| 265 |
|
It is possible that the partial-field simulation is meta-stable and |
| 266 |
|
given enough time, it would eventually find a nematic-ordered phase, |
| 267 |
|
but the partial-field simulation was stable as an isotropic phase for |
| 268 |
< |
the full duration of a 60 ns simulation. |
| 269 |
< |
\begin{figure} |
| 270 |
< |
\includegraphics[trim = 5mm 10mm 3mm 10mm, clip, width=4in]{P2} |
| 271 |
< |
\caption{Evolution of the orientational order parameter for the |
| 268 |
> |
the full duration of a 60 ns simulation. Ellipsoidal renderings of the |
| 269 |
> |
final configurations of the runs shows that the full-field (0.024 |
| 270 |
> |
V/\AA\ ) experienced a isotropic-nematic phase transition and has |
| 271 |
> |
ordered with a director axis that is parallel to the direction of the |
| 272 |
> |
applied field. |
| 273 |
> |
|
| 274 |
> |
\begin{figure}[H] |
| 275 |
> |
\includegraphics[width=\linewidth]{Figure1} |
| 276 |
> |
\caption{Evolution of the orientational order parameters for the |
| 277 |
|
no-field, partial field, and full field simulations over the |
| 278 |
|
course of 60 ns. Each simulation was started from a |
| 279 |
< |
statistically-independent isotropic configuration.} |
| 279 |
> |
statistically-independent isotropic configuration. On the right |
| 280 |
> |
are ellipsoids representing the final configurations at three |
| 281 |
> |
different field strengths: zero field (bottom), partial field |
| 282 |
> |
(middle), and full field (top)} |
| 283 |
|
\label{fig:orderParameter} |
| 284 |
|
\end{figure} |
| 285 |
|
|
| 278 |
– |
The field-induced isotropic-nematic transition can be visualized in |
| 279 |
– |
figure \ref{fig:Cigars}, where each molecule has been represented |
| 280 |
– |
using and ellipsoids aligned along the long-axis of each molecule. |
| 281 |
– |
Both the zero field and partial field simulations appear isotropic, |
| 282 |
– |
while the full field simulations has been orientationally ordered |
| 283 |
– |
\begin{figure} |
| 284 |
– |
\includegraphics[width=7in]{Elip_3} |
| 285 |
– |
\caption{Ellipsoid reprsentation of 5CB at three different field |
| 286 |
– |
strengths, Zero Field (Left), Partial Field (Middle), and Full |
| 287 |
– |
Field (Right) Each image was created from the final configuration |
| 288 |
– |
of each 60 ns equilibration run.} |
| 289 |
– |
\label{fig:Cigars} |
| 290 |
– |
\end{figure} |
| 286 |
|
|
| 287 |
|
\section{Sampling the CN bond frequency} |
| 288 |
|
|
| 289 |
< |
The primary quantity of interest is the distribution of vibrational |
| 290 |
< |
frequencies exhibited by the 5CB nitrile bond under the different |
| 291 |
< |
electric fields. Three distinct methods for mapping classical |
| 292 |
< |
simulations onto vibrational spectra were brought to bear on these |
| 293 |
< |
simulations: |
| 289 |
> |
The vibrational frequency of the nitrile bond in 5CB is assumed to |
| 290 |
> |
depend on features of the local solvent environment of the individual |
| 291 |
> |
molecules as well as the bond's orientation relative to the applied |
| 292 |
> |
field. Therefore, the primary quantity of interest is the |
| 293 |
> |
distribution of vibrational frequencies exhibited by the 5CB nitrile |
| 294 |
> |
bond under the different electric fields. Three distinct methods for |
| 295 |
> |
mapping classical simulations onto vibrational spectra were brought to |
| 296 |
> |
bear on these simulations: |
| 297 |
|
\begin{enumerate} |
| 298 |
|
\item Isolated 5CB molecules and their immediate surroundings were |
| 299 |
|
extracted from the simulations, their nitrile bonds were stretched |
| 305 |
|
investigated. This method involves mapping the electrostatic |
| 306 |
|
potential around the bond to the vibrational frequency, and is |
| 307 |
|
similar in approach to field-frequency maps that were pioneered by |
| 308 |
< |
work done by Skinner {\it et al.}\cite{XXXX} |
| 308 |
> |
Skinner {\it et al.}\cite{XXXX} |
| 309 |
