| 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 |
| 158 |
|
4-Cyano-4'-n-alkylbiphenyl liquid crystals has not been investigated. |
| 159 |
|
While macroscopic electric fields applied across macro electrodes show |
| 160 |
|
the phase change of the molecule as a function of electric |
| 161 |
< |
field,\cite{Lim:2006xq} the effect of a microscopic field application |
| 161 |
> |
field,\cite{Lim:2006xq} the effect of a nanoscopic field application |
| 162 |
|
has not been probed. These previous studies have shown the nitrile |
| 163 |
|
group serves as an excellent indicator of the molecular orientation |
| 164 |
< |
within the field applied. Blank showed the 180 degree change in field |
| 164 |
> |
within the field applied. Lee et. al. showed the 180 degree change in field |
| 165 |
|
direction could be probed with the nitrile peak intensity as it |
| 166 |
|
decreased and increased with molecule alignment in the |
| 167 |
|
field.\cite{Lee:2006qd,Leyte:97} |
| 251 |
|
where $r_0$ is the equilibrium bond distance and $r(t)$ is the |
| 252 |
|
instantaneous bond displacement at time $t$. Once calculated, |
| 253 |
|
smoothing was applied by adding an exponential decay on top of the |
| 254 |
< |
decay with a $\tau$ of 3000 (have to check this). Further smoothing |
| 254 |
> |
decay with a $\tau$ of 6000. Further smoothing |
| 255 |
|
was applied by padding 20,000 zeros on each side of the symmetric |
| 256 |
|
data. This was done five times by allowing the systems to run 1 ns |
| 257 |
|
with a rigid bond followed by an equilibrium run with the bond |
| 258 |
< |
switched back on and the short production run. |
| 258 |
> |
switched back to a Morse oscillator and a short production run of 20 ps. |
| 259 |
|
|
| 260 |
|
\section{Results} |
| 261 |
|
|
| 321 |
|
analysis. First was the replacement of the static nitrile bond with a |
| 322 |
|
morse oscillator bond. This was then simulated for a period of time |
| 323 |
|
and a classical spetrum was calculated. Second, ab intio calcualtions |
| 324 |
< |
were performed to investigate quantum effects which lead to a change |
| 325 |
< |
in the spectral details. |
| 324 |
> |
were performed to investigate if the phase change caused any change |
| 325 |
> |
spectrum through quantum effects. |
| 326 |
|
|
| 327 |
|
The classical nitrile spectrum can be seen in Figure 2. Most noticably |
| 328 |
|
is the position of the two peaks. Obviously the experimental peak |
| 346 |
|
|
| 347 |
|
Before Gaussian silumations were carried out, it was attempt to apply |
| 348 |
|
the method developed by Cho et. al. This method involves the fitting |
| 349 |
< |
of multiple parameters to However, since these simulations |
| 350 |
< |
are done under the presence of external electric fields and in the |
| 351 |
< |
absence of water the equations had to be reworked. Originally, the |
| 352 |
< |
nitrile bond frequency was related to the potential of water around |
| 353 |
< |
the bond via |
| 349 |
> |
of multiple parameters to Gaussian calculated freuencies to find a |
| 350 |
> |
correlation between the potential around the bond and the |
| 351 |
> |
frequency. This is very similar to work done by Skinner et. al. with |
| 352 |
> |
water models like SPC/E. The general method is to find the shift in |
| 353 |
> |
the peak position through, |
| 354 |
|
\begin{equation} |
| 355 |
+ |
\delta\tilde{\nu} =\sum^{n}_{a=1} l_{a}\phi^{water}_{a} |
| 356 |
+ |
\end{equation} |
| 357 |
+ |
where $l_{a}$ are the fitting parameters and $\phi^{water}_{a}$ is the |
| 358 |
+ |
potential from the surrounding water cluster. This $\phi^{water}_{a}$ |
| 359 |
+ |
takes the form, |
| 360 |
+ |
\begin{equation} |
| 361 |
|
\phi_{a} = \frac{1}{4\pi \epsilon_{0}} \sum_{m} \sum_{j} |
| 362 |
|
\frac{C^{H_{2}O}_{j \left(m \right) }}{r_{aj \left(m\right)}} |
| 363 |
|
\end{equation} |
| 364 |
< |
After Gaussian calculations were performed on a set of snapshots for |
| 365 |
< |
the zero and full field simualtions, they were first investigated for |
| 366 |
< |
any dependence on the local, with external field included, electric |
| 367 |
< |
field. This was to see if a linear or non-linear relationship between |
| 368 |
< |
the two could be utilized for generating spectra. This was done in |
| 369 |
< |
part because of previous studies showing the frequency dependence of |
| 370 |
< |
nitrile bonds to the electric fields generated locally between |
| 371 |
< |
solvating water. It was seen that little to no dependence could be |
| 372 |
< |
directly shown. This data is not shown. |
| 364 |
> |
where $C^{H_{2}O}_{j \left(m \right) }$ indicates the partial charge |
| 365 |
> |
on the $j$th site of the $m$th water molecule and $r_{aj \left(m\right)}$ |
| 366 |
> |
is the distance between the site $a$ of the nitrile molecule and the $j$th |
| 367 |
> |
site of the $m$th water molecule. However, since these simulations |
| 368 |
> |
are done under the presence of external electric fields and in the |
| 369 |
> |
absence of water the equations must have a correction factor for the |
| 370 |
> |
external field change as well as the use of electric field site data |
| 371 |
> |
instead of charged site points. So by modifing the original |
| 372 |
> |
$\phi^{water}_{a}$ to $\phi^{5CB}_{a}$ we get, |
| 373 |
> |
\begin{equation} |
