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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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exploited in great detail in the last two decades\cite{Huh2004}. |
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Typically, these mesogens consist of a rigid aromatic core and one |
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or more attached aliphatic chains. For short chain molecules, only |
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nematic phases, in which positional order is limited or absent, can |
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be observed, because the entropy of mixing different parts of the |
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mesogens is paramount to the dispersion interaction. In contrast, |
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formation of the one dimension lamellar sematic phase in rod-like |
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molecules with sufficiently long aliphatic chains has been reported, |
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as well as the 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. |
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supramolecular chemistry\cite{Niori1996, Link1997, Pelzl1999}. |
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Unlike rods and disks, the polarity and biaxiality of the |
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banana-shaped molecules allow the molecules organize into a variety |
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of novel liquid crystalline phases which show interesting material |
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properties. Of particular interest is the spontaneous formation of |
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macroscopic chiral layers from achiral banana-shaped molecules, |
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where polar molecule orientational ordering is shown within the |
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layer plane as well as the tilted arrangement of the molecules |
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relative to the polar axis. As a consequence of supramolecular |
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chirality, the spontaneous polarization arises in ferroelectric (FE) |
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and antiferroelectic (AF) switching of smectic liquid crystal |
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phases, demonstrating some promising applications in second-order |
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nonlinear optical devices. The most widely investigated mesophase |
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formed by banana-shaped moleculed is the $\text{B}_2$ phase, which |
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is also referred to as $\text{SmCP}$\cite{Link1997}. 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.~\ref{LCFig:SMCP}). |
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The most widely investigated mesophase formed by banana-shaped |
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moleculed is the $\text{B}_2$ phase, which is also known as |
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$\text{SmCP}$. |
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\begin{figure} |
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\centering |
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\includegraphics[width=\linewidth]{smcp.eps} |
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\caption[] |
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{} |
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\label{LCFig:SMCP} |
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\end{figure} |
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%Previous Theoretical Studies |
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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\cite{Reddy2006}. |
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From a theoretical point of view, it is of fundamental interest to |
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study 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 transition and the |
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length scale required for representing bulk behavior, |
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models\cite{Perram1985, Gay1981}, which are based on the observation |
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that liquid crystal order is exhibited by a range of non-molecular |
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bodies with high shape anisotropies, became the dominant models in |
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the field of liquid crystal phase behavior. Previous simulation |
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studies using hard spherocylinder dimer model\cite{Camp1999} produce |
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nematic phases, while hard rod simulation studies identified a |
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Landau point\cite{Bates2005}, at which the isotropic phase undergoes |
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a direct transition to the biaxial nematic, as well as some possible |
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liquid crystal phases\cite{Lansac2003}. Other anisotropic models |
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using Gay-Berne(GB) potential, which produce interactions that favor |
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local alignment, give the evidence of the novel packing arrangements |
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of bent-core molecules\cite{Memmer2002,Orlandi2006}. |
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|
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Experimental studies by Levelut {\it et al.}~\cite{Levelut1981} |
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revealed that terminal cyano or nitro groups usually induce |
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permanent longitudinal dipole moments, which affect the phase |