|
\item Classical bond-length autocorrelation functions were Fourier |
| 310 |
|
transformed to directly obtain the vibrational spectrum from |
| 311 |
|
molecular dynamics simulations. |
| 312 |
|
\end{enumerate} |
| 313 |
|
|
| 314 |
|
\subsection{CN frequencies from isolated clusters} |
| 315 |
+ |
The size of the condensed phase system prevents direct computation of |
| 316 |
+ |
the nitrile bond frequencies using {\it ab initio} methods. In order |
| 317 |
+ |
to sample the nitrile frequencies present in the condensed-phase, |
| 318 |
+ |
individual molecules were selected randomly to serve as the center of |
| 319 |
+ |
a local (gas phase) cluster. To include steric, electrostatic, and |
| 320 |
+ |
other effects from molecules located near the targeted nitrile group, |
| 321 |
+ |
portions of other molecules nearest to the nitrile group were included |
| 322 |
+ |
in the calculations. The surrounding solvent molecules were divided |
| 323 |
+ |
into ``body'' (the two phenyl rings and the nitrile bond) and ``tail'' |
| 324 |
+ |
(the alkyl chain). Any molecule which had a body atom within 6~\AA of |
| 325 |
+ |
the midpoint of the target nitrile group |
| 326 |
|
|
| 327 |
< |
For quantum calculation of the nitrile bond frequency, Gaussian 09 was |
| 328 |
< |
used. A single 5CB molecule was selected for the center of the |
| 329 |
< |
cluster. For effects from molecules located near the chosen nitrile |
| 330 |
< |
group, parts of molecules nearest to the nitrile group were |
| 331 |
< |
included. For the body not including the tail, any atom within 6~\AA |
| 332 |
< |
of the midpoint of the nitrile group was included. For the tail |
| 333 |
< |
structure, the whole tail was included if a tail atom was within 4~\AA |
| 334 |
< |
of the midpoint. If the tail did not include any atoms from the ring |
| 335 |
< |
structure, it was considered a propane molecule and included as |
| 336 |
< |
such. Once the clusters were generated, input files were created that |
| 337 |
< |
stretched the nitrile bond along its axis from 0.87 to 1.52~\AA at |
| 338 |
< |
increments of 0.05~\AA. This generated 13 single point energies to be |
| 339 |
< |
calculated. The Gaussian files were run with B3LYP/6-311++G(d,p) with |
| 340 |
< |
no other keywords for the zero field simulation. Simulations with |
| 341 |
< |
fields applied included the keyword ''Field=Z+5'' to match the |
| 342 |
< |
external field applied in molecular dynamic runs. Once completed, the central nitrile bond frequency |
| 334 |
< |
was calculated with a Morse fit. Using this fit and the solved energy |
| 327 |
> |
|
| 328 |
> |
|
| 329 |
> |
or the body not including |
| 330 |
> |
the tail, any atom within 6~\AA of the midpoint of the nitrile group |
| 331 |
> |
was included. For the tail structure, the whole tail was included if a |
| 332 |
> |
tail atom was within 4~\AA of the midpoint. If the tail did not |
| 333 |
> |
include any atoms from the ring structure, it was considered a propane |
| 334 |
> |
molecule and included as such. Once the clusters were generated, input |
| 335 |
> |
files were created that stretched the nitrile bond along its axis from |
| 336 |
> |
0.87 to 1.52~\AA at increments of 0.05~\AA. This generated 13 single |
| 337 |
> |
point energies to be calculated. The Gaussian files were run with |
| 338 |
> |
B3LYP/6-311++G(d,p) with no other keywords for the zero field |
| 339 |
> |
simulation. Simulations with fields applied included the keyword |
| 340 |
> |
''Field=Z+5'' to match the external field applied in molecular dynamic |
| 341 |
> |
runs. Once completed, the central nitrile bond frequency was |
| 342 |
> |
calculated with a Morse fit. Using this fit and the solved energy |
| 343 |
|
levels for a Morse oscillator, the frequency was found. Each set of |
| 344 |
|
frequencies were then convolved together with a lorezian lineshape |
| 345 |
|
function over each value. The width value used was 1.5. For the zero |
