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\title{Nitrile vibrations as reporters of field-induced phase |
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transitions in 4-cyano-4'-pentylbiphenyl (5CB)} |
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\author{James M. Marr} |
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\author{J. Daniel Gezelter} |
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\email{gezelter@nd.edu} |
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\affiliation[University of Notre Dame]{251 Nieuwland Science Hall\\ |
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Department of Chemistry and Biochemistry\\ |
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University of Notre Dame\\ |
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Notre Dame, Indiana 46556} |
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|
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\date{\today} |
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|
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\begin{document} |
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|
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\maketitle |
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|
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\begin{doublespace} |
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|
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\begin{abstract} |
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4-cyano-4'-pentylbiphenyl (5CB) is a liquid-crystal-forming compound |
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with a terminal nitrile group aligned with the long axis of the |
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molecule. Simulations of condensed-phase 5CB were carried out both |
64 |
with and without applied electric fields to provide an understanding |
65 |
of the the Stark shift of the terminal nitrile group. A |
66 |
field-induced isotropic-nematic phase transition was observed in the |
67 |
simulations, and the effects of this transition on the distribution |
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of nitrile frequencies were computed. Classical bond displacement |
69 |
correlation functions exhibit a $\sim 40 \mathrm{~cm}^{-1}$ red |
70 |
shift of a portion of the main nitrile peak, and this shift was |
71 |
observed only when the fields were large enough to induce |
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orientational ordering of the bulk phase. Our simulations appear to |
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indicate that phase-induced changes to the local surroundings are a |
74 |
larger contribution to the change in the nitrile spectrum than |
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direct field contributions. |
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\end{abstract} |
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|
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\newpage |
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|
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\section{Introduction} |
81 |
|
82 |
Nitrile groups can serve as very precise electric field reporters via |
83 |
their distinctive Raman and IR signatures.\cite{Boxer:2009xw} The |
84 |
triple bond between the nitrogen and the carbon atom is very sensitive |
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} |
90 |
|
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} |
99 |
|
100 |
Recently 4-cyano-4'-pentylbiphenyl (5CB), a liquid crystalline |
101 |
molecule with a terminal nitrile group, has seen renewed interest as |
102 |
one way to impart order on the surfactant interfaces of |
103 |
nanodroplets,\cite{Moreno-Razo:2012rz} or to drive surface-ordering |
104 |
that can be used to promote particular kinds of |
105 |
self-assembly.\cite{PhysRevLett.111.227801} The nitrile group in 5CB |
106 |
is a particularly interesting case for studying electric field |
107 |
effects, as 5CB exhibits an isotropic to nematic phase transition that |
108 |
can be triggered by the application of an external field near room |
109 |
temperature.\cite{Gray:1973ca,Hatta:1991ee} This presents the |
