| 40 |
|
|
| 41 |
|
\begin{tocentry} |
| 42 |
|
%\includegraphics[width=9cm]{Elip_3} |
| 43 |
< |
\includegraphics[width=9cm]{Figure2} |
| 43 |
> |
\includegraphics[width=9cm]{cluster/cluster.pdf} |
| 44 |
|
\end{tocentry} |
| 45 |
|
|
| 46 |
|
\begin{abstract} |
| 52 |
|
isotropic-nematic phase transition was observed in the simulations, |
| 53 |
|
and the effects of this transition on the distribution of nitrile |
| 54 |
|
frequencies were computed. Classical bond displacement correlation |
| 55 |
< |
functions exhibit a $\sim~3~\mathrm{cm}^{-1}$ red shift of a |
| 56 |
< |
portion of the main nitrile peak, and this shift was observed only |
| 57 |
< |
when the fields were large enough to induce orientational ordering |
| 58 |
< |
of the bulk phase. Joint spatial-angular distribution functions |
| 59 |
< |
indicate that phase-induced anti-caging of the nitrile bond is |
| 60 |
< |
contributing to the change in the nitrile spectrum. |
| 55 |
> |
functions exhibit a $\sim~3~\mathrm{cm}^{-1}$ red shift of a portion |
| 56 |
> |
of the main nitrile peak, and this shift was observed only when the |
| 57 |
> |
fields were large enough to induce orientational ordering of the |
| 58 |
> |
bulk phase. Joint spatial-angular distribution functions indicate |
| 59 |
> |
that phase-induced anti-caging of the nitrile bond is contributing |
| 60 |
> |
to the change in the nitrile spectrum. Distributions of frequencies |
| 61 |
> |
obtained via cluster-based fits to quantum mechanical energies of |
| 62 |
> |
nitrile bond deformations exhibit a similar |
| 63 |
> |
$\sim~2.7~\mathrm{cm}^{-1}$ red shift. |
| 64 |
|
\end{abstract} |
| 65 |
|
|
| 66 |
|
\newpage |
| 67 |
|
|
| 68 |
|
\section{Introduction} |
| 69 |
|
|
| 70 |
< |
Nitrile groups can serve as very precise electric field reporters via |
| 71 |
< |
their distinctive Raman and IR signatures.\cite{Boxer:2009xw} The |
| 72 |
< |
triple bond between the nitrogen and the carbon atom is very sensitive |
| 73 |
< |
to local field changes and has been observed to have a direct impact |
| 74 |
< |
on the peak position within the spectrum. The Stark shift in the |
| 75 |
< |
spectrum can be quantified and mapped onto a field that is impinging |
| 76 |
< |
upon the nitrile bond. The response of nitrile groups to electric |
| 74 |
< |
fields has now been investigated for a number of small |
| 75 |
< |
molecules,\cite{Andrews:2000qv} as well as in biochemical settings, |
| 76 |
< |
where nitrile groups can act as minimally invasive probes of structure |
| 77 |
< |
and |
| 70 |
> |
Because the triple bond between nitrogen and carbon is sensitive to |
| 71 |
> |
local fields, nitrile groups can report on field strengths via their |
| 72 |
> |
distinctive Raman and IR signatures.\cite{Boxer:2009xw} The response |
| 73 |
> |
of nitrile groups to electric fields has now been investigated for a |
| 74 |
> |
number of small molecules,\cite{Andrews:2000qv} as well as in |
| 75 |
> |
biochemical settings, where nitrile groups can act as minimally |
| 76 |
> |
invasive probes of structure and |
| 77 |
|
dynamics.\cite{Tucker:2004qq,Webb:2008kn,Lindquist:2009fk,Fafarman:2010dq} |
| 78 |
|
The vibrational Stark effect has also been used to study the effects |
| 79 |
|
of electric fields on nitrile-containing self-assembled monolayers at |
| 80 |
|
metallic interfaces.\cite{Oklejas:2002uq,Schkolnik:2012ty} |
| 81 |
|
|
| 83 |
– |
|
| 82 |
|
Recently 4-cyano-4'-pentylbiphenyl (5CB), a liquid crystalline |
| 83 |
|
molecule with a terminal nitrile group, has seen renewed interest as |
| 84 |
|
one way to impart order on the surfactant interfaces of |
| 156 |
|
sufficient strength. For a gap of 5 nm between a lower electrode |
| 157 |
|
having a nanoelectrode placed near it via an atomic force microscope, |
| 158 |
|
a potential of 1 V applied across the electrodes is equivalent to a |
| 159 |
< |
field of 2x10\textsuperscript{8} $\frac{V}{M}$. This field is |
| 159 |
> |
field of $2 \times 10^8~\mathrm{V/m}$. This field is |
| 160 |
|
certainly strong enough to cause the isotropic-nematic phase change |
| 161 |
|
and as well as a visible Stark tuning of the nitrile bond. We expect |
| 162 |
|
that this would be readily visible experimentally through Raman or IR |
