| 40 |
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|
| 41 |
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\begin{tocentry} |
| 42 |
|
%\includegraphics[width=9cm]{Elip_3} |
| 43 |
< |
\includegraphics[width=9cm]{cluster/cluster.pdf} |
| 43 |
> |
\includegraphics[width=9cm]{cluster.pdf} |
| 44 |
|
\end{tocentry} |
| 45 |
|
|
| 46 |
|
\begin{abstract} |
| 47 |
< |
4-cyano-4'-pentylbiphenyl (5CB) is a liquid-crystal-forming compound |
| 47 |
> |
4-cyano-4'-pentylbiphenyl (5CB) is a liquid crystal forming compound |
| 48 |
|
with a terminal nitrile group aligned with the long axis of the |
| 49 |
|
molecule. Simulations of condensed-phase 5CB were carried out both |
| 50 |
|
with and without applied electric fields to provide an understanding |
| 68 |
|
\section{Introduction} |
| 69 |
|
|
| 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 |
| 71 |
> |
local electric fields, nitrile groups can report on field strengths |
| 72 |
> |
via their distinctive Raman and IR signatures.\cite{Boxer:2009xw} The |
| 73 |
> |
response of nitrile groups to electric fields has now been |
| 74 |
> |
investigated for a number of small molecules,\cite{Andrews:2000qv} as |
| 75 |
> |
well as in biochemical settings, where nitrile groups can act as |
| 76 |
> |
minimally 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 |
| 90 |
|
can be triggered by the application of an external field near room |
| 91 |
|
temperature.\cite{Gray:1973ca,Hatta:1991ee} This presents the |
| 92 |
|
possibility that the field-induced changes in the local environment |
| 93 |
< |
could have dramatic effects on the vibrations of this particular CN |
| 93 |
> |
could have dramatic effects on the vibrations of this particular nitrile |
| 94 |
|
bond. Although the infrared spectroscopy of 5CB has been |
| 95 |
|
well-investigated, particularly as a measure of the kinetics of the |
| 96 |
|
phase transition,\cite{Leyte:1997zl} the 5CB nitrile group has not yet |
| 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 $2 \times 10^8~\mathrm{V/m}$. This field is certainly strong |
| 160 |
< |
enough to cause the isotropic-nematic phase change and as well as a |
| 161 |
< |
visible Stark tuning of the nitrile bond. We expect that this would be |
| 162 |
< |
readily visible experimentally through Raman or IR spectroscopy. |
| 160 |
> |
enough to cause the isotropic-nematic phase change and an observable |
| 161 |
> |
Stark tuning of the nitrile bond. We expect that this would be readily |
| 162 |
> |
visible experimentally through Raman or IR spectroscopy. |
| 163 |
|
|
| 164 |
|
In the sections that follow, we outline a series of coarse-grained |
| 165 |
|
(united atom) classical molecular dynamics simulations of 5CB that |
| 172 |
|
\section{Computational Details} |
| 173 |
|
The force-field used to model 5CB was a united-atom model that was |
| 174 |
|
parameterized by Guo {\it et al.}\cite{Zhang:2011hh} However, for most |
| 175 |
< |
of the simulations, each of the phenyl rings was treated as a rigid |
| 176 |
< |
body to allow for larger time steps and longer simulation times. The |
| 177 |
< |
geometries of the rigid bodies were taken from equilibrium bond |
| 178 |
< |
distances and angles. Although the individual phenyl rings were held |
| 179 |
< |
rigid, bonds, bends, torsions and inversion centers that involved |
| 180 |
< |
atoms in these substructures (but with connectivity to the rest of the |
| 181 |
< |
molecule) were still included in the potential and force calculations. |
| 175 |
> |
of the simulations, both of the phenyl rings and the nitrile bond were |
| 176 |
> |
treated as rigid bodies to allow for larger time steps and longer |
| 177 |
> |
simulation times. The geometries of the rigid bodies were taken from |