110 |
possiblity that the field-induced changes in the local environment |
111 |
could have dramatic effects on the vibrations of this particular CN |
112 |
bond. Although the infrared spectroscopy of 5CB has been |
113 |
well-investigated, particularly as a measure of the kinetics of the |
114 |
phase transition,\cite{Leyte:1997zl} the 5CB nitrile group has not yet |
115 |
seen the detailed theoretical treatment that biologically-relevant |
116 |
small molecules have |
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received.\cite{Lindquist:2008bh,Lindquist:2008qf,Oh:2008fk,Choi:2008cr,Morales:2009fp,Waegele:2010ve} |
118 |
|
119 |
The fundamental characteristic of liquid crystal mesophases is that |
120 |
they maintain some degree of orientational order while translational |
121 |
order is limited or absent. This orientational order produces a |
122 |
complex direction-dependent response to external perturbations like |
123 |
electric fields and mechanical distortions. The anisotropy of the |
124 |
macroscopic phases originates in the anisotropy of the constituent |
125 |
molecules, which typically have highly non-spherical structures with a |
126 |
significant degree of internal rigidity. In nematic phases, rod-like |
127 |
molecules are orientationally ordered with isotropic distributions of |
128 |
molecular centers of mass. For example, 5CB has a solid to nematic |
129 |
phase transition at 18C and a nematic to isotropic transition at |
130 |
35C.\cite{Gray:1973ca} |
131 |
|
132 |
In smectic phases, the molecules arrange themselves into layers with |
133 |
their long (symmetry) axis normal ($S_{A}$) or tilted ($S_{C}$) with |
134 |
respect to the layer planes. The behavior of the $S_{A}$ phase can be |
135 |
partially explained with models mainly based on geometric factors and |
136 |
van der Waals interactions. The Gay-Berne potential, in particular, |
137 |
has been widely used in the liquid crystal community to describe this |
138 |
anisotropic phase |
139 |
behavior.~\cite{Gay:1981yu,Berne:1972pb,Kushick:1976xy,Luckhurst:1990fy,Cleaver:1996rt} |
140 |
However, these simple models are insufficient to describe liquid |
141 |
crystal phases which exhibit more complex polymorphic nature. |
142 |
Molecules which form $S_{A}$ phases can exhibit a wide variety of |
143 |
subphases like monolayers ($S_{A1}$), uniform bilayers ($S_{A2}$), |
144 |
partial bilayers ($S_{\tilde A}$) as well as interdigitated bilayers |
145 |
($S_{A_{d}}$), and often have a terminal cyano or nitro group. In |
146 |
particular, lyotropic liquid crystals (those exhibiting liquid crystal |
147 |
phase transitions as a function of water concentration), often have |
148 |
polar head groups or zwitterionic charge separated groups that result |
149 |
in strong dipolar interactions,\cite{Collings:1997rz} and terminal |
150 |
cyano groups (like the one in 5CB) can induce permanent longitudinal |
151 |
dipoles.\cite{Levelut:1981eu} Modeling of the phase behavior of these |
152 |
molecules either requires additional dipolar |
153 |
interactions,\cite{Bose:2012eu} or a unified-atom approach utilizing |
154 |
point charges on the sites that contribute to the dipole |
155 |
moment.\cite{Zhang:2011hh} |
156 |
|
157 |
Macroscopic electric fields applied using electrodes on opposing sides |
158 |
of a sample of 5CB have demonstrated the phase change of the molecule |
159 |
as a function of electric field.\cite{Lim:2006xq} These previous |
160 |
studies have shown the nitrile group serves as an excellent indicator |
161 |
of the molecular orientation within the applied field. Lee {\it et |
162 |
al.}~showed a 180 degree change in field direction could be probed |
163 |
with the nitrile peak intensity as it changed along with molecular |
164 |
alignment in the field.\cite{Lee:2006qd,Leyte:1997zl} |
165 |
|
166 |
While these macroscopic fields work well at indicating the bulk |
167 |
response, the atomic scale response has not been studied. With the |
168 |
advent of nano-electrodes and coupling them with atomic force |
169 |
microscopy, control of electric fields applied across nanometer |
170 |
distances is now possible.\cite{citation1} While macroscopic fields |
171 |