| 261 |
|
applied field. |
| 262 |
|
|
| 263 |
|
\begin{figure}[H] |
| 264 |
< |
\includegraphics[width=\linewidth]{Figure1} |
| 264 |
> |
\includegraphics[width=\linewidth]{orderParameter/orderParameter.pdf} |
| 265 |
|
\caption{Evolution of the orientational order parameters for the |
| 266 |
|
no-field, partial field, and full field simulations over the |
| 267 |
|
course of 60 ns. Each simulation was started from a |
| 323 |
|
capped propane molecule. |
| 324 |
|
|
| 325 |
|
\begin{figure}[H] |
| 326 |
< |
\includegraphics[width=\linewidth]{Figure2} |
| 326 |
> |
\includegraphics[width=\linewidth]{cluster/cluster.pdf} |
| 327 |
|
\caption{Cluster calculations were performed on randomly sampled 5CB |
| 328 |
< |
molecules (shown in red) from each of the simulations. Surrounding |
| 329 |
< |
molecular bodies were included if any body atoms were within 6 |
| 330 |
< |
\AA\ of the target nitrile bond, and tails were included if they |
| 331 |
< |
were within 4 \AA. Included portions of these molecules are shown |
| 332 |
< |
in green. The CN bond on the target molecule was stretched and |
| 333 |
< |
compressed, and the resulting single point energies were fit to |
| 334 |
< |
Morse oscillators to obtain a distribution of frequencies.} |
| 328 |
> |
molecules (shown in red) from the full-field and no-field |
| 329 |
> |
simulations. Surrounding molecular bodies were included if any |
| 330 |
> |
body atoms were within 6 \AA\ of the target nitrile bond, and |
| 331 |
> |
tails were included if they were within 4 \AA. Included portions |
| 332 |
> |
of these molecules are shown in green. The CN bond on the target |
| 333 |
> |
molecule was stretched and compressed, and the resulting single |
| 334 |
> |
point energies were fit to Morse oscillators to obtain a |
| 335 |
> |
distribution of frequencies.} |
| 336 |
|
\label{fig:cluster} |
| 337 |
|
\end{figure} |
| 338 |
|
|
| 354 |
|
each of the frequencies was convoluted with a Lorentzian lineshape |
| 355 |
|
with a width of 1.5 $\mathrm{cm}^{-1}$. Available computing resources |
| 356 |
|
limited the sampling to 100 clusters for both the zero-field and full |
| 357 |
< |
field soectra. Comparisons of the quantum mechanical spectrum to the |
| 358 |
< |
classical are shown in figure \ref{fig:spectra}. |
| 359 |
< |
|
| 360 |
< |
\begin{figure} |
| 362 |
< |
\includegraphics[width=\linewidth]{Figure3} |
| 363 |
< |
\caption{Spectrum of nitrile frequency shifts for the no-field |
| 364 |
< |
(black) and the full-field (red) simulations. Upper |
| 365 |
< |
panel: frequency shifts obtained from {\it ab initio} cluster |
| 366 |
< |
calculations. Lower panel: classical bond-length autocorrelation |
| 367 |
< |
spectrum for the flexible nitrile measured relative to the natural |
| 368 |
< |
frequency for the flexible bond.} |
| 369 |
< |
\label{fig:spectra} |
| 370 |
< |
\end{figure} |
| 357 |
> |
field spectra. Comparisons of the quantum mechanical spectrum to the |
| 358 |
> |
classical are shown in figure \ref{fig:spectra}. The mean frequencies |
| 359 |
> |
obtained from the distributions give a field-induced red shift of |
| 360 |
> |
$2.68~\mathrm{cm}^{-1}$. |
| 361 |
|
|
| 362 |
|
\subsection{CN frequencies from potential-frequency maps} |
| 363 |
|
|
| 424 |
|
components of the field. |
| 425 |
|
|
| 426 |
|
\begin{figure} |
| 427 |
< |
\includegraphics[width=\linewidth]{Figure7} |
| 427 |
> |
\includegraphics[width=\linewidth]{fieldMap/fieldMap.pdf} |
| 428 |
|
\caption{The observed cluster frequencies have no apparent |
| 429 |
|
correlation with the electric field felt at the centroid of the |
| 430 |
< |
nitrile bond. Lower panel: vibrational frequencies plotted |
| 431 |
< |
against the total field magnitude. Middle panel: mapped to the |
| 432 |
< |
component of the field parallel to the CN bond. Upper panel: |
| 433 |
< |
mapped to the magnitude of the field perpendicular to the CN |
| 434 |
< |
bond.} |
| 430 |
> |
nitrile bond. Upper panel: vibrational frequencies plotted |
| 431 |
> |
against the component of the field parallel to the CN bond. |
| 432 |
> |
Middle panel: mapped to the magnitude of the field components |
| 433 |
> |
perpendicular to the CN bond. Lower panel: mapped to the total |
| 434 |
> |
field magnitude.} |