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behavior considerably. A series of theoretical studies also drawn |
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equivalent conclusions. Monte Carlo studies of the GB potential with |
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fixed longitudinal dipoles (i.e. pointed along the principal axis of |
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rotation) were shown to enhance smectic phase |
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stability~\cite{Berardi1996,Satoh1996}. Molecular simulation of GB |
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ellipsoids with transverse dipoles at the terminus of the molecule |
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also demonstrated that partial striped bilayer structures were |
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developed from the smectic phase ~\cite{Berardi1996}. More |
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significant effects have been shown by including multiple |
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electrostatic moments. Adding longitudinal point quadrupole moments |
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to rod-shaped GB mesogens, Withers \textit{et al} induced tilted |
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smectic behaviour in the molecular system~\cite{Withers2003}. Thus, |
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it is clear that many liquid-crystal forming molecules, specially, |
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bent-core molecules, could be modeled more accurately by |
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incorporating electrostatic interaction. |
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|
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In this chapter, we consider system consisting of banana-shaped |
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molecule represented by three rigid GB particles with one or two |
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point dipoles at different location. Performing a series of |
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molecular dynamics simulations, we explore the structural properties |
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of tilted smectic phases as well as the effect of electrostatic |
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interactions. |
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|
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\section{\label{liquidCrystalSection:model}Model} |
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|
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A typical banana-shaped molecule consists of a rigid aromatic |
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central bent unit with several rod-like wings which are held |
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together by some linking units and terminal chains (see |
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Fig.~\ref{LCFig:BananaMolecule}). In this work, each banana-shaped |
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mesogen has been modeled as a rigid body consisting of three |
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equivalent prolate ellipsoidal GB particles. The GB interaction |
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potential used to mimic the apolar characteristics of liquid crystal |
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molecules takes the familiar form of Lennard-Jones function with |
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orientation and position dependent range ($\sigma$) and well depth |
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($\epsilon$) parameters. The potential between a pair of three-site |
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banana-shaped molecules $a$ and $b$ is given by |
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\begin{equation} |
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V_{ab}^{GB} = \sum\limits_{i \in a,j \in b} {V_{ij}^{GB} }. |
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\end{equation} |
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Every site-site interaction can can be expressed as, |
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\begin{equation} |
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V_{ij}^{GB} = 4\epsilon (\hat u_i ,\hat u_j ,\hat r_{ij} )\left[ |
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{\left( {\frac{{\sigma _0 }}{{r_{ij} - \sigma (\hat u_i ,\hat u_j |
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,\hat r_{ij} )}}} \right)^{12} - \left( {\frac{{\sigma _0 |
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}}{{r_{ij} - \sigma (\hat u_i ,\hat u_j ,\hat r_{ij} )}}} \right)^6 |
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} \right] \label{LCEquation:gb} |
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\end{equation} |
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where $\hat u_i,\hat u_j$ are unit vectors specifying the |
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orientation of two molecules $i$ and $j$ separated by intermolecular |
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vector $r_{ij}$. $\hat r_{ij}$ is the unit vector along the |
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intermolecular vector. A schematic diagram of the orientation |
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vectors is shown in Fig.\ref{LCFigure:GBScheme}. The functional form |
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for $\sigma$ is given by |
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\begin{equation} |
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\sigma (\hat u_i ,\hat u_i ,\hat r_{ij} ) = \sigma _0 \left[ {1 - |
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\frac{\chi }{2}\left( {\frac{{(\hat r_{ij} \cdot \hat u_i + \hat |
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r_{ij} \cdot \hat u_j )^2 }}{{1 + \chi \hat u_i \cdot \hat u_j }} |
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+ \frac{{(\hat r_{ij} \cdot \hat u_i - \hat r_{ij} \cdot \hat u_j |
