| 58 |
|
\begin{doublespace} |
| 59 |
|
|
| 60 |
|
\begin{abstract} |
| 61 |
< |
The behavior of the spectral lineshape of the nitrile group in |
| 62 |
< |
4-Cyano-4'-pentylbiphenyl (5CB) in response to an applied electric |
| 63 |
< |
field has been simulated using both classical molecular dynamics |
| 64 |
< |
simulations and {\it ab initio} quantum mechanical calculations of |
| 65 |
< |
liquid-like clusters. This nitrile group is a well-known reporter |
| 66 |
< |
of local field effects in other condensed phase settings, and our |
| 67 |
< |
simulations suggest that there is a significant response when 5CB |
| 68 |
< |
liquids are exposed to a relatively large external field. However, |
| 69 |
< |
this response is due largely to the field-induced phase transition. |
| 70 |
< |
We observe a peak shift to the red of nearly 40 |
| 71 |
< |
cm\textsuperscript{-1}. These results indicate that applied fields |
| 72 |
< |
can play a role in the observed peak shape and position even if |
| 73 |
< |
those fields are significantly weaker than the local electric fields |
| 74 |
< |
that are normally felt within polar liquids. |
| 61 |
> |
Nitrile Stark shift repsonses to electric fields have been used |
| 62 |
> |
extensively in biology for the probing of local internal fields of |
| 63 |
> |
structures like proteins and DNA. Intigration of these probes into |
| 64 |
> |
different areas of interest are important for studing local structure |
| 65 |
> |
and fields within confined, nanoscopic |
| 66 |
> |
systems. 4-Cyano-4'-pentylbiphenyl (5CB) is a liquid crystal with a known |
| 67 |
> |
macroscopic structure reordering from the isotropic to nematic |
| 68 |
> |
phase with the application of an external |
| 69 |
> |
field and as the name suggests has an inherent nitrile group. Through |
| 70 |
> |
simulations of this molecule where application of |
| 71 |
> |
large, nanoscale external fields were applied, the nitrile was invenstigated |
| 72 |
> |
as a local field sensor. It was |
| 73 |
> |
found that while most computational methods for nitrile spectral |
| 74 |
> |
calculations rely on a correlation between local electric field and |
| 75 |
> |
the nitrile bond, 5CB did not have an easily obtained |
| 76 |
> |
correlation. Instead classical calculation through correlation of the |
| 77 |
> |
cyanide bond displacement in time use enabled to show a spectral |
| 78 |
> |
change in the formation of a red |
| 79 |
> |
shifted peak from the main peak as an external field was applied. This indicates |
| 80 |
> |
that local structure has a larger impact on the nitrile frequency then |
| 81 |
> |
does the local electric field. By better understanding how nitrile |
| 82 |
> |
groups respond to local and external fields it will help |
| 83 |
> |
nitrile groups branch out beyond their biological |
| 84 |
> |
applications to uses in electronics and surface sciences. |
| 85 |
|
\end{abstract} |
| 86 |
|
|
| 87 |
|
\newpage |
| 133 |
|
|
| 134 |
|
Many of the technological applications of the lyotropic mesogens |
| 135 |
|
manipulate the orientation and structuring of the liquid crystal |
| 136 |
< |
through application of local electric fields.\cite{?} |
| 136 |
> |
through application of external electric fields.\cite{?} |
| 137 |
|
Macroscopically, this restructuring is visible in the interactions the |
| 138 |
|
bulk phase has with scattered or transmitted light.\cite{?} |
| 139 |
|
|
| 143 |
|
similar compounds) in 1973 in an effort to find a LC that had a |
| 144 |
|
melting point near room temperature.\cite{Gray:1973ca} It's known to |
| 145 |
|
have a crystalline to nematic phase transition at 18 C and a nematic |
| 146 |
< |
to isotropic transition at 35 C.\cite{Gray:1973ca} |
| 146 |
> |
to isotropic transition at 35 C.\cite{Gray:1973ca} Recently it has |
| 147 |
> |
seen new life with the application of droplets of the molecule in |
| 148 |
> |
water being used to study defect sites and nanoparticle |
| 149 |
> |
strcuturing.\cite{PhysRevLett.111.227801} |
| 150 |
|
|
| 151 |
|
Nitrile groups can serve as very precise electric field reporters via |
| 152 |
|
