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 |
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 |
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 |
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 |
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 |
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. |
200 |
|
|
201 |
|
\section{Results and Discussion} |
202 |
|
|
203 |
< |
A series of molecular dynamics simulations were perform to study the |
203 |
> |
A series of molecular dynamics simulations were performed to study the |
204 |
|
phase behavior of banana shaped liquid crystals. In each simulation, |
205 |
|
every banana shaped molecule has been represented by three GB |
206 |
|
particles which is characterized by $\mu = 1,~ \nu = 2, |
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 n |
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 |
286 |
|
director frame and $R$ is the radius of the cylindrical sampling |
287 |
|
region. The oscillation in density plot along the director in |
288 |
|
Fig.~\ref{LCFigure:gofrz}(b) implies the existence of the layered |
289 |
< |
structure, and the peak at 27 \AA is attributed to a defect in the |
289 |
> |
structure, and the peak at 27 $\rm{\AA}$ is attributed to a defect in the |
290 |
|
system. |
291 |
|
|
292 |
|
\subsection{Rotational Invariants} |
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 |
|
: |
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. |