| 144 |
|
partial bilayers ($S_{\tilde A}$) as well as interdigitated bilayers |
| 145 |
|
($S_{A_{d}}$), and often have a terminal cyano or nitro group. In |
| 146 |
|
particular, lyotropic liquid crystals (those exhibiting liquid crystal |
| 147 |
< |
phase transition as a function of water concentration), often have |
| 147 |
> |
phase transitions as a function of water concentration), often have |
| 148 |
|
polar head groups or zwitterionic charge separated groups that result |
| 149 |
< |
in strong dipolar interactions,\cite{Collings:1997rz} and terminal cyano |
| 150 |
< |
groups (like the one in 5CB) can induce permanent longitudinal |
| 151 |
< |
dipoles.\cite{Levelut:1981eu} |
| 149 |
> |
in strong dipolar interactions,\cite{Collings:1997rz} and terminal |
| 150 |
> |
cyano groups (like the one in 5CB) can induce permanent longitudinal |
| 151 |
> |
dipoles.\cite{Levelut:1981eu} Modeling of the phase behavior of these |
| 152 |
> |
molecules either requires additional dipolar |
| 153 |
> |
interactions,\cite{Bose:2012eu} or a unified-atom approach utilizing |
| 154 |
> |
point charges on the sites that contribute to the dipole |
| 155 |
> |
moment.\cite{Zhang:2011hh} |
| 156 |
|
|
| 157 |
|
Macroscopic electric fields applied using electrodes on opposing sides |
| 158 |
|
of a sample of 5CB have demonstrated the phase change of the molecule |
| 187 |
|
scanning electrochemical microscopy experiments. |
| 188 |
|
|
| 189 |
|
\section{Computational Details} |
| 190 |
< |
The force field used for 5CB was taken from Guo {\it et |
| 191 |
< |
al.}\cite{Zhang:2011hh} However, for most of the simulations, each |
| 192 |
< |
of the phenyl rings was treated as a rigid body to allow for larger |
| 193 |
< |
time steps and very long simulation times. The geometries of the |
| 194 |
< |
rigid bodies were taken from equilibrium bond distances and angles. |
| 195 |
< |
Although the phenyl rings were held rigid, bonds, bends, torsions and |
| 196 |
< |
inversion centers that involved atoms in these substructures (but with |
| 197 |
< |
connectivity to the rest of the molecule) were still included in the |
| 198 |
< |
potential and force calculations. |
| 190 |
> |
The force field used for 5CB was a united-atom model that was |
| 191 |
> |
parameterized by Guo {\it et al.}\cite{Zhang:2011hh} However, for most |
| 192 |
> |
of the simulations, each of the phenyl rings was treated as a rigid |
| 193 |
> |
body to allow for larger time steps and very long simulation times. |
| 194 |
> |
The geometries of the rigid bodies were taken from equilibrium bond |
| 195 |
> |
distances and angles. Although the phenyl rings were held rigid, |
| 196 |
> |
bonds, bends, torsions and inversion centers that involved atoms in |
| 197 |
> |
these substructures (but with connectivity to the rest of the |
| 198 |
> |
molecule) were still included in the potential and force calculations. |
| 199 |
|
|
| 200 |
|
Periodic simulations cells containing 270 molecules in random |
| 201 |
|
orientations were constructed and were locked at experimental |
| 204 |
|
were equilibrated for 1~ns at a temperature of 300K. Simulations with |
| 205 |
|
applied fields were carried out in the microcanonical (NVE) ensemble |
| 206 |
|
with an energy corresponding to the average energy from the canonical |
| 207 |
< |
(NVT) equilibration runs. Typical applied-field runs were more than |
| 208 |
< |
60ns in length. |
| 207 |
> |
(NVT) equilibration runs. Typical applied-field equilibration runs |
| 208 |
> |
were more than 60ns in length. |
| 209 |
|
|
| 210 |
|
Static electric fields with magnitudes similar to what would be |
| 211 |
|
available in an experimental setup were applied to the different |
| 244 |
|
primary quantity of interest is the nematic (orientational) order |
| 245 |
|
parameter. This was determined using the tensor |
| 246 |
|
\begin{equation} |
| 247 |