their distinctive Raman and IR signatures.\cite{Boxer:2009xw} The |
| 161 |
|
4-Cyano-4'-n-alkylbiphenyl liquid crystals has not been investigated. |
| 162 |
|
While macroscopic electric fields applied across macro electrodes show |
| 163 |
|
the phase change of the molecule as a function of electric |
| 164 |
< |
field,\cite{Lim:2006xq} the effect of a microscopic field application |
| 164 |
> |
field,\cite{Lim:2006xq} the effect of a nanoscopic field application |
| 165 |
|
has not been probed. These previous studies have shown the nitrile |
| 166 |
|
group serves as an excellent indicator of the molecular orientation |
| 167 |
< |
within the field applied. Blank showed the 180 degree change in field |
| 167 |
> |
within the field applied. Lee {\it et al.}~showed the 180 degree change in field |
| 168 |
|
direction could be probed with the nitrile peak intensity as it |
| 169 |
|
decreased and increased with molecule alignment in the |
| 170 |
|
field.\cite{Lee:2006qd,Leyte:97} |
| 186 |
|
bond. This should be readily visible experimentally through Raman or |
| 187 |
|
IR spectroscopy. |
| 188 |
|
|
| 189 |
< |
Herein, we show the computational investigation of these electric field effects through atomistic simulations. These are then coupled with ab intio and classical spectrum calculations to predict changes experiments should be able to replicate. |
| 189 |
> |
Herein, we show the computational investigation of these electric |
| 190 |
> |
field effects through atomistic simulations of 5CB with external |
| 191 |
> |
fields applied. These simulations are then coupled with ab intio and |
| 192 |
> |
classical spectrum calculations to predict changes. These changes are |
| 193 |
> |
easily varifiable with experiments and should be able to replicated |
| 194 |
> |
experimentally. |
| 195 |
|
|
| 196 |
|
\section{Computational Details} |
| 197 |
|
The force field was mainly taken from Guo et al.\cite{Zhang:2011hh} A |
| 238 |
|
external field applied in molecular dynamic runs. Once completed, the central nitrile bond frequency |
| 239 |
|
was calculated with a Morse fit. Using this fit and the solved energy |
| 240 |
|
levels for a Morse oscillator, the frequency was found. Each set of |
| 241 |
< |
frequencies were then convolved together with a guassian spread |
| 241 |
> |
frequencies were then convolved together with a lorezian lineshape |
| 242 |
|
function over each value. The width value used was 1.5. For the zero |
| 243 |
|
field spectrum, 67 frequencies were used and for the full field, 59 |
| 244 |
|
frequencies were used. |
| 259 |
|
where $r_0$ is the equilibrium bond distance and $r(t)$ is the |
| 260 |
|
instantaneous bond displacement at time $t$. Once calculated, |
| 261 |
|
smoothing was applied by adding an exponential decay on top of the |
| 262 |
< |
decay with a $\tau$ of 3000 (have to check this). Further smoothing |
| 262 |
> |
decay with a $\tau$ of 6000. Further smoothing |
| 263 |
|
was applied by padding 20,000 zeros on each side of the symmetric |
| 264 |
|
data. This was done five times by allowing the systems to run 1 ns |
| 265 |
|
with a rigid bond followed by an equilibrium run with the bond |
| 266 |
< |
switched back on and the short production run. |
| 266 |
> |
switched back to a Morse oscillator and a short production run of 20 ps. |
| 267 |
|
|
| 268 |
|
\section{Results} |
| 269 |
|
|
| 284 |
|
moved to the nematic and crystalline phases. |
| 285 |
|
|
| 286 |
|
This value indicates phases changes at temperature boundaries but also |
| 287 |
< |
when a phase changes occurs due to external field applications. In |
| 287 |
> |
when a phase change occurs due to external field applications. In |
| 288 |
|
Figure 1, this phase change can be clearly seen over the course of 60 |
| 289 |
|
ns. Each system starts with an ordering paramter near 0.1 to 0.2, |
| 290 |
|
which is an isotropic phase. Over the course 10 ns, the full external field |
| 292 |
|
of the liquid crystal. This change is consistent over the full 50 ns |
| 293 |
|
with no drop back into the isotropic phase. This change is clearly |
| 294 |
|
field induced and stable over a long period of simulation time. |
