiments are suggested.

Ultrasonic longitudinal waves were observed in a nematic liquid crystal (p‐azoxyanisole) which was ordered by a magnetic field. Attenuation in the direction of the field‐induced nematic axis was 30% greater than that perpendicular to the axis and was independent of field strength. No anisotropy in velocity was observed to an error of ± 0.1%.