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# Line 7 | Line 7 | exploited in great detail in the last two decades. Typ
7   anisotropy of the macroscopic phases originates in the shape
8   anisotropy of the constituent molecules. Among these anisotropy
9   mesogens, rod-like (calamitic) and disk-like molecules have been
10 < exploited in great detail in the last two decades. Typically, these
11 < mesogens consist of a rigid aromatic core and one or more attached
12 < aliphatic chains. For short chain molecules, only nematic phases, in
13 < which positional order is limited or absent, can be observed,
14 < because the entropy of mixing different parts of the mesogens is
15 < paramount to the dispersion interaction. In contrast, formation of
16 < the one dimension lamellar sematic phase in rod-like molecules with
17 < sufficiently long aliphatic chains has been reported, as well as the
18 < segregation phenomena in disk-like molecules.
10 > exploited in great detail in the last two decades\cite{Huh2004}.
11 > Typically, these mesogens consist of a rigid aromatic core and one
12 > or more attached aliphatic chains. For short chain molecules, only
13 > nematic phases, in which positional order is limited or absent, can
14 > be observed, because the entropy of mixing different parts of the
15 > mesogens is paramount to the dispersion interaction. In contrast,
16 > formation of the one dimension lamellar sematic phase in rod-like
17 > molecules with sufficiently long aliphatic chains has been reported,
18 > as well as the segregation phenomena in disk-like molecules.
19  
20   Recently, the banana-shaped or bent-core liquid crystal have became
21   one of the most active research areas in mesogenic materials and
22 < supramolecular chemistry. Unlike rods and disks, the polarity and
23 < biaxiality of the banana-shaped molecules allow the molecules
24 < organize into a variety of novel liquid crystalline phases which
25 < show interesting material properties. Of particular interest is the
26 < spontaneous formation of macroscopic chiral layers from achiral
27 < banana-shaped molecules, where polar molecule orientational ordering
28 < is shown within the layer plane as well as the tilted arrangement of
29 < the molecules relative to the polar axis. As a consequence of
30 < supramolecular chirality, the spontaneous polarization arises in
31 < ferroelectric (FE) and antiferroelectic (AF) switching of smectic
32 < liquid crystal phases, demonstrating some promising applications in
33 < second-order nonlinear optical devices. The most widely investigated
34 < mesophase formed by banana-shaped moleculed is the $\text{B}_2$
35 < phase, which is also referred to as $\text{SmCP}$. Of the most
22 > supramolecular chemistry\cite{Niori1996, Link1997, Pelzl1999}.
23 > Unlike rods and disks, the polarity and biaxiality of the
24 > banana-shaped molecules allow the molecules organize into a variety
25 > of novel liquid crystalline phases which show interesting material
26 > properties. Of particular interest is the spontaneous formation of
27 > macroscopic chiral layers from achiral banana-shaped molecules,
28 > where polar molecule orientational ordering is shown within the
29 > layer plane as well as the tilted arrangement of the molecules
30 > relative to the polar axis. As a consequence of supramolecular
31 > chirality, the spontaneous polarization arises in ferroelectric (FE)
32 > and antiferroelectic (AF) switching of smectic liquid crystal
33 > phases, demonstrating some promising applications in second-order
34 > nonlinear optical devices. The most widely investigated mesophase
35 > formed by banana-shaped moleculed is the $\text{B}_2$ phase, which
36 > is also referred to as $\text{SmCP}$\cite{Link1997}. Of the most
37   important discover in this tilt lamellar phase is the four distinct
38   packing arrangements (two conglomerates and two macroscopic
39   racemates), which depend on the tilt direction and the polar
40   direction of the molecule in adjacent layer (see
41 < Fig.~\cite{LCFig:SMCP}).
41 > Fig.~\ref{LCFig:SMCP}).
42  
43   \begin{figure}
44   \centering
# Line 49 | Line 50 | molecular structure and intermolecular interaction. Fr
50  
51   Many liquid crystal synthesis experiments suggest that the
52   occurrence of polarity and chirality strongly relies on the
53 < molecular structure and intermolecular interaction. From a
54 < theoretical point of view, it is of fundamental interest to study
55 < the structural properties of liquid crystal phases formed by
53 > molecular structure and intermolecular interaction\cite{Reddy2006}.
54 > From a theoretical point of view, it is of fundamental interest to
55 > study the structural properties of liquid crystal phases formed by
56   banana-shaped molecules and understand their connection to the
57   molecular structure, especially with respect to the spontaneous
58   achiral symmetry breaking. As a complementary tool to experiment,
# Line 62 | Line 63 | limitation of time scale required for phase
63   smectic arrangements\cite{Cook2000, Lansac2001}, as well as other
64   bulk properties, such as rotational viscosity and flexoelectric
65   coefficients\cite{Cheung2002, Cheung2004}. However, due to the
66 < limitation of time scale required for phase
67 < transition\cite{Wilson1999} and the length scale required for
68 < representing bulk behavior, the dominant models in the field of
69 < liquid crystal phase behavior are generic
70 < models\cite{Lebwohl1972,Perram1984, Gay1981}, which are based on the
71 < observation that liquid crystal order is exhibited by a range of
72 < non-molecular bodies with high shape anisotropies. Previous
73 < simulation studies using hard spherocylinder dimer
74 < model\cite{Camp1999} produce nematic phases, while hard rod
75 < simulation studies identified a Landau point\cite{Bates2005}, at
76 < which the isotropic phase undergoes a direct transition to the
77 < biaxial nematic, as well as some possible liquid crystal
78 < phases\cite{Lansac2003}. Other anisotropic models using
79 < Gay-Berne(GB) potential, which produce interactions that favor local
79 < alignment, give the evidence of the novel packing arrangements of
80 < bent-core molecules\cite{Memmer2002,Orlandi2006}.
66 > limitation of time scale required for phase transition and the
67 > length scale required for representing bulk behavior,
68 > models\cite{Perram1985, Gay1981}, which are based on the observation
69 > that liquid crystal order is exhibited by a range of non-molecular
70 > bodies with high shape anisotropies, became the dominant models in
71 > the field of liquid crystal phase behavior. Previous simulation
72 > studies using hard spherocylinder dimer model\cite{Camp1999} produce
73 > nematic phases, while hard rod simulation studies identified a
74 > Landau point\cite{Bates2005}, at which the isotropic phase undergoes
75 > a direct transition to the biaxial nematic, as well as some possible
76 > liquid crystal phases\cite{Lansac2003}. Other anisotropic models
77 > using Gay-Berne(GB) potential, which produce interactions that favor
78 > local alignment, give the evidence of the novel packing arrangements
79 > of bent-core molecules\cite{Memmer2002,Orlandi2006}.
80  
81   Experimental studies by Levelut {\it et al.}~\cite{Levelut1981}
82   revealed that terminal cyano or nitro groups usually induce
# Line 185 | Line 184 | ratio between \textit{end-to-end} well depth $\epsilon
184   \caption[]{} \label{LCFig:BananaMolecule}
185   \end{figure}
186  
187 < \begin{figure}
188 < \centering
189 < \includegraphics[width=\linewidth]{bananGB.eps}
190 < \caption[]{} \label{LCFigure:BananaGB}
191 < \end{figure}
187 > %\begin{figure}
188 > %\centering
189 > %\includegraphics[width=\linewidth]{bananGB.eps}
190 > %\caption[]{} \label{LCFigure:BananaGB}
191 > %\end{figure}
192  
193   \begin{figure}
194   \centering

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