| 85 |
|
to local field changes and has been observed to have a direct impact |
| 86 |
|
on the peak position within the spectrum. The Stark shift in the |
| 87 |
|
spectrum can be quantified and mapped onto a field that is impinging |
| 88 |
< |
upon the nitrile bond. This has been used extensively in biological |
| 89 |
< |
systems like proteins and enzymes.\cite{Tucker:2004qq,Webb:2008kn} |
| 88 |
> |
upon the nitrile bond. The response of nitrile groups to electric |
| 89 |
> |
fields has now been investigated for a number of small |
| 90 |
> |
molecules,\cite{Andrews:2000qv} as well as in biochemical settings, |
| 91 |
> |
where nitrile groups can act as minimally invasive probes of structure |
| 92 |
> |
and |
| 93 |
> |
dynamics.\cite{Tucker:2004qq,Webb:2008kn,Lindquist:2009fk,Fafarman:2010dq} |
| 94 |
> |
The vibrational Stark effect has also been used to study the effects |
| 95 |
> |
of electric fields on nitrile-containing self-assembled monolayers at |
| 96 |
> |
metallic interfaces.\cite{Oklejas:2002uq,Schkolnik:2012ty} |
| 97 |
|
|
| 91 |
– |
The response of nitrile groups to electric fields has now been |
| 92 |
– |
investigated for a number of small molecules,\cite{Andrews:2000qv} as |
| 93 |
– |
well as in biochemical settings, where nitrile groups can act as |
| 94 |
– |
minimally invasive probes of structure and |
| 95 |
– |
dynamics.\cite{Lindquist:2009fk,Fafarman:2010dq} The vibrational Stark |
| 96 |
– |
effect has also been used to study the effects of electric fields on |
| 97 |
– |
nitrile-containing self-assembled monolayers at metallic |
| 98 |
– |
interfaces.\cite{Oklejas:2002uq,Schkolnik:2012ty} |
| 98 |
|
|
| 99 |
|
Recently 4-cyano-4'-pentylbiphenyl (5CB), a liquid crystalline |
| 100 |
|
molecule with a terminal nitrile group, has seen renewed interest as |
| 163 |
|
alignment in the field.\cite{Lee:2006qd,Leyte:1997zl} |
| 164 |
|
|
| 165 |
|
While these macroscopic fields work well at indicating the bulk |
| 166 |
< |
response, the atomic scale response has not been studied. With the |
| 167 |
< |
advent of nano-electrodes and coupling them with atomic force |
| 168 |
< |
microscopy, control of electric fields applied across nanometer |
| 169 |
< |
distances is now possible.\cite{citation1} While macroscopic fields |
| 170 |
< |
are insufficient to cause a Stark effect without dielectric breakdown |
| 171 |
< |
of the material, small fields across nanometer-sized gaps may be of |
| 166 |
> |
response, the response at a molecular scale has not been studied. With |
| 167 |
> |
the advent of nano-electrodes and the ability to couple these |
| 168 |
> |
electrodes to atomic force microscopy, control of electric fields |
| 169 |
> |
applied across nanometer distances is now possible.\cite{citation1} In |
| 170 |
> |
special cases where the macroscopic fields are insufficient to cause |
| 171 |
> |
an observable Stark effect without dielectric breakdown of the |
| 172 |
> |
material, small potentials across nanometer-sized gaps may be of |
| 173 |
|
sufficient strength. For a gap of 5 nm between a lower electrode |
| 174 |
|
having a nanoelectrode placed near it via an atomic force microscope, |
| 175 |
|
a potential of 1 V applied across the electrodes is equivalent to a |
| 176 |
|
field of 2x10\textsuperscript{8} $\frac{V}{M}$. This field is |
| 177 |
|
certainly strong enough to cause the isotropic-nematic phase change |
| 178 |
< |
and as well as Stark tuning of the nitrile bond. This should be |
| 179 |
< |
readily visible experimentally through Raman or IR spectroscopy. |
| 178 |
> |
and as well as a visible Stark tuning of the nitrile bond. We expect |
| 179 |
> |
that this would be readily visible experimentally through Raman or IR |
| 180 |
> |
spectroscopy. |
| 181 |
|
|
| 182 |
|
In the sections that follow, we outline a series of coarse-grained |
| 183 |
|
classical molecular dynamics simulations of 5CB that were done in the |
| 193 |
|
of the simulations, each of the phenyl rings was treated as a rigid |
| 194 |
|
body to allow for larger time steps and very long simulation times. |