are insufficient to cause a Stark effect without dielectric breakdown |
172 |
of the material, small fields 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. |
180 |
|
181 |
In the sections that follow, we outline a series of coarse-grained |
182 |
classical molecular dynamics simulations of 5CB that were done in the |
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 |
187 |
scanning electrochemical microscopy experiments. |
188 |
|
189 |
\section{Computational Details} |
190 |
The force field used for 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 |
195 |
distances and angles. Although the phenyl rings were held rigid, |
196 |
bonds, bends, torsions and inversion centers that involved atoms in |
197 |
these substructures (but with connectivity to the rest of the |
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molecule) were still included in the potential and force calculations. |
199 |
|
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Periodic simulations cells containing 270 molecules in random |
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orientations were constructed and were locked at experimental |
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densities. Electrostatic interactions were computed using damped |
203 |
shifted force (DSF) electrostatics.\cite{Fennell:2006zl} The molecules |
204 |
were equilibrated for 1~ns at a temperature of 300K. Simulations with |
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. |
209 |
|
210 |
Static electric fields with magnitudes similar to what would be |
211 |
available in an experimental setup were applied to the different |
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simulations. With an assumed electrode seperation of 5 nm and an |
213 |
electrostatic potential that is limited by the voltage required to |
214 |
split water (1.23V), the maximum realistic field that could be applied |
215 |
is $\sim 0.024$ V/\AA. Three field environments were investigated: |
216 |
(1) no field applied, (2) partial field = 0.01 V/\AA\ , and (3) full |
217 |
field = 0.024 V/\AA\ . |
218 |
|
219 |
After the systems had come to equilibrium under the applied fields, |
220 |
additional simulations were carried out with a flexible (Morse) |
221 |
nitrile bond, |
222 |
\begin{displaymath} |
223 |
V(r_\ce{CN}) = D_e \left(1 - e^{-\beta (r_\ce{CN}-r_e)}\right)^2 |
224 |
\label{eq:morse} |
225 |
\end{displaymath} |
226 |
where $r_e= 1.157437$ \AA , $D_e = 212.95 \mathrm{~kcal~} / |
227 |
\mathrm{mol}^{-1}$ and $\beta = 2.67566 $\AA~$^{-1}$. These |
228 |
parameters correspond to a vibrational frequency of $2358 |
229 |
\mathrm{~cm}^{-1}$, somewhat higher than the experimental |
230 |
frequency. The flexible nitrile moiety required simulation time steps |
231 |
of 1~fs, so the additional flexibility was introducuced only after the |
232 |
rigid systems had come to equilibrium under the applied fields. |
233 |
Whenever time correlation functions were computed from the flexible |
234 |
simulations, statistically-independent configurations were sampled |
235 |
from the last ns of the induced-field runs. These configurations were |
236 |
then equilibrated with the flexible nitrile moiety for 100 ps, and |
237 |
time correlation functions were computed using data sampled from an |
238 |
additional 200 ps of run time carried out in the microcanonical |
239 |
ensemble. |
240 |
|
241 |
\section{Field-induced Nematic Ordering} |
242 |
|
243 |
In order to characterize the orientational ordering of the system, the |
244 |
primary quantity of interest is the nematic (orientational) order |
245 |
parameter. This was determined using the tensor |
246 |
\begin{equation} |
247 |
Q_{\alpha \beta} = \frac{1}{2N} \sum_{i=1}^{N} \left(3 \hat{u}_{i |
248 |
\alpha} \hat{u}_{i \beta} - \delta_{\alpha \beta} \right) |
249 |
\end{equation} |
250 |
where $\alpha, \beta = x, y, z$, and $\hat{u}_i$ is the molecular |
251 |
end-to-end unit vector for molecule $i$. The nematic order parameter |
252 |
$S$ is the largest eigenvalue of $Q_{\alpha \beta}$, and the |
253 |
corresponding eigenvector defines the director axis for the phase. |
254 |
$S$ takes on values close to 1 in highly ordered (smectic A) phases, |
255 |
but falls to much smaller values ($\sim 0-0.2$) for isotropic fluids. |