| 435 |
|
\label{fig:fieldMap} |
| 436 |
|
\end{figure} |
| 437 |
|
|
| 479 |
|
spectra are shown as a shift relative to the natural oscillation of |
| 480 |
|
the Morse bond. |
| 481 |
|
|
| 482 |
+ |
\begin{figure} |
| 483 |
+ |
\includegraphics[width=\linewidth]{spectra/spectra.pdf} |
| 484 |
+ |
\caption{Spectrum of nitrile frequency shifts for the no-field |
| 485 |
+ |
(black) and the full-field (red) simulations. Upper panel: |
| 486 |
+ |
frequency shifts obtained from {\it ab initio} cluster |
| 487 |
+ |
calculations. Lower panel: classical bond-length autocorrelation |
| 488 |
+ |
spectrum for the flexible nitrile measured relative to the natural |
| 489 |
+ |
frequency for the flexible bond. The dashed lines indicate the |
| 490 |
+ |
mean frequencies for each of the distributions. The cluster |
| 491 |
+ |
calculations exhibit a $2.68~\mathrm{cm}^{-1}$ field-induced red |
| 492 |
+ |
shift, while the classical correlation functions predict a red |
| 493 |
+ |
shift of $3.05~\mathrm{cm}^{-1}$.} |
| 494 |
+ |
\label{fig:spectra} |
| 495 |
+ |
\end{figure} |
| 496 |
|
|
| 497 |
|
The classical approach includes both intramolecular and electrostatic |
| 498 |
|
interactions, and so it implicitly couples \ce{CN} vibrations to other |
| 499 |
|
vibrations within the molecule as well as to nitrile vibrations on |
| 500 |
|
other nearby molecules. The classical frequency spectrum is |
| 501 |
< |
significantly broader because of this coupling. The {\it |
| 502 |
< |
ab |
| 503 |
< |
initio} cluster approach exercises only the targeted nitrile bond, |
| 504 |
< |
with no additional coupling to other degrees of freedom. As a result |
| 505 |
< |
the quantum calculations are quite narrowly peaked around the |
| 506 |
< |
experimental nitrile frequency. Although the spectra are quite noisy, |
| 507 |
< |
the main effect seen in both the classical and quantum frequency |
| 508 |
< |
distributions is a moderate shift $\sim 3~\mathrm{cm}^{-1}$ to the |
| 509 |
< |
red when the full electrostatic field had induced the nematic phase |
| 506 |
< |
transition. |
| 501 |
> |
significantly broader because of this coupling. The {\it ab initio} |
| 502 |
> |
cluster approach exercises only the targeted nitrile bond, with no |
| 503 |
> |
additional coupling to other degrees of freedom. As a result the |
| 504 |
> |
quantum calculations are quite narrowly peaked around the experimental |
| 505 |
> |
nitrile frequency. Although the spectra are quite noisy, the main |
| 506 |
> |
effect seen in both distributions is a moderate shift to the red |
| 507 |
> |
($3.05~\mathrm{cm}^{-1}$ classical and $2.68~\mathrm{cm}^{-1}$ |
| 508 |
> |
quantum) when the full electrostatic field had induced the nematic |
| 509 |
> |
phase transition. |
| 510 |
|
|
| 511 |
|
\section{Discussion} |
| 512 |
|
Our simulations show that the united-atom model can reproduce the |
| 539 |
|
are defined by vectors along the CN axis of each nitrile bond (see |
| 540 |
|
figure \ref{fig:definition}). |
| 541 |
|
\begin{figure} |
| 542 |
< |
\includegraphics[width=4in]{definition} |
| 542 |
> |
\includegraphics[width=4in]{definition/definition.pdf} |
| 543 |
|
\caption{Definitions of the angles between two nitrile bonds.} |
| 544 |
|
\label{fig:definition} |
| 545 |
|
\end{figure} |
| 553 |
|
aligned nitrile bonds in the first solvation shell. |
| 554 |
|
|
| 555 |
|
\begin{figure} |
| 556 |
< |
\includegraphics[width=\linewidth]{Figure4} |
| 556 |
> |
\includegraphics[width=\linewidth]{gofrOmega/gofrOmega.pdf} |
| 557 |
|
\caption{Contours of the angle-dependent pair distribution functions |
| 558 |
|
for nitrile bonds on 5CB in the no field (upper panel) and full |
| 559 |
|
field (lower panel) simulations. Dark areas signify regions of |
| 578 |
|
region that is directly in line with the nitrogen side of the CN bond. |
| 579 |
|
|
| 580 |
|
\begin{figure} |
| 581 |
< |
\includegraphics[width=\linewidth]{Figure6} |
| 581 |
> |
\includegraphics[width=\linewidth]{gofrTheta/gofrTheta.pdf} |
| 582 |
|
\caption{Contours of the angle-dependent pair distribution function, |
| 583 |
|
$g(r,\cos \theta)$, for finding any other atom at a distance and |
| 584 |
|
angular deviation from the center of a nitrile bond. The top edge |
