| 493 |
|
|
| 494 |
|
Our simulations show that the united-atom model can reproduce the |
| 495 |
|
field-induced nematic ordering of the 4-cyano-4'-pentylbiphenyl. |
| 496 |
< |
Because we are simulating a very small electrode separation (5nm), a |
| 497 |
< |
voltage drop as low as 1.2 V was sufficient to induce the phase |
| 498 |
< |
change. This potential is significantly lower than the 500V that is |
| 499 |
< |
known to cause dielectric breakdown in 5CB.\cite{XXX} |
| 496 |
> |
Because we are simulating a very small electrode separation (5~nm), a |
| 497 |
> |
voltage drop as low as 1.2~V was sufficient to induce the phase |
| 498 |
> |
change. This potential is significantly smaller than the 500~V that is |
| 499 |
> |
known to cause dielectric breakdown in 5CB,\cite{XXX} and suggests |
| 500 |
> |
that by using close electrode separation, it would be relatively |
| 501 |
> |
straightforward to observe the nitrile Stark shift in 5CB. |
| 502 |
|
|
| 503 |
|
Both the classical correlation function and the isolated cluster |
| 504 |
< |
approaches to estimating the field-induced changes to the IR spectrum |
| 505 |
< |
show an increase in the population of nitrile stretches that appear at |
| 506 |
< |
a shift of $\sim 40 \mathrm{cm}^{-1}$ to the red of the unperturbed |
| 507 |
< |
vibrational line. To understand the origin of this shift, a more |
| 508 |
< |
complete picture of the spatial ordering around the nitrile bonds is |
| 509 |
< |
required. The angle-dependent pair distribution functions, |
| 504 |
> |
approaches to estimating the IR spectrum show that a small population |
| 505 |
> |
of nitrile stretches shift by $\sim 40 \mathrm{cm}^{-1}$ to the red of |
| 506 |
> |
the unperturbed vibrational line. To understand the origin of this |
| 507 |
> |
shift, a more complete picture of the spatial ordering around the |
| 508 |
> |
nitrile bonds is required. We have computed the angle-dependent pair |
| 509 |
> |
distribution functions, |
| 510 |
|
\begin{align} |
| 511 |
|
g(r, \cos \omega) = & \frac{1}{\rho N} \left< \sum_{i} |
| 512 |
|
\sum_{j} \delta \left(r - r_{ij}\right) \delta\left(\cos \omega_{ij} - |
| 515 |
|
\sum_{j} \delta \left(r - r_{ij}\right) \delta\left(\cos \theta_{i} - |
| 516 |
|
\cos \theta \right) \right> |
| 517 |
|
\end{align} |
| 518 |
< |
provide information about the joint spatial and angular correlations |
| 519 |
< |
in the system. The angles $\omega$ and $\theta$ are defined by vectors |
| 520 |
< |
along the CN axis of each nitrile bond (see figure |
| 521 |
< |
\ref{fig:definition}). |
| 520 |
< |
|
| 518 |
> |
which provide information about the joint spatial and angular |
| 519 |
> |
correlations present in the system. The angles $\omega$ and $\theta$ |
| 520 |
> |
are defined by vectors along the CN axis of each nitrile bond (see |
| 521 |
> |
figure \ref{fig:definition}). |
| 522 |
|
\begin{figure} |
| 523 |
< |
\includegraphics[width=\linewidth]{definition} |
| 523 |
> |
\includegraphics[width=4in]{definition} |
| 524 |
|
\caption{Definitions of the angles between two nitrile bonds.} |
| 525 |
|
\label{fig:definition} |
| 526 |
|
\end{figure} |
| 527 |
|
|
| 528 |
< |
In figure \ref{fig:gofromega}, one of the structural effects of the |
| 529 |
< |
field-induced phase transition is clear. The nematic ordering |
| 530 |
< |
transfers population from the perpendicular or unaligned region ($\cos |
| 531 |
< |
\omega \approx 0$) to the nitrile-alinged peak near $\cos\omega = 1$, |
| 532 |
< |
leaving most other features are undisturbed. This change is visible |
| 533 |
< |
in the simulations as an increased population of aligned nitrile bonds |
| 534 |
< |
in the first solvation shell. |
| 528 |
> |
The primary structural effect of the field-induced phase transition is |
| 529 |
> |
apparent in figure \ref{fig:gofromega}. The nematic ordering transfers |
| 530 |
> |
population from the perpendicular ($\cos\omega\approx 0$) and |
| 531 |
> |
anti-aligned ($\cos\omega\approx -1$) to the nitrile-alinged peak |
| 532 |
> |
near $\cos\omega\approx 1$, leaving most other features undisturbed. This |
| 533 |
> |
change is visible in the simulations as an increased population of |
| 534 |
> |
aligned nitrile bonds in the first solvation shell. |
| 535 |
|
\begin{figure} |
| 536 |
|
\includegraphics[width=\linewidth]{Figure4} |
| 537 |
|
\caption{Contours of the angle-dependent pair distribution functions |
| 538 |
< |
for nitrile bonds on 5CB in the zero-field (upper panel) and full |
| 538 |
> |
for nitrile bonds on 5CB in the no field (upper panel) and full |
