60th Annual Report on Research 2015

The objective of this new direction (ND) project is aimed at fundamental understanding of liquid crystals (LCs) under a variety of engineered micro and nanoconfinements. Due to the long-range nature of orientational ordering, the anchoring conditions and boundary geometries plan a critical role in the formation of topological defects and the phase behaviours. LCs in confined geometries are related to many applications as exemplified by polymer dispersed liquid crystals (PDLC) and LC biosensors. Two distinctively different confined geometries studied in this project are (1) liquid crystal droplets formed on chemically patterned substrates, and (2) liquid crystals confined in thin cells and micron-channels. During the second year of this project, we established fundamental understanding of these two systems and expanded our efforts into a third project: thermophoresis of colloidal particles in nematic liquid crystals.

(1) LC droplets on Chemically Patterned Substrates: We have developed micro-contact printing process to pattern self-assembled monolayers and a drag-drop process to form liquid crystal droplets on these molecular patterns. To understand the defects textures observed in these patterned nematic liquid crystal droplets, we have developed Monte-Carlo simulation algorithms and our simulation results show that the domain structures of the patterned self-assembled monolayers have significant impacts on the the defects inside the droplets. When the domain sizes are small, only one single defect are normally observed, and the situation is similar to planar degenerate anchoring. When the domain size is increased, the defect structures are complex and highly sensitive to the domain structures.

(2) LCs in Micro/Nanochannels: We experimentally studied the microstructures and phase transitions of cholesteric liquid crystals confined in rectangular microchannels. For homeotropic surface anchoring, we have established the phase diagram of the microstructures as a function of the channel width and depth (Fig. 1). When the channel depth is below half the cholesteric pitch, the liquid crystals follow the homeotropic alignments of top and bottom surfaces with a director perpendicular to the channel plane. While for channel depth around 1.5 of cholesteric pitch, topological defects of skymions are observed. The skymion is non-singular defect which has homeotropic on top and bottom surfaces and twisted in the interior, or the magnitude of nematic order is constant throughout the structure without a disordered core region. It is stabilized, relative to a uniform homeotropic configuration, because of the chirality of the liquid crystal which favors twist. When the channel depth is of cholesteric pitch or larger, stripe patterns of of liquid crystals can be observed.

To gain insights into these defect structures, we carried out simulation studies using a finite difference relaxation technique. Our model is based on the Frank free energy expressed in terms of the nematic order tensor. Starting from a discrete representation of the director on a cubic lattice mesh spanning our model geometry, we relax the director at each site. By implementing this algorithm in the CUDA programming language on a GPU-equipped computer, we have achieved very impressive computational performance with a speed-up of a factor of 45 vs execution on a single processor. To study the dependence of defect structures on temperature, we considered the temperature dependence of the Frank elastic constants and the cholesteric pitch. This approach allowed modelling evolution of defect structures as a function of both geometry and temperature. An exemplary skymion structure simulated in the microchannels is shown Fig. 2.

(3) Thermophoresis in nematic liquid crystals: When particles suspended in a medium are subjected to a temperature gradient, a directional motion of the particles can be induced, a phenomenon known as thermophoresis. Since J. Tyndall firstly documented a dust-free region around a hot body in 1870, thermophoresis has been observed in different media including isotropic liquids and gasses. We studied for the first time thermophoresis of colloidal particles suspended in nematic liquid crystals. Our experiments show that in the opposite to the positive thermophoresis in isotropic solvents, the colloidal particles drift from low temperature to high temperature regimes in nematic liquid crystals. An exemplary result of the measured drift velocity is presented in Fig. 3 as a function of temperature for a 5mm colloidal particle in the nematic liquid crystal 5CB under a linear temperature gradient (~ 2K/mm). The observed negative thermophoresis roots in the elastic energy of the director field distortion and its decrease with the increase of temperature, an effect denoted here as elastophoresis. To understand these experimental results, we developed a simple model based on single K approximation and showed that the drift velocity as results of combining normal thermophoresis and elastophoresis can be expressed as where a and b are fitting parameters, T is the temperature, T* is N-I phase transition temperature, a=0.18 for 5CB, and  is the temperature dependent viscosity of the liquid crystal. The excellent agreement between this theoretical expression and experimental measurements can be seen in Fig. 3. The measured Soret coefficient for colloidal particles in 5CB is similar in magnitude with normal thermophoresis in water but is negative. Given that the viscosity of liquid crystals is much higher than that of water, the suppressed Brownian motion makes the elastophoresis in liquid crystals a potential approach for particle and potentially molecular sorting.

The NDI grant from PRF provides a significant support for the PI to extend his research into new areas in liquid crystals and to establish close collaborations with expert colleagues in liquid crystals. Direct support of this grant has benefited four graduate students and generated research results for three manuscripts.