Lena Lopatina

Theory of Ferroelectric Nanoparticles in Nematic Liquid Crystals

Recent experiments have reported that ferroelectric nanoparticles have drastic effects on nematic liquid crystals-increasing the isotropic-nematic transition temperature by about 5 K, and greatly increasing the sensitivity to applied electric fields. To understand these effects, we develop a theory for the statistical mechanics of ferroelectric nanoparticles in liquid crystals. This theory predicts the enhancements of liquid-crystal properties, in good agreement with experiments. These predictions apply even when electrostatic interactions are partially screened by moderate concentrations of ions.

Maier-Saupe-type theory of ferroelectric nanoparticles in nematic liquid crystals

Several experiments have reported that ferroelectric nanoparticles have drastic effects on nematic liquid crystals-increasing the isotropic-nematic transition temperature by about 5 K, and greatly increasing the sensitivity to applied electric fields. In a recent paper [Lopatina and Selinger, Phys. Rev. Lett. 102, 197802 (2009)], we modeled these effects through a Landau theory, based on coupled orientational order parameters for the liquid crystal and the nanoparticles. This model has one important limitation: Like all Landau theories, it involves an expansion of the free energy in powers of the order parameters, and hence it overestimates the order parameters that occur in the low-temperature phase. For that reason, we now develop a new Maier-Saupe-type model, which explicitly shows the low-temperature saturation of the order parameters. This model reduces to the Landau theory in the limit of high temperature or weak coupling, but shows different behavior in the opposite limit. We compare these calculations with experimental results on ferroelectric nanoparticles in liquid crystals.

Softening of stressed granular packings with resonant sound waves.

We perform numerical simulations of a two-dimensional bidisperse granular packing subjected to both a static confining pressure and a sinusoidal dynamic forcing applied by a wall on one edge of the packing. We measure the response experienced by a wall on the opposite edge of the packing and obtain the resonant frequency of the packing as the static or dynamic pressures are varied. Under increasing static pressure, the resonant frequency increases, indicating a velocity increase of elastic waves propagating through the packing. In contrast, when the dynamic amplitude is increased for fixed static pressure, the resonant frequency decreases, indicating a decrease in the wave velocity. This occurs both for compressional and for shear dynamic forcing, and is in agreement with experimental results. We find that the average contact number Zc at the resonant frequency decreases with increasing dynamic amplitude, indicating that the elastic softening of the packing is associated with a reduced number of grain-grain contacts through which the elastic waves can travel. We image the excitations created in the packing and show that there are localized disturbances or soft spots that become more prevalent with increasing dynamic amplitude. Our results are in agreement with experiments on glass bead packings and earth materials such as sandstone and granite, and may be relevant to the decrease in elastic wave velocities that has been observed to occur near fault zones after strong earthquakes, in surficial sediments during strong ground motion, and in structures during earthquake excitation.

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.