| 178 |
> |
equilibrium bond distances and angles. Although the individual phenyl |
| 179 |
> |
rings were held rigid, bonds, bends, torsions and inversion centers |
| 180 |
> |
that involved atoms in these substructures (but with connectivity to |
| 181 |
> |
the rest of the molecule) were still included in the potential and |
| 182 |
> |
force calculations. |
| 183 |
|
|
| 184 |
|
Periodic simulations cells containing 270 molecules in random |
| 185 |
|
orientations were constructed and were locked at experimental |
| 215 |
|
of 1~fs, so the additional flexibility was introduced only after the |
| 216 |
|
rigid systems had come to equilibrium under the applied fields. |
| 217 |
|
Whenever time correlation functions were computed from the flexible |
| 218 |
< |
simulations, statistically-independent configurations were sampled |
| 219 |
< |
from the last ns of the induced-field runs. These configurations were |
| 220 |
< |
then equilibrated with the flexible nitrile moiety for 100 ps, and |
| 221 |
< |
time correlation functions were computed using data sampled from an |
| 222 |
< |
additional 200 ps of run time carried out in the microcanonical |
| 223 |
< |
ensemble. |
| 218 |
> |
simulations, statistically-independent configurations (separated in |
| 219 |
> |
time by 10 ns) were sampled from the last 110 ns of the induced-field |
| 220 |
> |
runs. These configurations were then equilibrated with the flexible |
| 221 |
> |
nitrile moiety for 100 ps, and time correlation functions were |
| 222 |
> |
computed using data sampled from an additional 20 ps of run time |
| 223 |
> |
carried out in the microcanonical ensemble. |
| 224 |
|
|
| 225 |
|
\section{Field-induced Nematic Ordering} |
| 226 |
|
|
| 254 |
|
It is possible that the partial-field simulation is meta-stable and |
| 255 |
|
given enough time, it would eventually find a nematic-ordered phase, |
| 256 |
|
but the partial-field simulation was stable as an isotropic phase for |
| 257 |
< |
the full duration of a 60 ns simulation. Ellipsoidal renderings of the |
| 258 |
< |
final configurations of the runs shows that the full-field (0.024 |
| 257 |
> |
the full duration of the 60 ns simulation. Ellipsoidal renderings of |
| 258 |
> |
the final configurations of the runs show that the full-field (0.024 |
| 259 |
|
V/\AA\ ) experienced a isotropic-nematic phase transition and has |
| 260 |
|
ordered with a director axis that is parallel to the direction of the |
| 261 |
|
applied field. |
| 262 |
|
|
| 263 |
|
\begin{figure}[H] |
| 264 |
< |
\includegraphics[width=\linewidth]{orderParameter/orderParameter.pdf} |
| 264 |
> |
\includegraphics[width=\linewidth]{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]{cluster/cluster.pdf} |
| 326 |
> |
\includegraphics[width=\linewidth]{cluster.pdf} |
| 327 |
|
\caption{Cluster calculations were performed on randomly sampled 5CB |
| 328 |
|
molecules (shown in red) from the full-field and no-field |
| 329 |
|
simulations. Surrounding molecular bodies were included if any |
| 353 |
|
levels for this potential.\cite{Morse:1929xy} To obtain a spectrum, |
| 354 |
|
each of the frequencies was convoluted with a Lorentzian line shape |
| 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 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 |
< |
$2.68~\mathrm{cm}^{-1}$. |
| 356 |
> |
limited the sampling to 100 clusters for both the no-field and |
| 357 |
> |
full-field spectra. Comparisons of the quantum mechanical spectrum to |
| 358 |
> |
the classical are shown in figure \ref{fig:spectra}. The mean |
| 359 |
> |
frequencies obtained from the distributions give a field-induced red |
| 360 |
> |
shift of $2.68~\mathrm{cm}^{-1}$. |
| 361 |
|
|
| 362 |
