trunk/tengDissertation/LiquidCrystal.tex

\chapter{\label{chapt:liquidcrystal}LIQUID CRYSTAL}

\section{\label{liquidCrystalSection:introduction}Introduction}
% liquid crystal

Long range orientational order is one of the most fundamental
properties of liquid crystal mesophases. This orientational
anisotropy of the macroscopic phases originates in the shape
anisotropy of the constituent molecules. Among these anisotropy
mesogens, rod-like (calamitic) and disk-like molecules have been
exploited in great detail in the last two decades. Typically, these
mesogens consist of a rigid aromatic core and one or more attached
aliphatic chains. For short chain molecules, only nematic phases, in
which positional order is limited or absent, can be observed,
because the entropy of mixing different parts of the mesogens is
paramount to the dispersion interaction. In contrast, formation of
the one dimension lamellar sematic phase in rod-like molecules with
sufficiently long aliphatic chains has been reported, as well as the
segregation phenomena in disk-like molecules.

% banana shaped
Recently, the banana-shaped or bent-core liquid crystal have became
one of the most active research areas in mesogenic materials and
supramolecular chemistry. Unlike rods and disks, the polarity and
biaxiality of the banana-shaped molecules allow the molecules
organize into a variety of novel liquid crystalline phases which
show interesting material properties. Of particular interest is the
spontaneous formation of macroscopic chiral layers from achiral
banana-shaped molecules, where polar molecule orientational ordering
is shown within the layer plane as well as the tilted arrangement of
the molecules relative to the polar axis. As a consequence of
supramolecular chirality, the spontaneous polarization arises in
ferroelectric (FE) and antiferroelectic (AF) switching of smectic
liquid crystal phases, demonstrating some promising applications in
second-order nonlinear optical devices. The most widely investigated
mesophase formed by banana-shaped moleculed is the $\text{B}_2$
phase, which is also referred to as $\text{SmCP}$. Of the most
important discover in this tilt lamellar phase is the four distinct
packing arrangements (two conglomerates and two macroscopic
racemates), which depend on the tilt direction and the polar
direction of the molecule in adjacent layer (see
Fig.~\cite{LCFig:SMCP}).

%general banana-shaped molecule modeling
Many liquid crystal synthesis experiments suggest that the
occurrence of polarity and chirality strongly relies on the
molecular structure and intermolecular interaction. From a
theoretical point of view, it is of fundamental interest to study
the structural properties of liquid crystal phases formed by
banana-shaped molecules and understand their connection to the
molecular structure, especially with respect to the spontaneous
achiral symmetry breaking. As a complementary tool to experiment,
computer simulation can provide unique insight into molecular
ordering and phase behavior, and hence improve the development of
new experiments and theories. In the last two decades, all-atom
models have been adopted to investigate the structural properties of
smectic arrangements\cite{Cook2000, Lansac2001}, as well as other
bulk properties, such as rotational viscosity and flexoelectric
coefficients\cite{Cheung2002, Cheung2004}. However, due to the
limitation of time scale required for phase
transition\cite{Wilson1999} and the length scale required for
representing bulk behavior, the dominant models in the field of
liquid crystal phase behavior are generic
models\cite{Lebwohl1972,Perram1984, Gay1981}, which are based on the
observation that liquid crystal order is exhibited by a range of
non-molecular bodies with high shape anisotropies. Previous
simulation studies using hard spherocylinder dimer
model\cite{Camp1999} produce nematic phases, while hard rod
simulation studies identified a Landau point\cite{Bates2005}, at
which the isotropic phase undergoes a transition directly to the
biaxial nematic, as well as some possible liquid crystal
phases\cite{Lansac2003}. Other anisotropic models using Gay-Berne
potential give the evidence of the novel packing arrangement of
bent-core molecules\cite{Memmer2002,Orlandi2006}.

