| 66 |
|
isotropic-nematic phase transition was observed in the simulations, |
| 67 |
|
and the effects of this transition on the distribution of nitrile |
| 68 |
|
frequencies were computed. Classical bond displacement correlation |
| 69 |
< |
functions exhibit a $\sim 40 \mathrm{~cm}^{-1}$ red shift of a |
| 69 |
> |
functions exhibit a $\sim~10~\mathrm{cm}^{-1}$ red shift of a |
| 70 |
|
portion of the main nitrile peak, and this shift was observed only |
| 71 |
|
when the fields were large enough to induce orientational ordering |
| 72 |
|
of the bulk phase. Joint spatial-angular distribution functions |
| 165 |
|
response, the response at a molecular scale has not been studied. With |
| 166 |
|
the advent of nano-electrodes and the ability to couple these |
| 167 |
|
electrodes to atomic force microscopy, control of electric fields |
| 168 |
< |
applied across nanometer distances is now possible.\cite{C3AN01651J} In |
| 169 |
< |
special cases where the macroscopic fields are insufficient to cause |
| 170 |
< |
an observable Stark effect without dielectric breakdown of the |
| 168 |
> |
applied across nanometer distances is now possible.\cite{C3AN01651J} |
| 169 |
> |
In special cases where the macroscopic fields are insufficient to |
| 170 |
> |
cause an observable Stark effect without dielectric breakdown of the |
| 171 |
|
material, small potentials across nanometer-sized gaps may be of |
| 172 |
< |
sufficient strength. For a gap of 5 nm between a lower electrode |
| 172 |
> |
sufficient strength. For a gap of 5 nm between a lower electrode |
| 173 |
|
having a nanoelectrode placed near it via an atomic force microscope, |
| 174 |
|
a potential of 1 V applied across the electrodes is equivalent to a |
| 175 |
< |
field of 2x10\textsuperscript{8} $\frac{V}{M}$. This field is |
| 175 |
> |
field of 2x10\textsuperscript{8} $\frac{V}{M}$. This field is |
| 176 |
|
certainly strong enough to cause the isotropic-nematic phase change |
| 177 |
|
and as well as a visible Stark tuning of the nitrile bond. We expect |
| 178 |
|
that this would be readily visible experimentally through Raman or IR |
| 183 |
|
presence of static electric fields. These simulations were then |
| 184 |
|
coupled with both {\it ab intio} calculations of CN-deformations and |
| 185 |
|
classical bond-length correlation functions to predict spectral |
| 186 |
< |
shifts. These predictions made should be easily varifiable with |
| 186 |
> |
shifts. These predictions made should be easily verifiable with |
| 187 |
|
scanning electrochemical microscopy experiments. |
| 188 |
|
|
| 189 |
|
\section{Computational Details} |
| 190 |
< |
The force field used for 5CB was a united-atom model that was |
| 190 |
> |
The force-field used to model 5CB was a united-atom model that was |
| 191 |
|
parameterized by Guo {\it et al.}\cite{Zhang:2011hh} However, for most |
| 192 |
|
of the simulations, each of the phenyl rings was treated as a rigid |
| 193 |
< |
body to allow for larger time steps and very long simulation times. |
| 194 |
< |
The geometries of the rigid bodies were taken from equilibrium bond |
| 193 |
> |
body to allow for larger time steps and longer simulation times. The |
| 194 |
> |
geometries of the rigid bodies were taken from equilibrium bond |
| 195 |
|
distances and angles. Although the individual phenyl rings were held |
| 196 |
|
rigid, bonds, bends, torsions and inversion centers that involved |
| 197 |
|
atoms in these substructures (but with connectivity to the rest of the |
| 205 |
|
applied fields were carried out in the microcanonical (NVE) ensemble |
| 206 |
|
with an energy corresponding to the average energy from the canonical |
| 207 |
|
(NVT) equilibration runs. Typical applied-field equilibration runs |
| 208 |
< |
were more than 60ns in length. |
| 208 |
> |
were more than 60~ns in length. |
| 209 |
|
|
| 210 |
|
Static electric fields with magnitudes similar to what would be |
| 211 |
|