| 277 |
– |
|
| 278 |
– |
Interestingly, the field that is needed to switch the phase of 5CB |
| 279 |
– |
macroscopically is larger than 1 V. However, in this case, only a |
| 280 |
– |
voltage of 1.2 V was need to induce a phase change. This is impart due |
| 281 |
– |
to the distance the field is being applied across. At such a small |
| 282 |
– |
distance, the field is much larger than the macroscopic and thus |
| 283 |
– |
easily induces a field dependent phase change. |
| 284 |
– |
|
| 285 |
– |
This change in phase was followed by two courses of further |
| 286 |
– |
simulation. First, was replacement of the static nitrile bond with a |
| 287 |
– |
morse oscillator bond. This was then simulated for a period of time |
| 288 |
– |
and a classical spetrum was calculated. Second, ab intio calcualtions were performe to investigate |
| 289 |
– |
if the phase change caused any change spectrum from quantum |
| 290 |
– |
effects. |
| 291 |
– |
|
| 292 |
– |
In respect to the classical calculations, it was first seen if previous |
| 293 |
– |
studies of nitriles within water and neat simulation done by Cho |
| 294 |
– |
et. al. could be used for the spectrum. |
| 295 |
– |
|
| 296 |
– |
After Gaussian calculations were performed on a set of snapshots, any |
| 295 |
|
\begin{figure} |
| 296 |
|
\includegraphics[trim = 5mm 10mm 3mm 10mm, clip, width=3.25in]{P2} |
| 297 |
|
\caption{Ordering of each external field application over the course |
| 298 |
|
of 60 ns with a sampling every 100 ps. Each trajectory was started |
| 299 |
< |
after equilibration with zero field applied.} |
| 299 |
> |
after equilibration with zero field applied.} |
| 300 |
|
\label{fig:orderParameter} |
| 301 |
|
\end{figure} |
| 302 |
+ |
|
| 303 |
+ |
In the figure below, this phase change is represented nicely as |
| 304 |
+ |
ellipsoids that are created by the vector formed between the nitrogen |
| 305 |
+ |
of the nitrile group and the tail terminal carbon atom. These |
| 306 |
+ |
illistrate the change from isotropic phase to nematic change. Both the |
| 307 |
+ |
zero field and partial field images look mostly disordered. The |
| 308 |
+ |
partial field does look somewhat orded but without any overall order |
| 309 |
+ |
of the entire system. This is most likely a high point in the ordering |
| 310 |
+ |
for the trajectory. The full field image on the other hand looks much |
| 311 |
+ |
more ordered when compared to the two lower field simulations. |
| 312 |
|
\begin{figure} |
| 313 |
+ |
\includegraphics[width=7in]{Elip_3} |
| 314 |
+ |
\caption{Ellipsoid reprsentation of 5CB at three different |
| 315 |
+ |
field strengths, Zero Field (Left), Partial Field (Middle), and Full |
| 316 |
+ |
Field (Right) Each image was created by taking the final |
| 317 |
+ |
snapshot of each 60 ns run} |
| 318 |
+ |
\label{fig:Cigars} |
| 319 |
+ |
\end{figure} |
| 320 |
+ |
|
| 321 |
+ |
This change in phase was followed by two courses of further |
| 322 |
+ |
analysis. First was the replacement of the static nitrile bond with a |
| 323 |
+ |
morse oscillator bond. This was then simulated for a period of time |
| 324 |
+ |
and a classical spetrum was calculated. Second, ab intio calcualtions |
| 325 |
+ |
were performed to investigate if the phase change caused any change |
| 326 |
+ |
spectrum through quantum effects. |
| 327 |
+ |
|
| 328 |
+ |
The classical nitrile spectrum can be seen in Figure 2. Most noticably |
| 329 |
+ |
is the position of the two peaks. Obviously the experimental peak |
| 330 |
+ |
position is near 2226 cm\textsuperscript{-1}. However, in this case |
| 331 |
+ |
the peak position is shifted to the blue at a position of 2375 |
| 332 |
+ |
cm\textsuperscript{-1}. This shift is due solely to the choice of |
| 333 |
+ |
oscillator strength in the Morse oscillator parameters. While this |
| 334 |
+ |
shift makes the two spectra differ, it does not affect the ability to |
| 335 |
+ |
qualitatively compare peak changes to possible experimental changes. |
| 336 |
+ |
With this important fact out of the way, differences between the two |
| 337 |
+ |
states are subtle but are very much present. The first and |