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)^2 }}{{1 - \chi \hat u_i \cdot \hat u_j }}} \right)} \right]^{ - |
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\frac{1}{2}}, |
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\end{equation} |
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where the aspect ratio of the particles is governed by shape |
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anisotropy parameter |
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\begin{equation} |
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\chi = \frac{{(\sigma _e /\sigma _s )^2 - 1}}{{(\sigma _e /\sigma |
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_s )^2 + 1}}. |
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\label{LCEquation:chi} |
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\end{equation} |
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Here, $\sigma_ s$ and $\sigma_{e}$ refer to the side-by-side breadth |
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and the end-to-end length of the ellipsoid, respectively. The well |
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depth parameters takes the form |
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\begin{equation} |
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\epsilon (\hat u_i ,\hat u_j ,\hat r_{ij} ) = \epsilon _0 \epsilon |
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^v (\hat u_i ,\hat u_j )\epsilon '^\mu (\hat u_i ,\hat u_j ,\hat |
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r_{ij} ) |
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\end{equation} |
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where $\epsilon_{0}$ is a constant term and |
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\begin{equation} |
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\epsilon (\hat u_i ,\hat u_j ) = \frac{1}{{\sqrt {1 - \chi ^2 (\hat |
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u_i \cdot \hat u_j )^2 } }} |
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\end{equation} |
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and |
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\begin{equation} |
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\epsilon '(\hat u_i ,\hat u_j ,\hat r_{ij} ) = 1 - \frac{{\chi |
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'}}{2}\left[ {\frac{{(\hat r_{ij} \cdot \hat u_i + \hat r_{ij} |
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\cdot \hat u_j )^2 }}{{1 + \chi '\hat u_i \cdot \hat u_j }} + |
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\frac{{(\hat r_{ij} \cdot \hat u_i - \hat r_{ij} \cdot \hat u_j |
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)^2 }}{{1 - \chi '\hat u_i \cdot \hat u_j }}} \right] |
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\end{equation} |
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where the well depth anisotropy parameter $\chi '$ depends on the |
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ratio between \textit{end-to-end} well depth $\epsilon _e$ and |
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\textit{side-by-side} well depth $\epsilon_s$, |
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\begin{equation} |
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\chi ' = \frac{{1 - (\epsilon _e /\epsilon _s )^{1/\mu} }}{{1 + |
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(\epsilon _e /\epsilon _s )^{1/\mu} }}. |
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\end{equation} |
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|
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\begin{figure} |
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\centering |
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\includegraphics[width=\linewidth]{banana.eps} |
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\caption[]{} \label{LCFig:BananaMolecule} |
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\end{figure} |
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|
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%\begin{figure} |
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%\centering |
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%\includegraphics[width=\linewidth]{bananGB.eps} |
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%\caption[]{} \label{LCFigure:BananaGB} |
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%\end{figure} |
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|
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\begin{figure} |
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\centering |
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\includegraphics[width=\linewidth]{gb_scheme.eps} |
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\caption[]{Schematic diagram showing definitions of the orientation |
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vectors for a pair of Gay-Berne molecules} |
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\label{LCFigure:GBScheme} |
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\end{figure} |
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|
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To account for the permanent dipolar interactions, there should be |
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an electrostatic interaction term of the form |
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\begin{equation} |
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V_{ab}^{dp} = \sum\limits_{i \in a,j \in b} {\frac{1}{{4\pi |
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\epsilon _{fs} }}\left[ {\frac{{\mu _i \cdot \mu _j }}{{r_{ij}^3 }} |
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- \frac{{3\left( {\mu _i \cdot r_{ij} } \right)\left( {\mu _i \cdot |
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r_{ij} } \right)}}{{r_{ij}^5 }}} \right]} |
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\end{equation} |
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where $\epsilon _{fs}$ is the permittivity of free space. |
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|
