Polymer-disordered liquid crystals: Susceptibility to an electric field

When nematic liquid crystals are embedded in random polymer networks, the disordered environment disrupts the long-range order, producing a glassy state. If an electric field is applied, it induces large and fairly temperature-independent orientational order. To understand the experiments, we simulate a liquid crystal in a disordered polymer network, visualize the domain structure, and calculate the response to a field. Furthermore, using an Imry-Ma-like approach we predict the domain size and estimate the field-induced order. The simulations and analytic results agree with each other, and suggest how the materials can be optimized for electro-optic applications.

Figure 1

Director profile and polymer orientations in the simulations. Green sites (light gray) are liquid crystal; red sites (dark gray) are polymer. (a) At low temperature the directors form domains with local orientational order, which cannot extend over a long range. (b) The same region of material at high and low temperatures without electric field and under applied electric field. At low field there is partial alignment of the liquid-crystal directors with the electric field, and at high field the directors are completely aligned with the field.

Figure 2

Dependence of the correlation length on temperature for various anchoring strengths: points are results from computer simulations, and dashed red and solid green lines are fits for high and low temperatures, respectively. Inset: Correlation functions for various temperatures, fitted to an exponential form.

Figure 3

Dependence of the Kerr constant $\alpha$ on temperature for various anchoring strengths. Left inset: Dependence of the correlation length $\xi$ and Kerr constant $\alpha$ on polymer anchoring energy $H$ in the limit of low temperature. Right inset: Dependence of the scalar order parameter $S$ on external electric field $E$, for various temperatures, fitted to the functional form given in Eq. (2).