|
\subsection{CN frequencies from potential-frequency maps} |
| 363 |
|
|
| 378 |
|
\phi_{a} = \frac{1}{4\pi \epsilon_{0}} \sum_{j} |
| 379 |
|
\frac{q_j}{\left|r_{aj}\right|}. |
| 380 |
|
\end{equation} |
| 381 |
< |
Here $q_j$ is the partial site on atom $j$ (residing on a different |
| 381 |
> |
Here $q_j$ is the partial charge on atom $j$ (residing on a different |
| 382 |
|
molecule) and $r_{aj}$ is the distance between site $a$ and atom $j$. |
| 383 |
|
The original map was parameterized in liquid water and comprises a set |
| 384 |
|
of parameters, $l_a$, that predict the shift in nitrile peak |
| 417 |
|
addition to the potential-frequency map approach. |
| 418 |
|
|
| 419 |
|
We note that in 5CB there does not appear to be a particularly strong |
| 420 |
< |
correlation between the electric field observed at the nitrile |
| 421 |
< |
centroid and the calculated vibrational frequency. In |
| 420 |
> |
correlation between the electric field strengths observed at the |
| 421 |
> |
nitrile centroid and the calculated vibrational frequencies. In |
| 422 |
|
Fig. \ref{fig:fieldMap} we show the calculated frequencies plotted |
| 423 |
< |
against the field magnitude and the parallel and perpendicular |
| 424 |
< |
components of the field. |
| 423 |
> |
against the field magnitude as well as the parallel and perpendicular |
| 424 |
> |
components of that field. |
| 425 |
|
|
| 426 |
|
\begin{figure} |
| 427 |
< |
\includegraphics[width=\linewidth]{fieldMap/fieldMap.pdf} |
| 427 |
> |
\includegraphics[width=\linewidth]{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. 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.} |
| 432 |
> |
Middle panel: plotted against the magnitude of the field |
| 433 |
> |
components perpendicular to the CN bond. Lower panel: plotted |
| 434 |
> |
against the total field magnitude.} |
| 435 |
|
\label{fig:fieldMap} |
| 436 |
|
\end{figure} |
| 437 |
|
|
| 455 |
|
bond distance at time $t$. Because the other atomic sites have very |
| 456 |
|
small partial charges, this correlation function is an approximation |
| 457 |
|
to the dipole autocorrelation function for the molecule, which would |
| 458 |
< |
be particularly relevant to computing the IR spectrum. Ten |
| 458 |
> |
be particularly relevant to computing the IR spectrum. Eleven |
| 459 |
|
statistically-independent correlation functions were obtained by |
| 460 |
|
allowing the systems to run 10 ns with rigid \ce{CN} bonds followed by |
| 461 |
|
120 ps equilibration and data collection using the flexible \ce{CN} |
| 462 |
< |
bonds. This process was repeated 10 times, and the total sampling |
| 463 |
< |
time, from sample preparation to final configurations, exceeded 150 ns |
| 462 |
> |
bonds. This process was repeated 11 times, and the total sampling |
| 463 |
> |
time, from sample preparation to final configurations, exceeded 160 ns |
| 464 |
|
for each of the field strengths investigated. |
| 465 |
|
|
| 466 |
|
The correlation functions were filtered using exponential apodization |
| 477 |
|
shift does not effect the ability to qualitatively compare peaks from |
| 478 |
|
the classical and quantum mechanical approaches, so the classical |
| 479 |
|
spectra are shown as a shift relative to the natural oscillation of |
| 480 |
< |
the Morse bond. |
| 480 |
> |
the Morse bond. The quantum cluster values are referenced to the |
| 481 |
> |
actual experimental vibrational frequency. |
| 482 |
|
|
| 483 |
|
\begin{figure} |
| 484 |
< |
\includegraphics[width=\linewidth]{spectra/spectra.pdf} |
| 484 |
> |
\includegraphics[width=\linewidth]{spectra.pdf} |
| 485 |
|
\caption{Spectrum of nitrile frequency shifts for the no-field |
| 486 |
|
(black) and the full-field (red) simulations. Upper panel: |