| 338 |
+ |
most notable is the apperance for a strong band near 2300 |
| 339 |
+ |
cm\textsuperscript{-1}. |
| 340 |
+ |
\begin{figure} |
| 341 |
|
\includegraphics[width=3.25in]{2Spectra} |
| 342 |
|
\caption{The classically calculated nitrile bond spetrum for no |
| 343 |
|
external field application (black) and full external field |
| 344 |
|
application (red)} |
| 345 |
|
\label{fig:twoSpectra} |
| 346 |
|
\end{figure} |
| 347 |
+ |
|
| 348 |
+ |
Before Gaussian silumations were carried out, it was attempt to apply |
| 349 |
+ |
the method developed by Cho {\it et al.}~\cite{Oh:2008fk} This method involves the fitting |
| 350 |
+ |
of multiple parameters to Gaussian calculated freuencies to find a |
| 351 |
+ |
correlation between the potential around the bond and the |
| 352 |
+ |
frequency. This is very similar to work done by Skinner {\it et al.}~with |
| 353 |
+ |
water models like SPC/E. The general method is to find the shift in |
| 354 |
+ |
the peak position through, |
| 355 |
+ |
\begin{equation} |
| 356 |
+ |
\delta\tilde{\nu} =\sum^{n}_{a=1} l_{a}\phi^{water}_{a} |
| 357 |
+ |
\end{equation} |
| 358 |
+ |
where $l_{a}$ are the fitting parameters and $\phi^{water}_{a}$ is the |
| 359 |
+ |
potential from the surrounding water cluster. This $\phi^{water}_{a}$ |
| 360 |
+ |
takes the form, |
| 361 |
+ |
\begin{equation} |
| 362 |
+ |
\phi_{a} = \frac{1}{4\pi \epsilon_{0}} \sum_{m} \sum_{j} |
| 363 |
+ |
\frac{C^{H_{2}O}_{j \left(m \right) }}{r_{aj \left(m\right)}} |
| 364 |
+ |
\end{equation} |
| 365 |
+ |
where $C^{H_{2}O}_{j \left(m \right) }$ indicates the partial charge |
| 366 |
+ |
on the $j$th site of the $m$th water molecule and $r_{aj \left(m\right)}$ |
| 367 |
+ |
is the distance between the site $a$ of the nitrile molecule and the $j$th |
| 368 |
+ |
site of the $m$th water molecule. However, since these simulations |
| 369 |
+ |
are done under the presence of external fields and in the |
| 370 |
+ |
absence of water, the equations need a correction factor for the shift |
| 371 |
+ |
caused by the external field. The equation is also reworked to use |
| 372 |
+ |
electric field site data instead of partial charges from surrounding |
| 373 |
+ |
atoms. So by modifing the original |
| 374 |
+ |
$\phi^{water}_{a}$ to $\phi^{5CB}_{a}$ we get, |
| 375 |
+ |
\begin{equation} |
| 376 |
+ |
\phi^{5CB}_{a} = \frac{1}{4\pi \epsilon_{0}} \left( \vec{E}\bullet |
| 377 |
+ |
\left(\vec{r}_{a}-\vec{r}_{CN}\right) \right) + \phi^{5CB}_{0} |
| 378 |
+ |
\end{equation} |
| 379 |
+ |
where $\vec{E}$ is the electric field at each atom, $\left( \vec{r}_{a} - |
| 380 |
+ |
\vec{r}_{CN} \right)$ is the vector between the nitrile bond and the |
| 381 |
+ |
cooridinates described by Cho around the bond and $\phi^{5CB}_{0}$ is |
| 382 |
+ |
the correction factor for the system of parameters. After these |
| 383 |
+ |
changes, the correction factor was found for multiple values of an |
| 384 |
+ |
external field being applied. However, the factor was no linear and |
| 385 |
+ |
was overly large due to the fitting parameters being so small. |
| 386 |
+ |
|
| 387 |
+ |
Due to this, Gaussian calculations were performed in lieu of this |
| 388 |
+ |
method. A set of snapshots for the zero and full field simualtions, |
| 389 |
+ |
they were first investigated for any dependence on the local, with |
| 390 |
+ |
external field included, electric field. This was to see if a linear |
| 391 |
+ |
or non-linear relationship between the two could be utilized for |
| 392 |
+ |
generating spectra. This was done in part because of previous studies |
| 393 |
+ |
showing the frequency dependence of nitrile bonds to the electric |
| 394 |
+ |
fields generated locally between solvating water. It was seen that |
| 395 |
+ |
little to no dependence could be directly shown. This data is not |
| 396 |
+ |
shown. |
| 397 |
+ |
|
| 398 |
+ |
Since no explicit dependence was observed between the calculated |
| 399 |
+ |
frequency and the electric field, it was not a viable route for the |
| 400 |
+ |
calculation of a nitrile spectrum. Instead, the frequencies were taken |
| 401 |
