Statistical models of elasticity in main chain and smectic liquid ...

5.4. CONCLUSIONS 133Alternatively, one can think of imposing the λ yy extension to induce therotation φ of c, Fig. 5.6, and the sympathetic shears λ xz , λ yz and λ yx , Fig. 5.7.These plots of the explicit forms given for the elements of λ reveal singularedges to the rotation φ at 0,π and 2π analogously to those seen in nematicsoft elasticity. Although for r = 2 and θ = 30 ◦ the extend of soft extension isonly 7%.32φ101 1.02 1.04 1.06 1.08λ yyFigure 5.6: Director rotation φ about the layer normal againstelongation, λ yy , perpendicular to its initial direction (r =2,θ = 30 ◦ ).It should be noted that the sample can develop very large shears softly; atφ = π, λ xz ∼ − 1 2, see Fig. 5.7.5.4 ConclusionsA geometrical interpretation of the soft modes in two phases of smectic elastomershas been presented. It was found that there is only one soft trajectoryfor the director, excluding body rotations, as a consequence of the restrictionsimposed upon the elastomer by the fixed layer constraint. Specific examplesof this mode were presented for a monodomains of biaxial SmA or SmC. Theycan respond softly to a single imposed component of the deformation tensor.An illustration of imposed λ yy was given but in principle we could imposeany other component, including λ zz , through a combination of the single softtrajectory and a body rotation. The experimental boundary conditions of