\section{\label{liquidCrystalSection:model}Model}

\section{\label{liquidCrystalSection:methods}Methods}

\section{\label{liquidCrystalSection:resultDiscussion}Results and Discussion}
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#	Content
1	\chapter{\label{chapt:liquidcrystal}LIQUID CRYSTAL}
2
3	\section{\label{liquidCrystalSection:introduction}Introduction}
4	% liquid crystal
5
6	Long range orientational order is one of the most fundamental
7	properties of liquid crystal mesophases. This orientational
8	anisotropy of the macroscopic phases originates in the shape
9	anisotropy of the constituent molecules. Among these anisotropy
10	mesogens, rod-like (calamitic) and disk-like molecules have been
11	exploited in great detail in the last two decades. Typically, these
12	mesogens consist of a rigid aromatic core and one or more attached
13	aliphatic chains. For short chain molecules, only nematic phases, in
14	which positional order is limited or absent, can be observed,
15	because the entropy of mixing different parts of the mesogens is
16	paramount to the dispersion interaction. In contrast, formation of
17	the one dimension lamellar sematic phase in rod-like molecules with
18	sufficiently long aliphatic chains has been reported, as well as the
19	segregation phenomena in disk-like molecules.
20
21	% banana shaped
22	Recently, the banana-shaped or bent-core liquid crystal have became
23	one of the most active research areas in mesogenic materials and
24	supramolecular chemistry. Unlike rods and disks, the polarity and
25	biaxiality of the banana-shaped molecules allow the molecules
26	organize into a variety of novel liquid crystalline phases which
27	show interesting material properties. Of particular interest is the
28	spontaneous formation of macroscopic chiral layers from achiral
29	banana-shaped molecules, where polar molecule orientational ordering
30	is shown within the layer plane as well as the tilted arrangement of
31	the molecules relative to the polar axis. As a consequence of
32	supramolecular chirality, the spontaneous polarization arises in
33	ferroelectric (FE) and antiferroelectic (AF) switching of smectic
34	liquid crystal phases, demonstrating some promising applications in
35	second-order nonlinear optical devices. The most widely investigated
36	mesophase formed by banana-shaped moleculed is the $\text{B}_2$
37	phase, which is also referred to as $\text{SmCP}$. Of the most
38	important discover in this tilt lamellar phase is the four distinct
39	packing arrangements (two conglomerates and two macroscopic
40	racemates), which depend on the tilt direction and the polar
41	direction of the molecule in adjacent layer (see
42	Fig.~\cite{LCFig:SMCP}).
43
44	%general banana-shaped molecule modeling
45	Many liquid crystal synthesis experiments suggest that the
46	occurrence of polarity and chirality strongly relies on the
47	molecular structure and intermolecular interaction. From a
48	theoretical point of view, it is of fundamental interest to study
49	the structural properties of liquid crystal phases formed by
50	banana-shaped molecules and understand their connection to the
51	molecular structure, especially with respect to the spontaneous
52	achiral symmetry breaking. As a complementary tool to experiment,
53	computer simulation can provide unique insight into molecular
54	ordering and phase behavior, and hence improve the development of
55	new experiments and theories. In the last two decades, all-atom
56	models have been adopted to investigate the structural properties of
57	smectic arrangements\cite{Cook2000, Lansac2001}, as well as other
58	bulk properties, such as rotational viscosity and flexoelectric
59	coefficients\cite{Cheung2002, Cheung2004}. However, due to the
60	limitation of time scale required for phase
61	transition\cite{Wilson1999} and the length scale required for
62	representing bulk behavior, the dominant models in the field of
63	liquid crystal phase behavior are generic
64	models\cite{Lebwohl1972,Perram1984, Gay1981}, which are based on the
65	observation that liquid crystal order is exhibited by a range of
66	non-molecular bodies with high shape anisotropies. Previous
67	simulation studies using hard spherocylinder dimer
68	model\cite{Camp1999} produce nematic phases, while hard rod
69	simulation studies identified a Landau point\cite{Bates2005}, at
70	which the isotropic phase undergoes a transition directly to the
71	biaxial nematic, as well as some possible liquid crystal
72	phases\cite{Lansac2003}. Other anisotropic models using Gay-Berne
73	potential give the evidence of the novel packing arrangement of
74	bent-core molecules\cite{Memmer2002,Orlandi2006}.
75
76	\section{\label{liquidCrystalSection:model}Model}
77
78	\section{\label{liquidCrystalSection:methods}Methods}
79
80	\section{\label{liquidCrystalSection:resultDiscussion}Results and Discussion}