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Reports: ND753018-ND7: Experimental and Numerical Studies of Liquid Crystal Defects in Confined Geometries

Qi-Huo Wei, PhD, Kent State University

This new direction (ND) project aims 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 of liquid crystal (LC) molecule orientation by boundaries induces frustration, drives the formation of topological defects and affects the phase behaviours. LCs in confined geometries are important to many applications as exemplified by polymer dispersed liquid crystals (PDLC) and LC biosensors. Specifically in this project, two distinctive liquid crystal systems in confined geometries are studied: (1) patterned liquid crystal droplets of complex shapes with varied topologies, and (2) liquid crystals in ultra-thin cells and channels. To facilitate direct comparison between experimental observations and numerical simulations, we use state-of-the-art nanofabrication techniques to create confinement geometries with tailored surface anchoring and characterize the resulting defect structures by using optical microscopic observations. During the first year of this project, we made significant progresses in three aspects:

(1) Patterned LC droplets: To make liquid crystal droplets with designable shape and sizes, we have developed a robust process based on micro-contact printing technique. Firstly, a polydimethylsiloxane (PDMS) mold is fabricated by patterning an epoxy photoresist (SU8) using photolithography and then pouring/curing PDMS precursors on these SU8 microstructures. After the PDMS mold is separated from the master, ethanol solution of mercaptododacanoic acid (MDA) is used as ink to print patterns of self-assembled monolayers on thin Au films through the micro-contact printing technique (Fig. 1a). Then the remaining area of the Au film is covered with hexadecanethiol (HDT) by immersing the sample in ethanol solution of HDT. As the last step, a large liquid crystal droplet is formed on the substrate and moved around by using a needle (Fig. 1a). An exemplary PDMS mold is shown in Fig. 1b. Due to the high wettability of LCs on the patterned MDA areas, arrays of LC droplets are formed behind the big moving LC droplets: (Fig. 1c).

We found that the contact angle of 5CB LCs is around 5 degrees on the self-assembled MDA, indicating a low surface energy. In contrast, the 5CB LCs on self-assembled HDT exhibit much larger contact angle, indicating a larger surface energy at the LC-HDT interface. Another observation is that the contact angle with HDT shows a clear decrease with time, which indicates some adsorption and mixing of the 5CB molecules on the HDT monolayers. In addition, we have also measured the pretilt angle of 5CB on MDA, which is close to 20¡ã.

With circular patterns of MDA and circular LC droplets, we observed three different types of defects: (1) The most commonly observed are single defect with plus one topological charge; (2) the second most commonly observed are single defects plus a ring; and (3) the least commonly observed are two plus one and one minus one defects. Computer simulations are being performed to understand detailed molecular orientation fields in these defect structures.

 

 (2) LCs in Micro/Nanochannels: A series of simulation studies by Žumer et al demonstrate that with non-curved geometric confinements, complex and ordered defect structures may be induced in chiral nematic LCs. For example, for highly chiral liquid crystals confined in thin cells with fixed planar anchoring, stable states of defect lines such as ring arrays and Skyrmion lattices are predicted. In contrast to these intriguing phenomena observed by theoretical and numerical studies, experimental studies of such system have lagged behind somewhat due to the challenge of designing and fabricating appropriate confining structures with precise control of surface anchoring.

 During this project period, we have developed a reliable process for fabricating liquid crystal cells with cell thickness ranging from 100nm to a few micron meters (Fig. 3), and studied the structures of both nematic and cholesteric LCs confined in such geometries. A variety of defect textures have been observed in experiments. (1) In cells filled with periodic posts and homeotropic alignments at all boundaries, we observe chiral textures around the posts for large post spacing while defects lines connecting posts when the post spacing is small. (2) In rectangular microchannels, the channel size and aspect ratio plays an important role. For large channel widths, parallel and periodic defect lines are observed, while for small channel widths, defects similar to bubble domains are observed. (3) The nematic-isotropic phase transition is mediated by shape changes of the bubble domain defects.

(3) Numerical Modeling: Numerical Modeling: To gain insight into defect formation and the role of channel dimensions and temperatures in confined geometries, we have carried out simulation studies of this system. We write the elastic free energy density of the system in terms of the local nematic order tensor Qij(x,y,z) and evolve it forward in time via relaxation using the finite difference method, taking account of anchoring conditions at confining surfaces. As a simplifying assumption, we describe the material as uniaxial and with spatially uniform scalar order parameter, thus reducing the number of degrees of freedom at each site.

 We have also modelled microstructures of cholesteric liquid crystals confined to narrow channels and have successfully reproduced bubble domain structures like those in Fig. 4 as well as the fingerprint texture. In order to match simulation to experiment, we have taken into account the variation of the twist, bend, and splay elastic constants with temperature for the relevant material, 5CB. We are in the process of incorporating also the temperature dependence of the cholesteric pitch, which will be fitted to experimental measurements. This modeling capability allows us to gain insight into the relationship between confinement geometry and resulting microstructure. In the next phase of modeling for this project, we will examine more complex geometries including non-circular droplets and cells containing an array posts. We also plan to implement our modeling algorithm in the CUDA programming language to achieve faster performance in a GPU-enabled computing environment.