| 195 |
|
The geometries of the rigid bodies were taken from equilibrium bond |
| 196 |
< |
distances and angles. Although the phenyl rings were held rigid, |
| 197 |
< |
bonds, bends, torsions and inversion centers that involved atoms in |
| 198 |
< |
these substructures (but with connectivity to the rest of the |
| 196 |
> |
distances and angles. Although the individual phenyl rings were held |
| 197 |
> |
rigid, bonds, bends, torsions and inversion centers that involved |
| 198 |
> |
atoms in these substructures (but with connectivity to the rest of the |
| 199 |
|
molecule) were still included in the potential and force calculations. |
| 200 |
|
|
| 201 |
|
Periodic simulations cells containing 270 molecules in random |
| 215 |
|
split water (1.23V), the maximum realistic field that could be applied |
| 216 |
|
is $\sim 0.024$ V/\AA. Three field environments were investigated: |
| 217 |
|
(1) no field applied, (2) partial field = 0.01 V/\AA\ , and (3) full |
| 218 |
< |
field = 0.024 V/\AA\ . |
| 218 |
> |
field = 0.024 V/\AA\ . |
| 219 |
|
|
| 220 |
|
After the systems had come to equilibrium under the applied fields, |
| 221 |
|
additional simulations were carried out with a flexible (Morse) |
| 253 |
|
$S$ is the largest eigenvalue of $Q_{\alpha \beta}$, and the |
| 254 |
|
corresponding eigenvector defines the director axis for the phase. |
| 255 |
|
$S$ takes on values close to 1 in highly ordered (smectic A) phases, |
| 256 |
< |
but falls to much smaller values ($\sim 0-0.2$) for isotropic fluids. |
| 257 |
< |
Note that the nitrogen and the terminal chain atom were used to define |
| 258 |
< |
the vectors for each molecule, so the typical order parameters are |
| 259 |
< |
lower than if one defined a vector using only the rigid core of the |
| 260 |
< |
molecule. In nematic phases, typical values for $S$ are close to 0.5. |
| 256 |
> |
but falls to much smaller values ($0 \rightarrow 0.3$) for isotropic |
| 257 |
> |
fluids. Note that the nitrogen and the terminal chain atom were used |
| 258 |
> |
to define the vectors for each molecule, so the typical order |
| 259 |
> |
parameters are lower than if one defined a vector using only the rigid |
| 260 |
> |
core of the molecule. In nematic phases, typical values for $S$ are |
| 261 |
> |
close to 0.5. |
| 262 |
|
|
| 263 |
|
The field-induced phase transition can be clearly seen over the course |
| 264 |
|
of a 60 ns equilibration runs in figure \ref{fig:orderParameter}. All |
| 303 |
|
perturbation theory approach,\cite{Morales:2009fp} the use of an |
| 304 |
|
optimized QM/MM approach coupled with the fluctuating frequency |
| 305 |
|
approximation,\cite{Lindquist:2008qf} and empirical frequency |
| 306 |
< |
correlation maps.\cite{Oh:2008fk} Three distinct (and somewhat |
| 306 |
> |
correlation maps.\cite{Oh:2008fk} Three distinct (and comparatively |
| 307 |
|
primitive) methods for mapping classical simulations onto vibrational |
| 308 |
< |
spectra were brought to bear on the simulations here: |
| 308 |
> |
spectra were brought to bear on the simulations in this work: |
| 309 |
|
\begin{enumerate} |
| 310 |
|
\item Isolated 5CB molecules and their immediate surroundings were |
| 311 |
< |
extracted from the simulations. These nitrile bonds were stretched |
| 311 |
> |
extracted from the simulations. These nitrile bonds were stretched |
| 312 |
|
and single-point {\em ab initio} calculations were used to obtain |
| 313 |
|
Morse-oscillator fits for the local vibrational motion along that |
| 314 |
|
bond. |
| 315 |
< |
\item The empirical frequency correlation maps developed by Cho {\it |
| 316 |
< |
et al.}~\cite{Oh:2008fk} for nitrile moieties in water were |
| 317 |
< |
investigated. This method involves mapping the electrostatic |
| 316 |
< |
potential around the bond to the vibrational frequency, and is |
| 317 |
< |
similar in approach to field-frequency maps for OH stretches that |
| 318 |
< |
were pioneered by the Skinner |
| 319 |
< |
group.\cite{Corcelli:2004ai,Auer:2007dp} |
| 315 |
> |
\item A static-field extension of the empirical frequency correlation |