256 |
Note that the nitrogen and the terminal chain atom were used to define |
257 |
the vectors for each molecule, so the typical order parameters are |
258 |
lower than if one defined a vector using only the rigid core of the |
259 |
molecule. In nematic phases, typical values for $S$ are close to 0.5. |
260 |
|
261 |
The field-induced phase transition can be clearly seen over the course |
262 |
of a 60 ns equilibration runs in figure \ref{fig:orderParameter}. All |
263 |
three of the systems started in a random (isotropic) packing, with |
264 |
order parameters near 0.2. Over the course 10 ns, the full field |
265 |
causes an alignment of the molecules (due primarily to the interaction |
266 |
of the nitrile group dipole with the electric field). Once this |
267 |
system began exhibiting nematic ordering, the orientational order |
268 |
parameter became stable for the remaining 150 ns of simulation time. |
269 |
It is possible that the partial-field simulation is meta-stable and |
270 |
given enough time, it would eventually find a nematic-ordered phase, |
271 |
but the partial-field simulation was stable as an isotropic phase for |
272 |
the full duration of a 60 ns simulation. Ellipsoidal renderings of the |
273 |
final configurations of the runs shows that the full-field (0.024 |
274 |
V/\AA\ ) experienced a isotropic-nematic phase transition and has |
275 |
ordered with a director axis that is parallel to the direction of the |
276 |
applied field. |
277 |
|
278 |
\begin{figure}[H] |
279 |
\includegraphics[width=\linewidth]{Figure1} |
280 |
\caption{Evolution of the orientational order parameters for the |
281 |
no-field, partial field, and full field simulations over the |
282 |
course of 60 ns. Each simulation was started from a |
283 |
statistically-independent isotropic configuration. On the right |
284 |
are ellipsoids representing the final configurations at three |
285 |
different field strengths: zero field (bottom), partial field |
286 |
(middle), and full field (top)} |
287 |
\label{fig:orderParameter} |
288 |
\end{figure} |
289 |
|
290 |
|
291 |
\section{Sampling the CN bond frequency} |
292 |
|
293 |
The vibrational frequency of the nitrile bond in 5CB depends on |
294 |
features of the local solvent environment of the individual molecules |
295 |
as well as the bond's orientation relative to the applied field. The |
296 |
primary quantity of interest for interpreting the condensed phase |
297 |
spectrum of this vibration is the distribution of frequencies |
298 |
exhibited by the 5CB nitrile bond under the different electric fields. |
299 |
There have been a number of elegant techniques for obtaining |
300 |
vibrational lineshapes from classical simulations, including a |
301 |
perturbation theory approach,\cite{Morales:2009fp} the use of an |
302 |
optimized QM/MM approach coupled with the fluctuating frequency |
303 |
approximation,\cite{Lindquist:2008qf} and empirical frequency |
304 |
correlation maps.\cite{Oh:2008fk} Three distinct (and somewhat |
305 |
primitive) methods for mapping classical simulations onto vibrational |
306 |
spectra were brought to bear on the simulations here: |
307 |
\begin{enumerate} |
308 |
\item Isolated 5CB molecules and their immediate surroundings were |
309 |
extracted from the simulations. These nitrile bonds were stretched |
310 |
and single-point {\em ab initio} calculations were used to obtain |
311 |
Morse-oscillator fits for the local vibrational motion along that |
312 |
bond. |
313 |
\item The empirical frequency correlation maps developed by Cho {\it |
314 |
et al.}~\cite{Oh:2008fk} for nitrile moieties in water were |
315 |
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} |
320 |
\item Classical bond-length autocorrelation functions were Fourier |
321 |
transformed to directly obtain the vibrational spectrum from |
322 |
molecular dynamics simulations. |
323 |
\end{enumerate} |
324 |
|
325 |
\subsection{CN frequencies from isolated clusters} |
326 |
The size of the periodic condensed phase system prevented direct |
327 |
computation of the complete library of nitrile bond frequencies using |
328 |
{\it ab initio} methods. In order to sample the nitrile frequencies |
329 |
