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# Line 4 | Line 4 | been investigated in great detail in the last two
4  
5   Rod-like (calamitic) and disk-like anisotropy liquid crystals have
6   been investigated in great detail in the last two
7 < decades\cite{Huh2004}. Typically, these mesogens consist of a rigid
7 > decades.\cite{Huh2004} Typically, these mesogens consist of a rigid
8   aromatic core and one or more attached aliphatic chains. For short
9   chain molecules, only nematic phases, in which positional order is
10   limited or absent, can be observed, because the entropy of mixing
# Line 12 | Line 12 | chains has been reported, as well as the segregation p
12   interaction. In contrast, formation of one dimension lamellar
13   smectic phase in rod-like molecules with sufficiently long aliphatic
14   chains has been reported, as well as the segregation phenomena in
15 < disk-like molecules\cite{McMillan1971}. Recently, banana-shaped or
15 > disk-like molecules.\cite{McMillan1971} Recently, banana-shaped or
16   bent-core liquid crystals have became one of the most active
17   research areas in mesogenic materials and supramolecular
18 < chemistry\cite{Niori1996, Link1997, Pelzl1999}. Unlike rods and
18 > chemistry.\cite{Niori1996, Link1997, Pelzl1999} Unlike rods and
19   disks, the polarity and biaxiality of the banana-shaped molecules
20   allow the molecules organize into a variety of novel liquid
21   crystalline phases which show interesting material properties. Of
# Line 29 | Line 29 | moleculed is the $\text{B}_2$ phase, which is also ref
29   promising applications in second-order nonlinear optical devices.
30   The most widely investigated mesophase formed by banana-shaped
31   moleculed is the $\text{B}_2$ phase, which is also referred to as
32 < $\text{SmCP}$\cite{Link1997}. Of the most important discoveries in
32 > $\text{SmCP}$.\cite{Link1997} Of the most important discoveries in
33   this tilt lamellar phase is the four distinct packing arrangements
34   (two conglomerates and two macroscopic racemates), which depend on
35   the tilt direction and the polar direction of the molecule in
36 < adjacent layer (see Fig.~\ref{LCFig:SMCP})\cite{Link1997}.
36 > adjacent layer (see Fig.~\ref{LCFig:SMCP}).\cite{Link1997}
37  
38   \begin{figure}
39   \centering
# Line 47 | Line 47 | occurrence of polarity and chirality strongly relies o
47  
48   Many liquid crystal synthesis experiments suggest that the
49   occurrence of polarity and chirality strongly relies on the
50 < molecular structure and intermolecular interaction\cite{Reddy2006}.
50 > molecular structure and intermolecular interaction.\cite{Reddy2006}
51   From a theoretical point of view, it is of fundamental interest to
52   study the structural properties of liquid crystal phases formed by
53   banana-shaped molecules and understand their connection to the
# Line 57 | Line 57 | models have been adopted to investigate the structural
57   ordering and phase behavior, and hence improve the development of
58   new experiments and theories. In the last two decades, all-atom
59   models have been adopted to investigate the structural properties of
60 < smectic arrangements\cite{Cook2000, Lansac2001}, as well as other
60 > smectic arrangements,\cite{Cook2000, Lansac2001} as well as other
61   bulk properties, such as rotational viscosity and flexoelectric
62 < coefficients\cite{Cheung2002, Cheung2004}. However, due to the
62 > coefficients.\cite{Cheung2002, Cheung2004} However, due to the
63   limitation of time scales required for phase transition and the
64   length scale required for representing bulk behavior,
65 < models\cite{Perram1985, Gay1981}, which are based on the observation
65 > models,\cite{Perram1985, Gay1981} which are based on the observation
66   that liquid crystal order is exhibited by a range of non-molecular
67   bodies with high shape anisotropies, have become the dominant models
68   in the field of liquid crystal phase behavior. Previous simulation
69   studies using a hard spherocylinder dimer model\cite{Camp1999}
70   produced nematic phases, while hard rod simulation studies
71   identified a direct transition to the biaxial nematic and other
72 < possible liquid crystal phases\cite{Lansac2003}. Other anisotropic
72 > possible liquid crystal phases.\cite{Lansac2003} Other anisotropic
73   models using the Gay-Berne(GB) potential, which produces
74   interactions that favor local alignment, give evidence of the novel
75 < packing arrangements of bent-core molecules\cite{Memmer2002}.