| 487 |
|
frequency shifts obtained from {\it ab initio} cluster |
| 506 |
|
nitrile frequency. Although the spectra are quite noisy, the main |
| 507 |
|
effect seen in both distributions is a moderate shift to the red |
| 508 |
|
($3.05~\mathrm{cm}^{-1}$ classical and $2.68~\mathrm{cm}^{-1}$ |
| 509 |
< |
quantum) when the full electrostatic field had induced the nematic |
| 510 |
< |
phase transition. |
| 509 |
> |
quantum) after the electrostatic field had induced the nematic phase |
| 510 |
> |
transition. |
| 511 |
|
|
| 512 |
|
\section{Discussion} |
| 513 |
|
Our simulations show that the united-atom model can reproduce the |
| 538 |
|
which provide information about the joint spatial and angular |
| 539 |
|
correlations present in the system. The angles $\omega$ and $\theta$ |
| 540 |
|
are defined by vectors along the CN axis of each nitrile bond (see |
| 541 |
< |
figure \ref{fig:definition}). |
| 541 |
> |
figure \ref{fig:definition}). |
| 542 |
|
\begin{figure} |
| 543 |
< |
\includegraphics[width=4in]{definition/definition.pdf} |
| 543 |
> |
\includegraphics[width=4in]{definition.pdf} |
| 544 |
|
\caption{Definitions of the angles between two nitrile bonds.} |
| 545 |
|
\label{fig:definition} |
| 546 |
|
\end{figure} |
| 554 |
|
aligned nitrile bonds in the first solvation shell. |
| 555 |
|
|
| 556 |
|
\begin{figure} |
| 557 |
< |
\includegraphics[width=\linewidth]{gofrOmega/gofrOmega.pdf} |
| 557 |
> |
\includegraphics[width=\linewidth]{gofrOmega.pdf} |
| 558 |
|
\caption{Contours of the angle-dependent pair distribution functions |
| 559 |
|
for nitrile bonds on 5CB in the no field (upper panel) and full |
| 560 |
|
field (lower panel) simulations. Dark areas signify regions of |
| 569 |
|
second two-dimensional pair distribution function, $g(r,\cos\theta)$, |
| 570 |
|
shows that nematic ordering also transfers population that is directly |
| 571 |
|
in line with the nitrile bond (see figure \ref{fig:gofrtheta}) to the |
| 572 |
< |
sides of the molecule, thereby freeing steric blockage can directly |
| 573 |
< |
influence the nitrile vibration. This is confirmed by observing the |
| 574 |
< |
one-dimensional $g(z)$ obtained by following the \ce{C -> N} vector |
| 575 |
< |
for each nitrile bond and observing the local density ($\rho(z)/\rho$) |
| 576 |
< |
of other atoms at a distance $z$ along this direction. The full-field |
| 577 |
< |
simulation shows a significant drop in the first peak of $g(z)$, |
| 578 |
< |
indicating that the nematic ordering has moved density away from the |
| 579 |
< |
region that is directly in line with the nitrogen side of the CN bond. |
| 572 |
> |
sides of the molecule, thereby freeing steric blockage which can |
| 573 |
> |
directly influence the nitrile vibration. This is confirmed by |
| 574 |
> |
observing the one-dimensional $g(z)$ obtained by following the \ce{C |
| 575 |
> |
-> N} vector for each nitrile bond and observing the local density |
| 576 |
> |
($\rho(z)/\rho$) of other atoms at a distance $z$ along this |
| 577 |
> |
direction. The full-field simulation shows a significant drop in the |
| 578 |
> |
first peak of $g(z)$, indicating that the nematic ordering has moved |
| 579 |
> |
density away from the region that is directly in line with the |
| 580 |
> |
nitrogen side of the CN bond. |
| 581 |
|
|
| 582 |
|
\begin{figure} |
| 583 |
< |
\includegraphics[width=\linewidth]{gofrTheta/gofrTheta.pdf} |
| 583 |
> |
\includegraphics[width=\linewidth]{gofrTheta.pdf} |
| 584 |
|
\caption{Contours of the angle-dependent pair distribution function, |
| 585 |
|
$g(r,\cos \theta)$, for finding any other atom at a distance and |
| 586 |
|
angular deviation from the center of a nitrile bond. The top edge |