present in the condensed-phase, individual molecules were selected |
330 |
randomly to serve as the center of a local (gas phase) cluster. To |
331 |
include steric, electrostatic, and other effects from molecules |
332 |
located near the targeted nitrile group, portions of other molecules |
333 |
nearest to the nitrile group were included in the quantum mechanical |
334 |
calculations. The surrounding solvent molecules were divided into |
335 |
``body'' (the two phenyl rings and the nitrile bond) and ``tail'' (the |
336 |
alkyl chain). Any molecule which had a body atom within 6~\AA\ of the |
337 |
midpoint of the target nitrile bond had its own molecular body (the |
338 |
4-cyano-biphenyl moiety) included in the configuration. Likewise, the |
339 |
entire alkyl tail was included if any tail atom was within 4~\AA\ of |
340 |
the target nitrile bond. If tail atoms (but no body atoms) were |
341 |
included within these distances, only the tail was included as a |
342 |
capped propane molecule. |
343 |
|
344 |
\begin{figure}[H] |
345 |
\includegraphics[width=\linewidth]{Figure2} |
346 |
\caption{Cluster calculations were performed on randomly sampled 5CB |
347 |
molecules (shown in red) from each of the simulations. Surrounding |
348 |
molecular bodies were included if any body atoms were within 6 |
349 |
\AA\ of the target nitrile bond, and tails were included if they |
350 |
were within 4 \AA. Included portions of these molecules are shown |
351 |
in green. The CN bond on the target molecule was stretched and |
352 |
compressed, and the resulting single point energies were fit to |
353 |
Morse oscillators to obtain a distribution of frequencies.} |
354 |
\label{fig:cluster} |
355 |
\end{figure} |
356 |
|
357 |
Inferred hydrogen atom locations were added to the cluster geometries, |
358 |
and the nitrile bond was stretched from 0.87 to 1.52~\AA\ at |
359 |
increments of 0.05~\AA. This generated 13 configurations per gas phase |
360 |
cluster. Single-point energies were computed using the B3LYP |
361 |
functional~\cite{Becke:1993kq,Lee:1988qf} and the 6-311++G(d,p) basis |
362 |
set. For the cluster configurations that had been generated from |
363 |
molecular dynamics running under applied fields, the density |
364 |
functional calculations had a field of $5 \times 10^{-4}$ atomic units |
365 |
($E_h / (e a_0)$) applied in the $+z$ direction in order to match the |
366 |
molecular dynamics simulations. |
367 |
|
368 |
The energies for the stretched / compressed nitrile bond in each of |
369 |
the clusters were used to fit Morse potentials, and the frequencies |
370 |
were obtained from the $0 \rightarrow 1$ transition for the energy |
371 |
levels for this potential.\cite{Morse:1929xy} To obtain a spectrum, |
372 |
each of the frequencies was convoluted with a Lorentzian lineshape |
373 |
with a width of 1.5 $\mathrm{cm}^{-1}$. Available computing resources |
374 |
limited the sampling to 67 clusters for the zero-field spectrum, and |
375 |
59 for the full field. Comparisons of the quantum mechanical spectrum |
376 |
to the classical are shown in figure \ref{fig:spectrum}. |
377 |
|
378 |
\subsection{CN frequencies from potential-frequency maps} |
379 |
|
380 |
One approach which has been used to successfully analyze the spectrum |
381 |
of nitrile and thiocyanate probes in aqueous environments was |
382 |
developed by Choi {\it et al.}~\cite{Choi:2008cr,Oh:2008fk} This |
383 |
method involves finding a multi-parameter fit that maps between the |
384 |
local electrostatic potential at selected sites surrounding the |
385 |
nitrile bond and the vibrational frequency of that bond obtained from |
386 |
more expensive {\it ab initio} methods. This approach is similar in |
387 |
character to the field-frequency maps developed by the Skinner group |
388 |
for OH stretches in liquid water.\cite{Corcelli:2004ai,Auer:2007dp} |
389 |
|
390 |
To use the potential-frequency maps, the local electrostatic |
391 |
potential, $\phi_a$, is computed at 20 sites ($a = 1 \rightarrow 20$) |
392 |
that surround the nitrile bond, |
393 |
\begin{equation} |
394 |
\phi_{a} = \frac{1}{4\pi \epsilon_{0}} \sum_{j} |
395 |
\frac{q_j}{\left|r_{aj}\right|}. |
396 |
\end{equation} |
397 |