available in an experimental setup were applied to the different |
| 370 |
|
with a width of 1.5 $\mathrm{cm}^{-1}$. Available computing resources |
| 371 |
|
limited the sampling to 67 clusters for the zero-field spectrum, and |
| 372 |
|
59 for the full field. Comparisons of the quantum mechanical spectrum |
| 373 |
< |
to the classical are shown in figure \ref{fig:spectrum}. |
| 373 |
> |
to the classical are shown in figure \ref{fig:spectra}. |
| 374 |
> |
|
| 375 |
> |
\begin{figure} |
| 376 |
> |
\includegraphics[width=\linewidth]{Figure3} |
| 377 |
> |
\caption{Spectrum of nitrile frequency shifts for the no-field |
| 378 |
> |
(black) and the full-field (red) simulations. Upper |
| 379 |
> |
panel: frequency shifts obtained from {\it ab initio} cluster |
| 380 |
> |
calculations. Lower panel: classical bond-length autocorrelation |
| 381 |
> |
spectrum for the flexible nitrile measured relative to the natural |
| 382 |
> |
frequency for the flexible bond.} |
| 383 |
> |
\label{fig:spectra} |
| 384 |
> |
\end{figure} |
| 385 |
|
|
| 386 |
|
\subsection{CN frequencies from potential-frequency maps} |
| 387 |
|
|
| 483 |
|
spectra are shown as a shift relative to the natural oscillation of |
| 484 |
|
the Morse bond. |
| 485 |
|
|
| 475 |
– |
\begin{figure} |
| 476 |
– |
\includegraphics[width=3.25in]{Convolved} |
| 477 |
– |
\includegraphics[width=3.25in]{2Spectra} |
| 478 |
– |
\caption{Quantum mechanical nitrile spectrum for the no-field simulation |
| 479 |
– |
(black) and the full field simulation (red). The lower panel |
| 480 |
– |
shows the corresponding classical bond-length autocorrelation |
| 481 |
– |
spectrum for the flexible nitrile measured relative to the natural |
| 482 |
– |
frequency for the flexible bond.} |
| 483 |
– |
\label{fig:spectra} |
| 484 |
– |
\end{figure} |
| 486 |
|
|
| 487 |
< |
Note that due to electrostatic interactions, the classical approach |
| 488 |
< |
implicitly couples \ce{CN} vibrations to the same vibrational mode on |
| 489 |
< |
other nearby molecules. This coupling is not handled in the {\it ab |
| 490 |
< |
initio} cluster approach. |
| 487 |
> |
The classical approach includes both intramolecular and electrostatic |
| 488 |
> |
interactions, and so it implicitly couples \ce{CN} vibrations to other |
| 489 |
> |
vibrations within the molecule as well as to nitrile vibrations on |
| 490 |
> |
other nearby molecules. The classical frequency spectrum is |
| 491 |
> |
significantly broader because of this coupling. The {\it |
| 492 |
> |
ab |
| 493 |
> |
initio} cluster approach exercises only the targeted nitrile bond, |
| 494 |
> |
with no additional coupling to other degrees of freedom. As a result |
| 495 |
> |
the quantum calculations are quite narrowly peaked around the |
| 496 |
> |
experimental nitrile frequency. Although the spectra are quite noisy, |
| 497 |
> |
the main effect seen in both the classical and quantum frequency |
| 498 |
> |
distributions is a moderate shift $\sim 10~\mathrm{cm}^{-1}$ to the |
| 499 |
> |
red when the full electrostatic field had induced the nematic phase |
| 500 |
> |
transition. |
| 501 |
|
|
| 502 |
|
\section{Discussion} |
| 492 |
– |
|
| 503 |
|
Our simulations show that the united-atom model can reproduce the |
| 504 |
|
field-induced nematic ordering of the 4-cyano-4'-pentylbiphenyl. |
| 505 |
|
Because we are simulating a very small electrode separation (5~nm), a |
| 506 |
|
voltage drop as low as 1.2~V was sufficient to induce the phase |
| 507 |
< |
change. This potential is significantly smaller than 100~V that has |
| 508 |
< |
used within a 5~um gap for electrochemiluminescence of rubrene,\cite{Kojima19881789} and suggests |
| 509 |
< |
that by using close electrode separation, it would be relatively |
| 507 |
> |
change. This potential is significantly smaller than 100~V that was |
| 508 |
> |
used with a 5~$\mu$m gap to study the electrochemiluminescence of |
| 509 |
> |
rubrene in neat 5CB,\cite{Kojima19881789} and suggests that by using |
