Nematic fluctuations and semisoft elasticity in swollen liquid-crystal elastomers

Dynamic light scattering (DLS) experiments were performed on stretched sheets of liquid crystal elastomers (LCEs) swollen with a nematic solvent with different swelling ratios. We show that the obtained stress-strain curve and DLS data can still be explained with the concepts of semisoft elasticity. The stress-strain curve shows a typical semisoft response with a threshold strain and a plateau region where stress increases only a little with the applied strain. The width of the plateau decreases with the increase of the swelling ratio because the polymer backbone anisotropy reduces during the swelling. The relaxation rate of thermally excited director fluctuations, however, still shows a typical response, and our measurements indicate the presence of a soft dynamic director-shear mode, as predicted by the theory of semisoft elasticity.

Figure 1

The geometry of the scattering experiment. The incoming light ${\mathbf{k}}_i$ was vertically polarized, and horizontally polarized scattered light ${\mathbf{k}}_f$ was detected and analyzed as a function of scattering angle $\theta$ and applied extension $\lambda$ parallel to $\mathbf{n}$. The scattering vector $\mathbf{q}={\mathbf{k}}_i-{\mathbf{k}}_f$ was approximately parallel to the director (bend mode detection). $\vartheta$ is a misalignment between the director and the scattering vector.

Figure 2

The chain conformation parameter is obtained from the ratio $r={(L/L_{\mathrm{iso}})}^3$ of the length of the sample to its reference length. Chain anisotropy $r$ reduces and the nematic to isotropic transition temperature decreases with the increase of the swelling ratio $X$.

Figure 3

Stress-strain curve for stretching along the director (left) and for the soft geometry (right). Solid lines show fits to the semisoft model from which the shear constants ${\mu }_{\parallel }$ and ${\mu }_{\perp }$ are obtained.

Figure 4

Bend mode relaxation rate as a function of imposed extension $\lambda$ along the director measured at $q={10}^7{\text{m}}^{-1}$ (left), and as a function of wave vector $q$ at a fixed deformation $\lambda =1.1$. The relaxation rate increases with $\lambda$, and extrapolation of results to negative strain reveals the existence of a dynamic soft mode. The relaxation rate is also proportional to the square of the wave vector, as expected.