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\chapter{\label{chapt:liquidcrystal}LIQUID CRYSTAL} |
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\section{\label{liquidCrystalSection:introduction}Introduction} |
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% liquid crystal |
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Long range orientational order is one of the most fundamental |
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properties of liquid crystal mesophases. This orientational |
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anisotropy of the macroscopic phases originates in the shape |
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anisotropy of the constituent molecules. Among these anisotropy |
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mesogens, rod-like (calamitic) and disk-like molecules have been |
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exploited in great detail in the last two decades. Typically, these |
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mesogens consist of a rigid aromatic core and one or more attached |
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aliphatic chains. For short chain molecules, only nematic phases, in |
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which positional order is limited or absent, can be observed, |
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because the entropy of mixing different parts of the mesogens is |
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paramount to the dispersion interaction. In contrast, formation of |
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the one dimension lamellar sematic phase in rod-like molecules with |
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sufficiently long aliphatic chains has been reported, as well as the |
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segregation phenomena in disk-like molecules. |
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% banana shaped |
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Recently, the banana-shaped or bent-core liquid crystal have became |
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one of the most active research areas in mesogenic materials and |
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supramolecular chemistry. Unlike rods and disks, the polarity and |
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biaxiality of the banana-shaped molecules allow the molecules |
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organize into a variety of novel liquid crystalline phases which |
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show interesting material properties. Of particular interest is the |
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spontaneous formation of macroscopic chiral layers from achiral |
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banana-shaped molecules, where polar molecule orientational ordering |
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is shown within the layer plane as well as the tilted arrangement of |
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the molecules relative to the polar axis. As a consequence of |
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supramolecular chirality, the spontaneous polarization arises in |
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ferroelectric (FE) and antiferroelectic (AF) switching of smectic |
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liquid crystal phases, demonstrating some promising applications in |
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second-order nonlinear optical devices. The most widely investigated |
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mesophase formed by banana-shaped moleculed is the $\text{B}_2$ |
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phase, which is also referred to as $\text{SmCP}$. Of the most |
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important discover in this tilt lamellar phase is the four distinct |
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packing arrangements (two conglomerates and two macroscopic |
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racemates), which depend on the tilt direction and the polar |
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direction of the molecule in adjacent layer (see |
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Fig.~\cite{LCFig:SMCP}). |
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%general banana-shaped molecule modeling |
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Many liquid crystal synthesis experiments suggest that the |
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occurrence of polarity and chirality strongly relies on the |
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molecular structure and intermolecular interaction. From a |
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theoretical point of view, it is of fundamental interest to study |
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the structural properties of liquid crystal phases formed by |
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banana-shaped molecules and understand their connection to the |
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molecular structure, especially with respect to the spontaneous |
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achiral symmetry breaking. As a complementary tool to experiment, |
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computer simulation can provide unique insight into molecular |
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ordering and phase behavior, and hence improve the development of |
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new experiments and theories. In the last two decades, all-atom |
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models have been adopted to investigate the structural properties of |
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smectic arrangements\cite{Cook2000, Lansac2001}, as well as other |
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bulk properties, such as rotational viscosity and flexoelectric |
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coefficients\cite{Cheung2002, Cheung2004}. However, due to the |
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limitation of time scale required for phase |
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transition\cite{Wilson1999} and the length scale required for |
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representing bulk behavior, the dominant models in the field of |
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liquid crystal phase behavior are generic |
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models\cite{Lebwohl1972,Perram1984, Gay1981}, which are based on the |
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observation that liquid crystal order is exhibited by a range of |
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non-molecular bodies with high shape anisotropies. Previous |
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simulation studies using hard spherocylinder dimer |
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model\cite{Camp1999} produce nematic phases, while hard rod |
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simulation studies identified a Landau point\cite{Bates2005}, at |
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which the isotropic phase undergoes a transition directly to the |
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biaxial nematic, as well as some possible liquid crystal |
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phases\cite{Lansac2003}. Other anisotropic models using Gay-Berne |
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potential give the evidence of the novel packing arrangement of |
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bent-core molecules\cite{Memmer2002,Orlandi2006}. |
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\section{\label{liquidCrystalSection:model}Model} |
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\section{\label{liquidCrystalSection:methods}Methods} |