| 316 |
> |
maps developed by Cho {\it et al.}~\cite{Oh:2008fk} for nitrile |
| 317 |
> |
moieties in water was attempted. |
| 318 |
|
\item Classical bond-length autocorrelation functions were Fourier |
| 319 |
|
transformed to directly obtain the vibrational spectrum from |
| 320 |
|
molecular dynamics simulations. |
| 446 |
|
\end{equation} |
| 447 |
|
% |
| 448 |
|
where $\delta r(t) = r(t) - r_0$ is the deviation from the equilibrium |
| 449 |
< |
bond distance at time $t$. Ten statistically-independent correlation |
| 450 |
< |
functions were obtained by allowing the systems to run 10 ns with |
| 451 |
< |
rigid \ce{CN} bonds followed by 120 ps equilibration and data |
| 452 |
< |
collection using the flexible \ce{CN} bonds, and repeating this |
| 453 |
< |
process. The total sampling time, from sample preparation to final |
| 454 |
< |
configurations, exceeded 150 ns for each of the field strengths |
| 455 |
< |
investigated. |
| 449 |
> |
bond distance at time $t$. Because the other atomic sites have very |
| 450 |
> |
small partial charges, this correlation function is an approximation |
| 451 |
> |
to the dipole autocorrelation function for the molecule, which would |
| 452 |
> |
be particularly relevant to computing the IR spectrum. Ten |
| 453 |
> |
statistically-independent correlation functions were obtained by |
| 454 |
> |
allowing the systems to run 10 ns with rigid \ce{CN} bonds followed by |
| 455 |
> |
120 ps equilibration and data collection using the flexible \ce{CN} |
| 456 |
> |
bonds. This process was repeated 10 times, and the total sampling |
| 457 |
> |
time, from sample preparation to final configurations, exceeded 150 ns |
| 458 |
> |
for each of the field strengths investigated. |
| 459 |
|
|
| 460 |
|
The correlation functions were filtered using exponential apodization |
| 461 |
|
functions,\cite{FILLER:1964yg} $f(t) = e^{-|t|/c}$, with a time |
| 462 |
< |
constant, $c =$ 6 ps, and were Fourier transformed to yield a |
| 462 |
> |
constant, $c =$ 3.5 ps, and were Fourier transformed to yield a |
| 463 |
|
spectrum, |
| 464 |
|
\begin{equation} |
| 465 |
|
I(\omega) = \int_{-\infty}^{\infty} C(t) f(t) e^{-i \omega t} dt. |
| 491 |
|
|
| 492 |
|
\section{Discussion} |
| 493 |
|
|
| 494 |
< |
It is clear that united-atom simulations can reproduce the |
| 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 what is in effect a small electrode |
| 497 |
|
separation (5nm), a voltage drop as low as 1.2 V was sufficient to |
| 504 |
|
a shift of $\sim 40 \mathrm{cm}^{-1}$ to the red of the unperturbed |
| 505 |
|
vibrational line. The cause of this shift does not appear to be |
| 506 |
|
related to the alignment of those nitrile bonds with the field, but |
| 507 |
< |
rather to the change in local ordering that is brought about by the |
| 507 |
> |
rather to the change in local environment that is brought about by the |
| 508 |
|
isotropic-nematic transition. |
| 509 |
|
|
| 509 |
– |
|
| 510 |
– |
Ordering corresponds to shift of a portion of the nitrile spectrum to |
| 511 |
– |
the red. At the same time, the system exhibits an increase in aligned |
| 512 |
– |
and anti-a |
| 513 |
– |
|
| 514 |
– |
|
| 515 |
– |
|
| 516 |
– |
While this makes the application of nitrile Stark effects in |
| 517 |
– |
simulations without water harder, these data show |
| 518 |
– |
that it is not a deal breaker. The classically calculated nitrile |
| 519 |
– |
spectrum shows changes in the spectra that will be easily seen through |
| 520 |
– |
experimental routes. It indicates a shifted peak lower in energy |
| 521 |
– |
should arise. This peak is a few wavenumbers from the leading edge of |
| 522 |
– |
the larger peak and almost 75 wavenumbers from the center. This |
| 523 |
– |
seperation between the two peaks means experimental results will show |
| 524 |
– |
an easily resolved peak. |
| 525 |
– |
|
| 526 |
– |
The Gaussian derived spectra do indicate an applied field |
| 527 |
– |
and subsiquent phase change does cause a narrowing of freuency |
| 528 |
– |
distrobution. With narrowing, it would indicate an increased |