| 510 |
> |
electrodes separated by a nanometer-scale gap, it will be relatively |
| 511 |
|
straightforward to observe the nitrile Stark shift in 5CB. |
| 512 |
|
|
| 513 |
|
Both the classical correlation function and the isolated cluster |
| 514 |
< |
approaches to estimating the IR spectrum show that a small population |
| 515 |
< |
of nitrile stretches shift by $\sim 40 \mathrm{cm}^{-1}$ to the red of |
| 516 |
< |
the unperturbed vibrational line. To understand the origin of this |
| 514 |
> |
approaches to estimating the IR spectrum show that a population of |
| 515 |
> |
nitrile stretches shift by $\sim~10~\mathrm{cm}^{-1}$ to the red of |
| 516 |
> |
the unperturbed vibrational line. To understand the origin of this |
| 517 |
|
shift, a more complete picture of the spatial ordering around the |
| 518 |
< |
nitrile bonds is required. We have computed the angle-dependent pair |
| 519 |
< |
distribution functions, |
| 518 |
> |
nitrile bonds is required. We have computed the angle-dependent pair |
| 519 |
> |
distribution functions, |
| 520 |
|
\begin{align} |
| 521 |
< |
g(r, \cos \omega) = & \frac{1}{\rho N} \left< \sum_{i} |
| 522 |
< |
\sum_{j} \delta \left(r - r_{ij}\right) \delta\left(\cos \omega_{ij} - |
| 521 |
> |
g(r, \cos \omega) = & \frac{1}{\rho N} \left< \sum_{i} \sum_{j} |
| 522 |
> |
\delta \left(r - r_{ij}\right) \delta\left(\cos \omega_{ij} - |
| 523 |
|
\cos \omega\right) \right> \\ \nonumber \\ |
| 524 |
|
g(r, \cos \theta) = & \frac{1}{\rho N} \left< \sum_{i} |
| 525 |
|
\sum_{j} \delta \left(r - r_{ij}\right) \delta\left(\cos \theta_{i} - |
| 542 |
|
near $\cos\omega\approx 1$, leaving most other features undisturbed. This |
| 543 |
|
change is visible in the simulations as an increased population of |
| 544 |
|
aligned nitrile bonds in the first solvation shell. |
| 545 |
+ |
|
| 546 |
|
\begin{figure} |
| 547 |
|
\includegraphics[width=\linewidth]{Figure4} |
| 548 |
|
\caption{Contours of the angle-dependent pair distribution functions |
| 550 |
|
field (lower panel) simulations. Dark areas signify regions of |
| 551 |
|
enhanced density, while light areas signify depletion relative to |
| 552 |
|
the bulk density.} |
| 553 |
< |
\label{fig:gofromega} |
| 554 |
< |
\end{figure} |
| 553 |
> |
\label{fig:gofromega} |
| 554 |
> |
\end{figure} |
| 555 |
> |
|
| 556 |
|
Although it is certainly possible that the coupling between |
| 557 |
|
closely-spaced nitrile pairs is responsible for some of the red-shift, |
| 558 |
< |
that is not the only structural change that is taking place. The |
| 558 |
> |
that is not the only structural change that is taking place. The |
| 559 |
|
second two-dimensional pair distribution function, $g(r,\cos\theta)$, |
| 560 |
|
shows that nematic ordering also transfers population that is directly |
| 561 |
|
in line with the nitrile bond (see figure \ref{fig:gofrtheta}) to the |
| 562 |
|
sides of the molecule, thereby freeing steric blockage can directly |
| 563 |
< |
influence the nitrile vibration. We are suggesting here that the |
| 564 |
< |
nematic ordering provides an anti-caging of the nitrile vibration, and |
| 565 |
< |
given that the oscillator is fairly anharmonic, this provides a |
| 566 |
< |
fraction of the nitrile bonds with a significant red-shift. |
| 563 |
> |
influence the nitrile vibration. This is confirmed by observing the |
| 564 |
> |
one-dimensional $g(z)$ obtained by following the \ce{C -> N} vector |
| 565 |
> |
for each nitrile bond and observing the local density ($\rho(z)/\rho$) |
| 566 |
> |
of other atoms at a distance $z$ along this direction. The full-field |
| 567 |
> |
simulation shows a significant drop in the first peak of $g(z)$, |
| 568 |
> |
indicating that the nematic ordering has moved density away from the |
| 569 |
> |
region that is directly in line with the nitrogen side of the CN bond. |
| 570 |
> |
|
| 571 |
|
\begin{figure} |
| 572 |
|
\includegraphics[width=\linewidth]{Figure6} |
| 573 |
|