75 > packing arrangements of bent-core molecules.\cite{Memmer2002}
76  
77   Experimental studies by Levelut {\it et al.}~\cite{Levelut1981}
78   revealed that terminal cyano or nitro groups usually induce
# Line 81 | Line 81 | principal axis of rotation) were shown to enhance smec
81   from a series of theoretical studies. Monte Carlo studies of the GB
82   potential with fixed longitudinal dipoles (i.e. pointed along the
83   principal axis of rotation) were shown to enhance smectic phase
84 < stability~\cite{Berardi1996,Satoh1996}. Molecular simulation of GB
84 > stability.\cite{Berardi1996,Satoh1996} Molecular simulation of GB
85   ellipsoids with transverse dipoles at the terminus of the molecule
86   also demonstrated that partial striped bilayer structures were
87 < developed from the smectic phase ~\cite{Berardi1996}. More
87 > developed from the smectic phase.~\cite{Berardi1996} More
88   significant effects have been shown by including multiple
89   electrostatic moments. Adding longitudinal point quadrupole moments
90   to rod-shaped GB mesogens, Withers \textit{et al} induced tilted
91 < smectic behaviour in the molecular system~\cite{Withers2003}. Thus,
91 > smectic behaviour in the molecular system.~\cite{Withers2003} Thus,
92   it is clear that many liquid-crystal forming molecules, specially,
93   bent-core molecules, could be modeled more accurately by
94   incorporating electrostatic interaction.
# Line 271 | Line 271 | The diagonal view in Fig~\ref{LCFigure:snapshot}(a) sh
271   The molecular organization obtained at temperature $T = 460K$ (below
272   transition temperature) is shown in Figure~\ref{LCFigure:snapshot}.
273   The diagonal view in Fig~\ref{LCFigure:snapshot}(a) shows the
274 < stacking of the banana shaped molecules while the side view in
274 > stacking of the banana shaped molecules while the side view in
275   Figure~\ref{LCFigure:snapshot}(b) demonstrates formation of a
276   chevron structure. The first peak of the radial distribution
277   function $g(r)$ in Fig.~\ref{LCFigure:gofrz}(a) shows that the
# Line 294 | Line 294 | applied in a spherical symmetric system to study x-ray
294   As a useful set of correlation functions to describe
295   position-orientation correlation, rotation invariants were first
296   applied in a spherical symmetric system to study x-ray and light
297 < scatting\cite{Blum1972}. Latterly, expansion of the orientation pair
297 > scatting.\cite{Blum1972} Latterly, expansion of the orientation pair
298   correlation in terms of rotation invariant for molecules of
299   arbitrary shape has been introduced by Stone\cite{Stone1978} and
300   adopted by other researchers in liquid crystal
301 < studies\cite{Berardi2003}. In order to study the correlation between
301 > studies.\cite{Berardi2003} In order to study the correlation between
302   biaxiality and molecular separation distance $r$, we calculate a
303   rotational invariant function $S_{22}^{220} (r)$, which is given by
304   :
# Line 357 | Line 357 | the type of mesophase formed have been studied
357   can be broken by using NPTf integrator in further simulations. The
358   role of terminal chain in controlling transition temperatures and
359   the type of mesophase formed have been studied
360 < extensively\cite{Pelzl1999}. The lack of flexibility in our model
360 > extensively.\cite{Pelzl1999} The lack of flexibility in our model
361   due to the missing terminal chains could explain the fact that we
362   did not find evidence of chirality.

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