Here $q_j$ is the partial site on atom $j$ (residing on a different |
398 |
molecule) and $r_{aj}$ is the distance between site $a$ and atom $j$. |
399 |
The original map was parameterized in liquid water and comprises a set |
400 |
of parameters, $l_a$, that predict the shift in nitrile peak |
401 |
frequency, |
402 |
\begin{equation} |
403 |
\delta\tilde{\nu} =\sum^{20}_{a=1} l_{a}\phi_{a}. |
404 |
\end{equation} |
405 |
|
406 |
The simulations of 5CB were carried out in the presence of |
407 |
externally-applied uniform electric fields. Although uniform fields |
408 |
exert forces on charge sites, they only contribute to the potential if |
409 |
one defines a reference point that can serve as an origin. One simple |
410 |
modification to the potential at each of the probe sites is to use the |
411 |
centroid of the \ce{CN} bond as the origin for that site, |
412 |
\begin{equation} |
413 |
\phi_a^\prime = \phi_a + \frac{1}{4\pi\epsilon_{0}} \vec{E} \cdot |
414 |
\left(\vec{r}_a - \vec{r}_\ce{CN} \right) |
415 |
\end{equation} |
416 |
where $\vec{E}$ is the uniform electric field, $\left( \vec{r}_{a} - |
417 |
\vec{r}_\ce{CN} \right)$ is the displacement between the |
418 |
cooridinates described by Choi {\it et |
419 |
al.}~\cite{Choi:2008cr,Oh:2008fk} and the \ce{CN} bond centroid. |
420 |
$\phi_a^\prime$ then contains an effective potential contributed by |
421 |
the uniform field in addition to the local potential contributions |
422 |
from other molecules. |
423 |
|
424 |
The sites $\{\vec{r}_a\}$ and weights $\left\{l_a \right\}$ |
425 |
developed by Choi {\it et al.}~\cite{Choi:2008cr,Oh:2008fk} are quite |
426 |
symmetric around the \ce{CN} centroid, and even at large uniform field |
427 |
values we observed nearly-complete cancellation of the potenial |
428 |
contributions from the uniform field. In order to utilize the |
429 |
potential-frequency maps for this problem, one would therefore need |
430 |
extensive reparameterization of the maps to include explicit |
431 |
contributions from the external field. This reparameterization is |
432 |
outside the scope of the current work, but would make a useful |
433 |
addition to the potential-frequency map approach. |
434 |
|
435 |
\subsection{CN frequencies from bond length autocorrelation functions} |
436 |
|
437 |
The distribution of nitrile vibrational frequencies can also be found |
438 |
using classical time correlation functions. This was done by |
439 |
replacing the rigid \ce{CN} bond with a flexible Morse oscillator |
440 |
described in Eq. \ref{eq:morse}. Since the systems were perturbed by |
441 |
the addition of a flexible high-frequency bond, they were allowed to |
442 |
re-equilibrate in the canonical (NVT) ensemble for 100 ps with 1 fs |
443 |
timesteps. After equilibration, each configuration was run in the |
444 |
microcanonical (NVE) ensemble for 20 ps. Configurations sampled every |
445 |
fs were then used to compute bond-length autocorrelation functions, |
446 |
\begin{equation} |
447 |
C(t) = \langle \delta r(t) \cdot \delta r(0) ) \rangle |
448 |
\end{equation} |
449 |
% |
450 |
where $\delta r(t) = r(t) - r_0$ is the deviation from the equilibrium |
451 |
bond distance at time $t$. Ten statistically-independent correlation |
452 |
functions were obtained by allowing the systems to run 10 ns with |
453 |
rigid \ce{CN} bonds followed by 120 ps equilibration and data |
454 |
collection using the flexible \ce{CN} bonds, and repeating this |
455 |
process. The total sampling time, from sample preparation to final |
456 |
configurations, exceeded 150 ns for each of the field strengths |
457 |
investigated. |
458 |
|
459 |
The correlation functions were filtered using exponential apodization |
460 |
functions,\cite{FILLER:1964yg} $f(t) = e^{-|t|/c}$, with a time |
461 |
constant, $c =$ 6 ps, and were Fourier transformed to yield a |
462 |
spectrum, |
463 |
\begin{equation} |
464 |
I(\omega) = \int_{-\infty}^{\infty} C(t) f(t) e^{-i \omega t} dt. |
465 |
\end{equation} |
466 |
The sample-averaged classical nitrile spectrum can be seen in Figure |
467 |
\ref{fig:spectra}. Note that the Morse oscillator parameters listed |
468 |
above yield a natural frequency of 2358 $\mathrm{cm}^{-1}$, somewhat |
469 |