\caption{Contours of the angle-dependent pair distribution function, |
| 582 |
|
\label{fig:gofrtheta} |
| 583 |
|
\end{figure} |
| 584 |
|
|
| 585 |
+ |
We are suggesting an anti-caging mechanism here -- the nematic |
| 586 |
+ |
ordering provides additional space directly inline with the nitrile |
| 587 |
+ |
vibration, and since the oscillator is fairly anharmonic, this freedom |
| 588 |
+ |
provides a fraction of the nitrile bonds with a significant red-shift. |
| 589 |
+ |
|
| 590 |
|
The cause of this shift does not appear to be related to the alignment |
| 591 |
|
of those nitrile bonds with the field, but rather to the change in |
| 592 |
< |
local environment that is brought about by the isotropic-nematic |
| 593 |
< |
transition. We have compared configurations for many of the cluster |
| 594 |
< |
calculations that exhibited the frequencies between (2190 and 2215 |
| 595 |
< |
$\mathrm{cm}^{-1}$) , and have observed some similar features. The |
| 596 |
< |
lowest frequencies appear to come from configurations which have |
| 597 |
< |
nearly-empty pockets directly opposite the nitrogen atom from the |
| 598 |
< |
nitrile carbon. Because we have so few clusters, this is certainly not |
| 599 |
< |
quantitative confirmation of this effect. |
| 592 |
> |
local steric environment that is brought about by the |
| 593 |
> |
isotropic-nematic transition. We have compared configurations for many |
| 594 |
> |
of the cluster that exhibited the lowest frequencies (between 2190 and |
| 595 |
> |
2215 $\mathrm{cm}^{-1}$) and have observed some similar structural |
| 596 |
> |
features. The lowest frequencies appear to come from configurations |
| 597 |
> |
which have nearly-empty pockets directly opposite the nitrogen atom |
| 598 |
> |
from the nitrile carbon. Because we do not have a particularly large |
| 599 |
> |
cluster population to interrogate, this is certainly not quantitative |
| 600 |
> |
confirmation of this effect. |
| 601 |
|
|
| 602 |
+ |
The prediction of a small red-shift of the nitrile peak in 5CB in |
| 603 |
+ |
response to a field-induced nematic ordering is the primary result of |
| 604 |
+ |
this work, and although the proposed anti-caging mechanism is somewhat |
| 605 |
+ |
speculative, this work provides some impetus for further theory and |
| 606 |
+ |
experiments. |
| 607 |
|
|
| 580 |
– |
While this makes the application of nitrile Stark effects in |
| 581 |
– |
simulations without water harder, these data show |
| 582 |
– |
that it is not a deal breaker. The classically calculated nitrile |
| 583 |
– |
spectrum shows changes in the spectra that will be easily seen through |
| 584 |
– |
experimental routes. It indicates a shifted peak lower in energy |
| 585 |
– |
should arise. This peak is a few wavenumbers from the leading edge of |
| 586 |
– |
the larger peak and almost 75 wavenumbers from the center. This |
| 587 |
– |
seperation between the two peaks means experimental results will show |
| 588 |
– |
an easily resolved peak. |
| 589 |
– |
|
| 590 |
– |
The Gaussian derived spectra do indicate an applied field |
| 591 |
– |
and subsiquent phase change does cause a narrowing of freuency |
| 592 |
– |
distrobution. With narrowing, it would indicate an increased |
| 593 |
– |
homogeneous distrobution of the local field near the nitrile. |
| 594 |
– |
|
| 595 |
– |
|
| 596 |
– |
|
| 597 |
– |
\section{Conclusions} |
| 598 |
– |
Field dependent changes |
| 599 |
– |
|
| 608 |
|
\section{Acknowledgements} |
| 609 |
< |
The authors thank Steven Corcelli for helpful comments and |
| 610 |
< |
suggestions. Support for this project was provided by the National |
| 609 |
> |
The authors thank Steven Corcelli and Zac Schultz for helpful comments |
| 610 |
> |
and suggestions. Support for this project was provided by the National |
| 611 |
|
Science Foundation under grant CHE-0848243. Computational time was |
| 612 |
|
provided by the Center for Research Computing (CRC) at the University |
| 613 |
|
of Notre Dame. |