| 529 |
– |
homogeneous distrobution of the local field near the nitrile. |
| 530 |
– |
|
| 510 |
|
The angle-dependent pair distribution functions, |
| 511 |
|
\begin{align} |
| 512 |
|
g(r, \cos \omega) = & \frac{1}{\rho N} \left< \sum_{i} |
| 527 |
|
\label{fig:definition} |
| 528 |
|
\end{figure} |
| 529 |
|
|
| 530 |
< |
In figure \ref{fig:gofromega} the effects of the field-induced phase |
| 531 |
< |
transition are clear. The nematic ordering transfers population from |
| 532 |
< |
the perpendicular or unaligned region in the center of the plot to the |
| 533 |
< |
nitrile-alinged peak near $\cos\omega = 1$. Most other features are |
| 534 |
< |
undisturbed. This increased population of aligned nitrile bonds in |
| 535 |
< |
the close solvation shells is also the population that contributes |
| 536 |
< |
most heavily to the low-frequency peaks in the vibrational spectrum. |
| 530 |
> |
In figure \ref{fig:gofromega}, one of the structural effects of the |
| 531 |
> |
field-induced phase transition is clear. The nematic ordering |
| 532 |
> |
transfers population from the perpendicular or unaligned region in the |
| 533 |
> |
center of the plot to the nitrile-alinged peak near $\cos\omega = |
| 534 |
> |
1$. Most other features are undisturbed. The major change visible is |
| 535 |
> |
the increased population of aligned nitrile bonds in the first |
| 536 |
> |
solvation shells. |
| 537 |
|
|
| 538 |
|
\begin{figure} |
| 539 |
|
\includegraphics[width=\linewidth]{Figure4} |
| 545 |
|
\label{fig:gofromega} |
| 546 |
|
\end{figure} |
| 547 |
|
|
| 548 |
+ |
Although it is possible that the coupling between closely-spaced |
| 549 |
+ |
nitrile pairs is responsible for some of the red-shift, that is not |
| 550 |
+ |
the complete picture. The other two dimensional pair distribution |
| 551 |
+ |
function, $g(r,\cos\theta)$, shows that nematic ordering also |
| 552 |
+ |
transfers population that is directly in line with the nitrile bond |
| 553 |
+ |
(see figure \ref{fig:gofrtheta}) to the sides of the molecule, thereby |
| 554 |
+ |
freeing steric blockage that directly blocks the nitrile vibratio |
| 555 |
+ |
\begin{figure} |
| 556 |
|
|
| 557 |
+ |
\includegraphics[width=\linewidth]{Figure5} |
| 558 |
+ |
\caption{Contours of the angle-dependent pair distribution function, |
| 559 |
+ |
$g(r,\cos \theta)$, for finding any atom at a distance and angular |
| 560 |
+ |
deviation from the nitrile bond centroid. The right side of each |
| 561 |
+ |
plot corresponds to local density directly the direction of |
| 562 |
+ |
nitrile bond. Increased density at $\cos\theta = 1$ corresponds |
| 563 |
+ |
to steric hindrance of the nitrile bond.} |
| 564 |
+ |
\label{fig:gofromega} |
| 565 |
+ |
\end{figure} |
| 566 |
+ |
|
| 567 |
+ |
.At the same time, the system exhibits an increase in aligned |
| 568 |
+ |
and anti-a |
| 569 |
+ |
|
| 570 |
+ |
|
| 571 |
+ |
|
| 572 |
+ |
|
| 573 |
+ |
|
| 574 |
+ |
|
| 575 |
+ |
|
| 576 |
+ |
While this makes the application of nitrile Stark effects in |
| 577 |
+ |
simulations without water harder, these data show |
| 578 |
+ |
that it is not a deal breaker. The classically calculated nitrile |
| 579 |
+ |
spectrum shows changes in the spectra that will be easily seen through |
| 580 |
+ |
experimental routes. It indicates a shifted peak lower in energy |
| 581 |
+ |
should arise. This peak is a few wavenumbers from the leading edge of |
| 582 |
+ |
the larger peak and almost 75 wavenumbers from the center. This |
| 583 |
+ |
seperation between the two peaks means experimental results will show |
| 584 |
+ |
an easily resolved peak. |
| 585 |
+ |
|
| 586 |
+ |
The Gaussian derived spectra do indicate an applied field |
| 587 |
+ |
and subsiquent phase change does cause a narrowing of freuency |
| 588 |
+ |
distrobution. With narrowing, it would indicate an increased |
| 589 |
+ |
homogeneous distrobution of the local field near the nitrile. |
| 590 |
+ |
|
| 591 |
+ |
|
| 592 |
+ |
|
| 593 |
|
\section{Conclusions} |
| 594 |
|
Field dependent changes |
| 595 |
|
|