| 374 |
> |
\phi^{5CB}_{a} = \frac{1}{4\pi \epsilon_{0}} \left( \vec{E}\bullet |
| 375 |
> |
\left(\vec{r}_{a}-\vec{r}_{CN}\right) \right) + \phi^{5CB}_{0} |
| 376 |
> |
\end{equation} |
| 377 |
> |
where $\vec{E}$ is the electric field at each atom, $\left( \vec{r}_{a} - |
| 378 |
> |
\vec{r}_{CN} \right)$ is the vector between the nitrile bond and the |
| 379 |
> |
cooridinates described by Cho around the bond and $\phi^{5CB}_{0}$ is |
| 380 |
> |
the correction factor for the system of parameters. After these |
| 381 |
> |
changes, the correction factor was found for multiple values of an |
| 382 |
> |
external field being applied. However, the factor was no linear and |
| 383 |
> |
was overly large due to the fitting parameters being so small. |
| 384 |
|
|
| 385 |
+ |
Due to this, Gaussian calculations were performed in lieu of this |
| 386 |
+ |
method. A set of snapshots for the zero and full field simualtions, |
| 387 |
+ |
they were first investigated for any dependence on the local, with |
| 388 |
+ |
external field included, electric field. This was to see if a linear |
| 389 |
+ |
or non-linear relationship between the two could be utilized for |
| 390 |
+ |
generating spectra. This was done in part because of previous studies |
| 391 |
+ |
showing the frequency dependence of nitrile bonds to the electric |
| 392 |
+ |
fields generated locally between solvating water. It was seen that |
| 393 |
+ |
little to no dependence could be directly shown. This data is not |
| 394 |
+ |
shown. |
| 395 |
+ |
|
| 396 |
|
Since no explicit dependence was observed between the calculated |
| 397 |
|
frequency and the electric field, it was not a viable route for the |
| 398 |
|
calculation of a nitrile spectrum. Instead, the frequencies were taken |
| 399 |
|
and convolved together. These two spectra are seen below in Figure |
| 400 |
|
4. While the spectrum without a field is lower in intensity and is |
| 401 |
|
almost bimodel in distrobuiton, the external field spectrum is much |
| 402 |
< |
more unimodel. This narrowing has the affect of increasing the |
| 402 |
> |
more unimodel. This tighter clustering has the affect of increasing the |
| 403 |
|
intensity around 2226 cm\textsuperscript{-1} where the peak is |
| 404 |
< |
centered. The external field also has fewer frequencies higher to the |
| 405 |
< |
blue of the spectra. Unlike the the zero field, where some frequencies reach as high |
| 406 |
< |
as 2280 cm\textsuperscript{-1}. |
| 404 |
> |
centered. The external field also has fewer frequencies of higher |
| 405 |
> |
energy in the spectrum. Unlike the the zero field, where some frequencies |
| 406 |
> |
reach as high as 2280 cm\textsuperscript{-1}. |
| 407 |
|
\begin{figure} |
| 408 |
|
\includegraphics[width=3.25in]{Convolved} |
| 409 |
|
\caption{Lorentzian convolved Gaussian frequencies of the zero field |
| 413 |
|
\section{Discussion} |
| 414 |
|
The absence of any electric field dependency of the freuquency with |
| 415 |
|
the Gaussian simulations is strange. A large base of research has been |
| 416 |
< |
built upon the known tuning the nitrile bond as local field |
| 416 |
> |
built upon the known tuning of the nitrile bond as local field |
| 417 |
|
changes. This differences may be due to the absence of water. Many of |
| 418 |
< |
the nitrile bond fitting maps are done in the presence of |
| 418 |
> |
the nitrile bond fitting maps are done in the presence of liquid |
| 419 |
|
water. Liquid water is known to have a very high internal field which |
| 420 |
|
is much larger than the internal fields of neat 5CB. Even though the |
| 421 |
< |
application of running Gaussian simulations followed by mappying to |
| 421 |
> |
application of Gaussian simulations followed by mappying to |
| 422 |
|
some classical parameter is easy and straight forward, this system |
| 423 |
|
illistrates how that 'go to' method can break down. |
| 424 |
|
|
| 425 |
|
While this makes the application of nitrile Stark effects in |
| 426 |
< |
simulations of liquid water absent simulations harder, these data show |
| 426 |
> |
simulations of water absent simulations harder, these data show |
| 427 |
|
that it is not a deal breaker. The classically calculated nitrile |
| 428 |
|
spectrum shows changes in the spectra that will be easily seen through |
| 429 |
|
experimental routes. It indicates a shifted peak lower in energy |
| 430 |
|
should arise. This peak is a few wavenumbers from the larger peak and |
| 431 |
< |
almost 75 wavenmubers from the center. This seperation between the two |
| 432 |
< |
peaks means experimental results will show a well resolved peak. |
| 431 |
> |
almost 75 wavenumbers from the center. This seperation between the two |
| 432 |
> |
peaks means experimental results will have an easily resolved peak. |
| 433 |
|
|
| 434 |
< |
The Gaussian derived frequencies and subsiquent spectra also indicate |
| 435 |
< |
changes that can be observed experimentally. |
| 434 |
> |
The Gaussian derived spectra do indicate that with an applied field |
| 435 |
> |
and subsiquent phase change does cause a narrowing of freuency |
| 436 |
> |
distrobution. |
| 437 |
|
\section{Conclusions} |
| 438 |
+ |
Field dependent changes in the phase of a system are |
| 439 |
|
Jonathan K. Whitmer |
| 440 |
|
cho stuff |
| 441 |
|
\newpage |