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\section{Computational Methodology} |
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|
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A series of molecular dynamics simulations were perform to study the |
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phase behavior of banana shaped liquid crystals. |
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|
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In each simulation, rod-like polar molecules have been represented |
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by polar ellipsoidal Gay-Berne (GB) particles. The four parameters |
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characterizing G-B potential were taken as $\mu = 1,~ \nu = 2, |
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~\epsilon_{e}/\epsilon_{s} |
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= 1/5$ and $\sigma_{e}/\sigma_{s} = 3$. The components of the |
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scaled moment of inertia $(I^{*} = I/m \sigma_{s}^{2})$ along the |
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major and minor axes were $I_{z}^{*} = 0.2$ and $I_{\perp}^{*} = |
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1.0$. We used the reduced dipole moments $ \mu^{*} = \mu/(4 \pi |
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\epsilon_{fs} \sigma_{0}^{3})^{1/2}= 1.0$ for terminal dipole and |
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$ \mu^{*} = \mu/(4 |
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\pi \epsilon_{fs} \sigma_{0}^{3})^{1/2}= 0.5$ for second dipole, |
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where $\epsilon_{fs}$ was the permitivitty of free space. For all |
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simulations the position of the terminal dipole |
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has been kept |
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at a fixed distance $d^{*} = d/\sigma_{s} = 1.0 $ from the |
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centre of mass on the molecular symmetry axis. The second dipole |
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takes $d^{*} = d/\sigma_{s} = 0.0 $ i.e. it is on the centre of |
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mass. To investigate the molecular organization behaviour due to |
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different dipolar orientation with respect to the symmetry axis, we |
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selected dipolar angle $\alpha_{d} = 0$ to model terminal outward |
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longitudinal dipole and $\alpha_{d} = \pi/2$ to model transverse |
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outward dipole where the second dipole takes relative anti |
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antiparallel orientation with respect to the first. System of |
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molecules having a single transverse terminal dipole has also been |
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studied. We ran a series of simulations to investigate the effect of |
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dipoles on molecular organization. |
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|
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In each of the simulations 864 molecules were confined in a cubic |
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box with periodic boundary conditions. The run started from a |
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density $\rho^{*} = \rho \sigma_{0}^{3}$ = 0.01 with nonpolar |
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molecules loacted on the sites of FCC lattice and having parallel |
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orientation. This structure was not a stable structure at this |
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density and it was melted at a reduced temperature $T^{*} = k_{B}T/ |
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\epsilon_{0} = 4.0$ . We used this isotropic configuration which was |
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both orientationally and translationally disordered, as the initial |
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configuration for each simulation. The dipoles were also switched on |
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from this point. Initial translational and angular velocities were |
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assigned from the gaussian distribution of velocities. |
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|
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To get the ordered structure for each system of particular dipolar |
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angles we increased the density from $\rho^{*} = 0.01$ to $\rho_{*} |
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= 0.3$ with an increament size of 0.002 upto $\rho^{*} = 0.1$ and |
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0.01 for the rest at some higher temperature. Temperature was then |
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lowered in finer steps to avoid ending up with disordered glass |
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phase and thus to help the molecules set with more order. For each |
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system this process required altogether $5 \times 10^{6}$ MC cycles |
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for equilibration. |
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|
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The torques and forces were calculated using velocity verlet |
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algorithm. The time step size $\delta t^{*} = \delta t/(m |
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\sigma_{0}^{2} / \epsilon_{0})^{1/2}$ was set at 0.0012 during the |
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process. The orientations of molecules were described by quaternions |
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instead of Eulerian angles to get the singularity-free orientational |