+ |
and convolved together with a lorentzian line shape applied around the |
| 402 |
+ |
frequency value. These spectra are seen below in Figure |
| 403 |
+ |
4. While the spectrum without a field is lower in intensity and is |
| 404 |
+ |
almost bimodel in distrobution, the external field spectrum is much |
| 405 |
+ |
more unimodel. This tighter clustering has the affect of increasing the |
| 406 |
+ |
intensity around 2226 cm\textsuperscript{-1} where the peak is |
| 407 |
+ |
centered. The external field also has fewer frequencies of higher |
| 408 |
+ |
energy in the spectrum. Unlike the the zero field, where some frequencies |
| 409 |
+ |
reach as high as 2280 cm\textsuperscript{-1}. |
| 410 |
|
\begin{figure} |
| 411 |
|
\includegraphics[width=3.25in]{Convolved} |
| 412 |
< |
\caption{Gaussian frequencies added together with gaussian } |
| 412 |
> |
\caption{Lorentzian convolved Gaussian frequencies of the zero field |
| 413 |
> |
system (black) and the full field system (red)} |
| 414 |
|
\label{fig:Con} |
| 415 |
|
\end{figure} |
| 316 |
– |
\begin{figure} |
| 317 |
– |
\includegraphics[width=7in]{Elip_3} |
| 318 |
– |
\caption{Ellipsoid reprsentation of 5CB at three different |
| 319 |
– |
field strengths, Zero Field (Left), Partial Field (Middle), and Full |
| 320 |
– |
Field (Right)} |
| 321 |
– |
\label{fig:Cigars} |
| 322 |
– |
\end{figure} |
| 323 |
– |
|
| 416 |
|
\section{Discussion} |
| 417 |
+ |
Interestingly, the field that is needed to switch the phase of 5CB |
| 418 |
+ |
macroscopically is larger than 1 V. However, in this case, only a |
| 419 |
+ |
voltage of 1.2 V was need to induce a phase change. This is impart due |
| 420 |
+ |
to the short distance of 5 nm the field is being applied across. At such a small |
| 421 |
+ |
distance, the field is much larger than the macroscopic and thus |
| 422 |
+ |
easily induces a field dependent phase change. However, this field |
| 423 |
+ |
will not cause a breakdown of the 5CB since electrochemistry studies |
| 424 |
+ |
have shown that it can be used in the presence of fields as high as |
| 425 |
+ |
500 V macroscopically. This large of a field near the surface of the |
| 426 |
+ |
elctrode would cause breakdown of 5CB if it could happen. |
| 427 |
|
|
| 428 |
+ |
The absence of any electric field dependency of the freuquency with |
| 429 |
+ |
the Gaussian simulations is interesting. A large base of research has been |
| 430 |
+ |
built upon the known tuning of the nitrile bond as the local field |
| 431 |
+ |
changes. This difference may be due to the absence of water or a |
| 432 |
+ |
molecule that induces a large internal field. Liquid water is known to have a very high internal field which |
| 433 |
+ |
is much larger than the internal fields of neat 5CB. Even though the |
| 434 |
+ |
application of Gaussian simulations followed by mapping it to |
| 435 |
+ |
some classical parameter is easy and straight forward, this system |
| 436 |
+ |
illistrates how that 'go to' method can break down. |
| 437 |
+ |
|
| 438 |
+ |
While this makes the application of nitrile Stark effects in |
| 439 |
+ |
simulations without water harder, these data show |
| 440 |
+ |
that it is not a deal breaker. The classically calculated nitrile |
| 441 |
+ |
spectrum shows changes in the spectra that will be easily seen through |
| 442 |
+ |
experimental routes. It indicates a shifted peak lower in energy |
| 443 |
+ |
should arise. This peak is a few wavenumbers from the leading edge of |
| 444 |
+ |
the larger peak and almost 75 wavenumbers from the center. This |
| 445 |
+ |
seperation between the two peaks means experimental results will show |
| 446 |
+ |
an easily resolved peak. |
| 447 |
+ |
|
| 448 |
+ |
The Gaussian derived spectra do indicate an applied field |
| 449 |
+ |
and subsiquent phase change does cause a narrowing of freuency |
| 450 |
+ |
distrobution. With narrowing, it would indicate an increased |
| 451 |
+ |
homogeneous distrobution of the local field near the nitrile. |
| 452 |
|
\section{Conclusions} |
| 453 |
+ |
Field dependent changes |
| 454 |
|
\newpage |
| 455 |
|
|
| 456 |
|
\bibliography{5CB} |