| 539 |
|
field (lower panel) simulations. Dark areas signify regions of |
| 540 |
|
enhanced density, while light areas signify depletion relative to |
| 541 |
|
the bulk density.} |
| 542 |
|
\label{fig:gofromega} |
| 543 |
|
\end{figure} |
| 544 |
< |
Although it is possible that the coupling between closely-spaced |
| 545 |
< |
nitrile pairs is responsible for some of the red-shift, that is not |
| 546 |
< |
the only structural change that is taking place. The other two |
| 547 |
< |
dimensional pair distribution function, $g(r,\cos\theta)$, shows that |
| 548 |
< |
nematic ordering also transfers population that is directly in line |
| 549 |
< |
with the nitrile bond (see figure \ref{fig:gofrtheta}) to the sides of |
| 550 |
< |
the molecule, thereby freeing steric blockage that is more directly |
| 551 |
< |
influencing the nitrile vibration. |
| 544 |
> |
Although it is certainly possible that the coupling between |
| 545 |
> |
closely-spaced nitrile pairs is responsible for some of the red-shift, |
| 546 |
> |
that is not the only structural change that is taking place. The |
| 547 |
> |
second two-dimensional pair distribution function, $g(r,\cos\theta)$, |
| 548 |
> |
shows that nematic ordering also transfers population that is directly |
| 549 |
> |
in line with the nitrile bond (see figure \ref{fig:gofrtheta}) to the |
| 550 |
> |
sides of the molecule, thereby freeing steric blockage can directly |
| 551 |
> |
influence the nitrile vibration. We are suggesting here that the |
| 552 |
> |
nematic ordering provides an anti-caging of the nitrile vibration, and |
| 553 |
> |
given that the oscillator is fairly anharmonic, this provides a |
| 554 |
> |
fraction of the nitrile bonds with a significant red-shift. |
| 555 |
|
\begin{figure} |
| 556 |
|
\includegraphics[width=\linewidth]{Figure6} |
| 557 |
|
\caption{Contours of the angle-dependent pair distribution function, |
| 558 |
< |
$g(r,\cos \theta)$, for finding any atom at a distance and angular |
| 559 |
< |
deviation from the centrile of a nitrile bond. The top of each |
| 560 |
< |
contour plot corresponds to local density along the direction of |
| 561 |
< |
the nitrogen in the CN bond, while the bottom is in the direction |
| 562 |
< |
of the carbon atom. $g(z)$ data taken by following the |
| 563 |
< |
\ce{C -> N} vector for each nitrile bond (bottom panel) shows |
| 564 |
< |
that the field-induced phase transition reduces the population |
| 565 |
< |
atoms that are directly in line with the vibrational motion.} |
| 558 |
> |
$g(r,\cos \theta)$, for finding any other atom at a distance and |
| 559 |
> |
angular deviation from the center of a nitrile bond. The top edge |
| 560 |
> |
of each contour plot corresponds to local density along the |
| 561 |
> |
direction of the nitrogen in the CN bond, while the bottom is in |
| 562 |
> |
the direction of the carbon atom. Bottom panel: $g(z)$ data taken |
| 563 |
> |
by following the \ce{C -> N} vector for each nitrile bond shows |
| 564 |
> |
that the field-induced phase transition reduces the population of |
| 565 |
> |
atoms that are directly in line with the nitrogen motion.} |
| 566 |
|
\label{fig:gofrtheta} |
| 567 |
|
\end{figure} |
| 568 |
|
|
| 569 |
+ |
The cause of this shift does not appear to be related to the alignment |
| 570 |
+ |
of those nitrile bonds with the field, but rather to the change in |
| 571 |
+ |
local environment that is brought about by the isotropic-nematic |
| 572 |
+ |
transition. We have compared configurations for many of the cluster |
| 573 |
+ |
calculations that exhibited the frequencies between (2190 and 2215 |
| 574 |
+ |
$\mathrm{cm}^{-1}$) , and have observed some similar features. The |
| 575 |
+ |
lowest frequencies appear to come from configurations which have |
| 576 |
+ |
nearly-empty pockets directly opposite the nitrogen atom from the |
| 577 |
+ |
nitrile carbon. Because we have so few clusters, this is certainly not |
| 578 |
+ |
quantitative confirmation of this effect. |
| 579 |
|
|
| 580 |
|
|
| 567 |
– |
|
| 568 |
– |
The cause of this shift does not appear to be |
| 569 |
– |
related to the alignment of those nitrile bonds with the field, but |
| 570 |
– |
rather to the change in local environment that is brought about by the |
| 571 |
– |
isotropic-nematic transition. |
| 572 |
– |
|
| 573 |
– |
|
| 581 |
|
While this makes the application of nitrile Stark effects in |
| 582 |
|
simulations without water harder, these data show |
| 583 |
|
that it is not a deal breaker. The classically calculated nitrile |