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equations of motion. |
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|
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The interaction potential was truncated at a cut-off radius $r_{c} = |
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3.8 \sigma_{0}$. The long range dipole-dipole interaction potential |
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and torque were handled by the application of reaction field method |
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~\cite{Allen87}. |
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|
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To investigate the phase structure of the model liquid crystal |
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family we calculated the orientational order parameter, correlation |
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functions. To identify a particular phase we took configurational |
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snapshots at the onset of each layered phase. |
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|
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The orientational order parameter for uniaxial phase was calculated |
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from the largest eigen value obtained by diagonalization of the |
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order parameter tensor |
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|
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\begin{equation} |
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\begin{array}{lr} |
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Q_{\alpha \beta} = \frac{1}{2 N} \sum(3 e_{i \alpha} e_{i \beta} |
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- \delta_{\alpha \beta}) & \alpha, \beta = x,y,z \\ |
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\end{array} |
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\end{equation} |
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|
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where $e_{i \alpha}$ was the $\alpha$ th component of the unit |
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vector $e_{i}$ along the symmetry axis of the i th molecule. |
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Corresponding eigenvector gave the director which defines the |
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average direction of molecular alignment. |
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|
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The density correlation along the director is $g(z) = < \delta |
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(z-z_{ij})>_{ij} / \pi R^{2} \rho $, where $z_{ij} = r_{ij} cos |
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\beta_{r_{ij}}$ was measured in the director frame and $R$ is the |
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radius of the cylindrical sampling region. |
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|
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|
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\section{Results and Conclusion} |
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\label{sec:results and conclusion} |
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|
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Analysis of the simulation results shows that relative dipolar |
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orientation angle of the molecules can give rise to rich |
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polymorphism of polar mesophases. |
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|
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The correlation function g(z) shows layering along perpendicular |
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direction to the plane for a system of G-B molecules with two |
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transverse outward pointing dipoles in fig. \ref{fig:1}. Both the |
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+ |
correlation plot and the snapshot (fig. \ref{fig:4}) of their |
| 314 |
+ |
organization indicate a bilayer phase. Snapshot for larger system of |
| 315 |
+ |
1372 molecules also confirms bilayer structure (Fig. \ref{fig:7}). |
| 316 |
+ |
Fig. \ref{fig:2} shows g(z) for a system of molecules having two |
| 317 |
+ |
antiparallel longitudinal dipoles and the snapshot of their |
| 318 |
+ |
organization shows a monolayer phase (Fig. \ref{fig:5}). Fig. |
| 319 |
+ |
\ref{fig:3} gives g(z) for a system of G-B molecules with single |
| 320 |
+ |
transverse outward pointing dipole and fig. \ref{fig:6} gives the |
| 321 |
+ |
snapshot. Their organization is like a wavy antiphase (stripe |
| 322 |
+ |
domain). Fig. \ref{fig:8} gives the snapshot for 1372 molecules |
| 323 |
+ |
with single transverse dipole near the end of the molecule. |
| 324 |
+ |
|
| 325 |
+ |
\begin{figure} |
| 326 |
+ |
\begin{center} |
| 327 |
+ |
\epsfxsize=3in \epsfbox{fig1.ps} |
| 328 |
+ |
\end{center} |
| 329 |
+ |
\caption { Density projection of molecular centres (solid) and |
| 330 |
+ |
terminal dipoles (broken) with respect to the director g(z) for a |
| 331 |
+ |
system of G-B molecules with two transverse outward pointing |
| 332 |
+ |
dipoles, the first dipole having $d^{*}=1.0$, $\mu^{*}=1.0$ and the |
| 333 |
+ |
second dipole having $d^{*}=0.0$, $\mu^{*}=0.5$} \label{fig:1} |
| 334 |
+ |
\end{figure} |
| 335 |
+ |
|
| 336 |
+ |
|
| 337 |
+ |
\begin{figure} |
| 338 |
+ |
\begin{center} |
| 339 |
+ |
\epsfxsize=3in \epsfbox{fig2.ps} |
| 340 |
+ |
\end{center} |
| 341 |
+ |
\caption { Density projection of molecular centres (solid) and |
| 342 |
+ |
terminal dipoles (broken) with respect to the director g(z) for a |
| 343 |
+ |
system of G-B molecules with two antiparallel longitudinal dipoles, |
| 344 |
+ |
the first outward pointing dipole having $d^{*}=1.0$, $\mu^{*}=1.0$ |
| 345 |
+ |
and the second dipole having $d^{*}=0.0$, $\mu^{*}=0.5$} |
| 346 |
+ |
\label{fig:2} |
| 347 |
+ |
\end{figure} |
| 348 |
+ |
|
| 349 |
+ |