higher than the experimental peak near 2226 $\mathrm{cm}^{-1}$. This |
470 |
shift does not effect the ability to qualitatively compare peaks from |
471 |
the classical and quantum mechanical approaches, so the classical |
472 |
spectra are shown as a shift relative to the natural oscillation of |
473 |
the Morse bond. |
474 |
|
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} |
485 |
|
486 |
Note that due to electrostatic interactions, the classical approach |
487 |
implicitly couples \ce{CN} vibrations to the same vibrational mode on |
488 |
other nearby molecules. This coupling is not handled in the {\it ab |
489 |
initio} cluster approach. |
490 |
|
491 |
\section{Discussion} |
492 |
|
493 |
It is clear that united-atom simulations can reproduce the |
494 |
field-induced nematic ordering of the 4-cyano-4'-pentylbiphenyl. |
495 |
Because we are simulating what is in effect a small electrode |
496 |
separation (5nm), a voltage drop as low as 1.2 V was sufficient to |
497 |
induce the phase change. This potential is significantly lower than |
498 |
the 500V that is known to cause dielectric breakdown in 5CB.\cite{XXX} |
499 |
|
500 |
Both the classical correlation function and the isolated cluster |
501 |
approaches to estimating the field-induced changes to the IR spectrum |
502 |
show an increase in the population of nitrile stretches that appear at |
503 |
a shift of $\sim 40 \mathrm{cm}^{-1}$ to the red of the unperturbed |
504 |
vibrational line. The cause of this shift does not appear to be |
505 |
related to the alignment of those nitrile bonds with the field, but |
506 |
rather to the change in local ordering that is brought about by the |
507 |
isotropic-nematic transition. |
508 |
|
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 |
|
531 |
The angle-dependent pair distribution functions, |
532 |
\begin{align} |
533 |
g(r, \cos \omega) = & \frac{1}{\rho N} \left< \sum_{i} |
534 |
\sum_{j} \delta \left(r - r_{ij}\right) \delta\left(\cos \omega_{ij} - |
535 |
\cos \omega\right) \right> \\ \nonumber \\ |
536 |
g(r, \cos \theta) = & \frac{1}{\rho N} \left< \sum_{i} |
537 |
\sum_{j} \delta \left(r - r_{ij}\right) \delta\left(\cos \theta_{i} - |
538 |
\cos \theta \right) \right> |
539 |
\end{align} |
540 |
provide information about the joint spatial and angular correlations |
541 |
in the system. The angles $\omega$ and $\theta$ are defined by vectors |
542 |
along the CN axis of each nitrile bond (see figure |
543 |
\ref{fig:definition}). |
544 |
|
545 |
\begin{figure} |
546 |
\includegraphics[width=\linewidth]{definition} |
547 |
\caption{Definitions of the angles between two nitrile bonds.} |
548 |
\label{fig:definition} |
549 |
\end{figure} |
550 |
|
551 |
In figure \ref{fig:gofromega} the effects of the field-induced phase |
552 |
transition are clear. The nematic ordering transfers population from |
553 |
the perpendicular or unaligned region in the center of the plot to the |
554 |
nitrile-alinged peak near $\cos\omega = 1$. Most other features are |
555 |
undisturbed. This increased population of aligned nitrile bonds in |
556 |
the close solvation shells is also the population that contributes |
557 |
most heavily to the low-frequency peaks in the vibrational spectrum. |
558 |
|
559 |
\begin{figure} |
560 |
\includegraphics[width=\linewidth]{Figure4} |
561 |
\caption{Contours of the angle-dependent pair distribution functions |
562 |
for nitrile bonds on 5CB in the zero-field (upper panel) and full |
563 |
field (lower panel) simulations. Dark areas signify regions of |
564 |
enhanced density, while light areas signify depletion relative to |
565 |
the bulk density.} |
566 |
\label{fig:gofromega} |
567 |
\end{figure} |
568 |
|
569 |
|
570 |
\section{Conclusions} |
571 |
Field dependent changes |
572 |
|
573 |
\section{Acknowledgements} |
574 |
The authors thank Steven Corcelli for helpful comments and |
575 |
suggestions. Support for this project was provided by the National |
576 |
Science Foundation under grant CHE-0848243. Computational time was |
577 |
provided by the Center for Research Computing (CRC) at the University |
578 |
of Notre Dame. |
579 |
|
580 |
\newpage |
581 |
|
582 |
\bibliography{5CB} |
583 |
|
584 |
\end{doublespace} |
585 |
\end{document} |