< |
Q_{\alpha \beta} = \frac{1}{2N} \sum_{i=1}^{N} \left(3 \hat{e}_{i |
| 248 |
< |
\alpha} \hat{e}_{i \beta} - \delta_{\alpha \beta} \right) |
| 247 |
> |
Q_{\alpha \beta} = \frac{1}{2N} \sum_{i=1}^{N} \left(3 \hat{u}_{i |
| 248 |
> |
\alpha} \hat{u}_{i \beta} - \delta_{\alpha \beta} \right) |
| 249 |
|
\end{equation} |
| 250 |
< |
where $\alpha, \beta = x, y, z$, and $\hat{e}_i$ is the molecular |
| 250 |
> |
where $\alpha, \beta = x, y, z$, and $\hat{u}_i$ is the molecular |
| 251 |
|
end-to-end unit vector for molecule $i$. The nematic order parameter |
| 252 |
|
$S$ is the largest eigenvalue of $Q_{\alpha \beta}$, and the |
| 253 |
|
corresponding eigenvector defines the director axis for the phase. |
| 254 |
|
$S$ takes on values close to 1 in highly ordered (smectic A) phases, |
| 255 |
< |
but falls to zero for isotropic fluids. Note that the nitrogen and |
| 256 |
< |
the terminal chain atom were used to define the vectors for each |
| 257 |
< |
molecule, so the typical order parameters are lower than if one |
| 258 |
< |
defined a vector using only the rigid core of the molecule. In |
| 259 |
< |
nematic phases, typical values for $S$ are close to 0.5. |
| 255 |
> |
but falls to much smaller values ($\sim 0-0.2$) for isotropic fluids. |
| 256 |
> |
Note that the nitrogen and the terminal chain atom were used to define |
| 257 |
> |
the vectors for each molecule, so the typical order parameters are |
| 258 |
> |
lower than if one defined a vector using only the rigid core of the |
| 259 |
> |
molecule. In nematic phases, typical values for $S$ are close to 0.5. |
| 260 |
|
|
| 261 |
|
The field-induced phase transition can be clearly seen over the course |
| 262 |
|
of a 60 ns equilibration runs in figure \ref{fig:orderParameter}. All |
| 539 |
|
and subsiquent phase change does cause a narrowing of freuency |
| 540 |
|
distrobution. With narrowing, it would indicate an increased |
| 541 |
|
homogeneous distrobution of the local field near the nitrile. |
| 538 |
– |
|
| 542 |
|
|
| 543 |
< |
The angle-dependent pair distribution function, |
| 544 |
< |
\begin{equation} |
| 545 |
< |
g(r, \cos \omega) = \frac{1}{\rho N} \left< \sum_{i} |
| 546 |
< |
\sum_{j} \delta \left(r - r_{ij}\right) \delta\left(\cos \omega_{ij} - \cos \omega\right) \right> |
| 547 |
< |
\end{equation} |
| 548 |
< |
provides information about the spatial and angular correlations in the |
| 549 |
< |
system. The angle $\omega$ is defined by vectors along the CN axis of |
| 550 |
< |
each nitrile bond (see figure \ref{fig:definition}). |
| 543 |
> |
The angle-dependent pair distribution functions, |
| 544 |
> |
\begin{align} |
| 545 |
> |
g(r, \cos \omega) = & \frac{1}{\rho N} \left< \sum_{i} |
| 546 |
> |
\sum_{j} \delta \left(r - r_{ij}\right) \delta\left(\cos \omega_{ij} - |
| 547 |
> |
\cos \omega\right) \right> \\ \nonumber \\ |
| 548 |
> |
g(r, \cos \theta) = & \frac{1}{\rho N} \left< \sum_{i} |
| 549 |
> |
\sum_{j} \delta \left(r - r_{ij}\right) \delta\left(\cos \theta_{i} - |
| 550 |
> |
\cos \theta \right) \right> |
| 551 |
> |
\end{align} |
| 552 |
> |
provide information about the joint spatial and angular correlations |
| 553 |
> |
in the system. The angles $\omega$ and $\theta$ are defined by vectors |
| 554 |
> |
along the CN axis of each nitrile bond (see figure |
| 555 |
> |
\ref{fig:definition}). |
| 556 |
|
|
| 557 |
|
\begin{figure} |
| 558 |
|
\includegraphics[width=\linewidth]{definition} |
| 559 |
< |
\caption{Definitions of the angles between two nitrile bonds. All |
| 552 |
< |
pairs of CN bonds in the simulation have three angles ($\theta_i$, |
| 553 |
< |
$\theta_j$ and $\omega$). $\cos\omega$ values range from -1 |
| 554 |
< |
(anti-aligned) to +1 for aligned nitrile bonds.} |
| 559 |
> |
\caption{Definitions of the angles between two nitrile bonds.} |
| 560 |
|
\label{fig:definition} |
| 561 |
|
\end{figure} |
| 562 |
|
|