\begin{figure} |
| 350 |
+ |
\begin{center} |
| 351 |
+ |
\epsfxsize=3in \epsfbox{fig3.ps} |
| 352 |
+ |
\end{center} |
| 353 |
+ |
\caption {Density projection of molecular centres (solid) and |
| 354 |
+ |
terminal |
| 355 |
+ |
dipoles (broken) with respect to the director g(z) |
| 356 |
+ |
for a system of G-B molecules with single transverse outward |
| 357 |
+ |
pointing dipole, having $d^{*}=1.0$, $\mu^{*}=1.0$} \label{fig:3} |
| 358 |
+ |
\end{figure} |
| 359 |
+ |
|
| 360 |
+ |
\begin{figure} |
| 361 |
+ |
\centering \epsfxsize=2.5in \epsfbox{fig4.eps} \caption{Typical |
| 362 |
+ |
configuration for a system of 864 G-B molecules with two transverse |
| 363 |
+ |
dipoles, the first dipole having $d^{*}=1.0$, $\mu^{*}=1.0$ and the |
| 364 |
+ |
second dipole having $d^{*}=0.0$, $\mu^{*}=0.5$. The white caps |
| 365 |
+ |
indicate the location of the terminal dipole, while the orientation |
| 366 |
+ |
of the dipoles is indicated by the blue/gold coloring.} |
| 367 |
+ |
\label{fig:4} |
| 368 |
+ |
\end{figure} |
| 369 |
+ |
|
| 370 |
+ |
\begin{figure} |
| 371 |
+ |
\begin{center} |
| 372 |
+ |
\epsfxsize=3in \epsfbox{fig5.ps} |
| 373 |
+ |
\end{center} |
| 374 |
+ |
\caption {Snapshot of molecular configuration for a system of 864 |
| 375 |
+ |
G-B molecules with two antiparallel longitudinal dipoles, the first |
| 376 |
+ |
outward pointing dipole |
| 377 |
+ |
having $d^{*}=1.0$, $\mu^{*}=1.0$ and the second dipole having $d^{*}=0.0$, |
| 378 |
+ |
$\mu^{*}=0.5$ (fine lines are molecular symmetry axes and small |
| 379 |
+ |
thick lines show terminal dipolar direction, central dipoles are not |
| 380 |
+ |
shown).} \label{fig:5} |
| 381 |
+ |
\end{figure} |
| 382 |
+ |
|
| 383 |
+ |
|
| 384 |
+ |
\begin{figure} |
| 385 |
+ |
\begin{center} |
| 386 |
+ |
\epsfxsize=3in \epsfbox{fig6.ps} |
| 387 |
+ |
\end{center} |
| 388 |
+ |
\caption {Snapshot of molecular configuration for a system of 864 |
| 389 |
+ |
G-B molecules with single transverse outward pointing dipole, having |
| 390 |
+ |
$d^{*}=1.0$, $\mu^{*}=1.0$ (fine lines are molecular symmetry axes |
| 391 |
+ |
and small thick lines show terminal dipolar direction).} |
| 392 |
+ |
\label{fig:6} |
| 393 |
+ |
\end{figure} |
| 394 |
+ |
|
| 395 |
+ |
\begin{figure} |
| 396 |
+ |
\begin{center} |
| 397 |
+ |
\epsfxsize=3in \epsfbox{fig7.ps} |
| 398 |
+ |
\end{center} |
| 399 |
+ |
\caption {Snapshot of molecular configuration for a system of 1372 |
| 400 |
+ |
G-B molecules with two transverse outward pointing dipoles, the |
| 401 |
+ |
first dipole having $d^{*}=1.0$, $\mu^{*}=1.0$ and the second dipole |
| 402 |
+ |
having $d^{*}=0.0$, $\mu^{*}=0.5$(fine lines are molecular symmetry |
| 403 |
+ |
axes and small thick lines show terminal dipolar direction, central |
| 404 |
+ |
dipoles are not shown).} \label{fig:7} |
| 405 |
+ |
\end{figure} |
| 406 |
+ |
|
| 407 |
+ |
\begin{figure} |
| 408 |
+ |
\begin{center} |
| 409 |
+ |
\epsfxsize=3in \epsfbox{fig8.ps} |
| 410 |
+ |
\end{center} |
| 411 |
+ |
\caption {Snapshot of molecular configuration for a system of 1372 |
| 412 |
+ |
G-B molecules with single transverse outward pointing dipole, having |
| 413 |
+ |
$d^{*}=1.0$, $\mu^{*}=1.0$ (fine lines are molecular symmetry axes |
| 414 |
+ |
and small thick lines show terminal dipolar direction).} |
| 415 |
+ |
\label{fig:8} |
| 416 |
+ |
\end{figure} |
| 417 |
+ |
|
| 418 |
+ |
Starting from an isotropic configuaration of polar Gay-Berne |
| 419 |
+ |
molecules, we could successfully simulate perfect bilayer, antiphase |
| 420 |
+ |
and monolayer structure. To break the up-down symmetry i.e. the |
| 421 |
+ |
nonequivalence of directions ${\bf \hat {n}}$ and ${ -\bf \hat{n}}$, |
| 422 |
+ |
the molecules should have permanent electric or magnetic dipoles. |
| 423 |
+ |
Longitudinal electric dipole interaction could not form polar |
| 424 |
+ |
nematic phase as orientationally disordered phase with larger |
| 425 |
+ |
entropy is stabler than polarly ordered phase. In fact, stronger |
| 426 |
+ |
central dipole moment opposes polar nematic ordering more |
| 427 |
+ |
effectively in case of rod-like molecules. However, polar ordering |
| 428 |
+ |
like bilayer $A_{2}$, interdigitated $A_{d}$, and wavy $\tilde A$ in |
| 429 |
+ |
smectic layers can be achieved, where adjacent layers with opposite |
| 430 |
+ |
polarities makes bulk phase a-polar. More so, lyotropic liquid |
| 431 |
+ |
crystals and bilayer bio-membranes can have polar layers. These |
| 432 |
+ |
arrangements appear to get favours with the shifting of longitudinal |
| 433 |
+ |
dipole moment to the molecular terminus, so that they can have |
| 434 |
+ |
anti-ferroelectric dipolar arrangement giving rise to local (within |
| 435 |
+ |
the sublayer) breaking of up-down symmetry along the director. |
| 436 |
+ |
Transverse polarity breaks two-fold rotational symmetry, which |
| 437 |
+ |
favours more in-plane polar order. However, the molecular origin of |
| 438 |
+ |
these phases requires something more which are apparent from the |
| 439 |
+ |
earlier simulation results. We have shown that to get perfect |
| 440 |
+ |
bilayer structure in a G-B system, alongwith transverse terminal |
| 441 |
+ |
dipole, another central dipole (or a polarizable core) is required |
| 442 |
+ |
so that polar head and a-polar tail of Gay-Berne molecules go to |
| 443 |
+ |
opposite directions within a bilayer. This gives some kind of |
| 444 |
+ |
clipping interactions which forbid the molecular tail go in other |
| 445 |
+ |
way. Moreover, we could simulate other varieties of polar smectic |
| 446 |
+ |
phases e.g. monolayer $A_{1}$, antiphase $\tilde A$ successfully. |
| 447 |
+ |
Apart from guiding chemical synthesization of ferroelectric, |
| 448 |
+ |
antiferroelectric liquid crystals for technological applications, |
| 449 |
+ |
the present study will be of scientific interest in understanding |
| 450 |
+ |
molecular level interactions of lyotropic liquid crystals as well as |
| 451 |
+ |
nature-designed bio-membranes. |
| 452 |
+ |
|
| 453 |
|
\section{\label{liquidCrystalSection:methods}Methods} |
| 454 |
|
|
| 455 |
|
\section{\label{liquidCrystalSection:resultDiscussion}Results and Discussion} |
| 456 |
+ |
|
| 457 |
+ |
\section{Conclusion} |
