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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 |
63 |
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 |
68 |
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 |
72 |
orientational ordering of the bulk phase. Our simulations appear to |
73 |
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. |
76 |
\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 into a field value that is |
88 |
impinging upon the nitrile bond. This has been used extensively in |
89 |
biological systems like proteins and |
90 |
enzymes.\cite{Tucker:2004qq,Webb:2008kn} |
91 |
|
92 |
The response of nitrile groups to electric fields has now been |
93 |
investigated for a number of small molecules,\cite{Andrews:2000qv} as |
94 |
well as in biochemical settings, where nitrile groups can act as |
95 |
minimally invasive probes of structure and |
96 |
dynamics.\cite{Lindquist:2009fk,Fafarman:2010dq} The vibrational Stark |
97 |
effect has also been used to study the effects of electric fields on |
98 |
nitrile-containing self-assembled monolayers at metallic |
99 |
interfaces.\cite{Oklejas:2002uq,Schkolnik:2012ty} |
100 |
|
101 |
Recently 4-cyano-4'-pentylbiphenyl (5CB), a liquid crystalline |
102 |
molecule with a terminal nitrile group, has seen renewed interest as |
103 |
one way to impart order on the surfactant interfaces of |
104 |
nanodroplets,\cite{Moreno-Razo:2012rz} or to drive surface-ordering |
105 |
that can be used to promote particular kinds of |
106 |
self-assembly.\cite{PhysRevLett.111.227801} The nitrile group in 5CB |
107 |
is a particularly interesting case for studying electric field |
108 |
effects, as 5CB exhibits an isotropic to nematic phase transition that |
109 |
can be triggered by the application of an external field near room |
110 |
temperature.\cite{Gray:1973ca,Hatta:1991ee} This presents the |
111 |
possiblity that the field-induced changes in the local environment |
112 |
could have dramatic effects on the vibrations of this particular CN |
113 |
bond. Although the infrared spectroscopy of 5CB has been |
114 |
well-investigated, particularly as a measure of the kinetics of the |
115 |
phase transition,\cite{Leyte:1997zl} the 5CB nitrile group has not yet |
116 |
seen the detailed theoretical treatment that biologically-relevant |
117 |
small molecules have |
118 |
received.\cite{Lindquist:2008bh,Lindquist:2008qf,Oh:2008fk,Choi:2008cr,Waegele:2010ve} |
119 |
|
120 |
The fundamental characteristic of liquid crystal mesophases is that |
121 |
they maintain some degree of orientational order while translational |
122 |
order is limited or absent. This orientational order produces a |
123 |
complex direction-dependent response to external perturbations like |
124 |
electric fields and mechanical distortions. The anisotropy of the |
125 |
macroscopic phases originates in the anisotropy of the constituent |
126 |
molecules, which typically have highly non-spherical structures with a |
127 |
significant degree of internal rigidity. In nematic phases, rod-like |
128 |
molecules are orientationally ordered with isotropic distributions of |
129 |
molecular centers of mass. For example, 5CB has a solid to nematic |
130 |
phase transition at 18C and a nematic to isotropic transition at |
131 |
35C.\cite{Gray:1973ca} |
132 |
|
133 |
In smectic phases, the molecules arrange themselves into layers with |
134 |
their long (symmetry) axis normal ($S_{A}$) or tilted ($S_{C}$) with |
135 |
respect to the layer planes. The behavior of the $S_{A}$ phase can be |
136 |
partially explained with models mainly based on geometric factors and |
137 |
van der Waals interactions. The Gay-Berne potential, in particular, |
138 |
has been widely used in the liquid crystal community to describe this |
139 |
anisotropic phase |
140 |
behavior.~\cite{Gay:1981yu,Berne72,Kushick:1976xy,Luckhurst90,Cleaver:1996rt} |
141 |
However, these simple models are insufficient to describe liquid |
142 |
crystal phases which exhibit more complex polymorphic nature. |
143 |
Molecules which form $S_{A}$ phases can exhibit a wide variety of |
144 |
subphases like monolayers ($S_{A1}$), uniform bilayers ($S_{A2}$), |
145 |
partial bilayers ($S_{\tilde A}$) as well as interdigitated bilayers |
146 |
($S_{A_{d}}$), and often have a terminal cyano or nitro group. In |
147 |
particular, lyotropic liquid crystals (those exhibiting liquid crystal |
148 |
phase transition as a function of water concentration), often have |
149 |
polar head groups or zwitterionic charge separated groups that result |
150 |
in strong dipolar interactions,\cite{Collings:1997rz} and terminal cyano |
151 |
groups (like the one in 5CB) can induce permanent longitudinal |
152 |
dipoles.\cite{Levelut:1981eu} |
153 |
|
154 |
Macroscopic electric fields applied using electrodes on opposing sides |
155 |
of a sample of 5CB have demonstrated the phase change of the molecule |
156 |
as a function of electric field.\cite{Lim:2006xq} These previous |
157 |
studies have shown the nitrile group serves as an excellent indicator |
158 |
of the molecular orientation within the applied field. Lee {\it et |
159 |
al.}~showed a 180 degree change in field direction could be probed |
160 |
with the nitrile peak intensity as it changed along with molecular |
161 |
alignment in the field.\cite{Lee:2006qd,Leyte:1997zl} |
162 |
|
163 |
While these macroscopic fields work well at indicating the bulk |
164 |
response, the atomic scale response has not been studied. With the |
165 |
advent of nano-electrodes and coupling them with atomic force |
166 |
microscopy, control of electric fields applied across nanometer |
167 |
distances is now possible.\cite{citation1} While macroscopic fields |
168 |
are insufficient to cause a Stark effect without dielectric breakdown |
169 |
of the material, small fields across nanometer-sized gaps may be of |
170 |
sufficient strength. For a gap of 5 nm between a lower electrode |
171 |
having a nanoelectrode placed near it via an atomic force microscope, |
172 |
a potential of 1 V applied across the electrodes is equivalent to a |
173 |
field of 2x10\textsuperscript{8} $\frac{V}{M}$. This field is |
174 |
certainly strong enough to cause the isotropic-nematic phase change |
175 |
and as well as Stark tuning of the nitrile bond. This should be |
176 |
readily visible experimentally through Raman or IR spectroscopy. |
177 |
|
178 |
In the sections that follow, we outline a series of coarse-grained |
179 |
classical molecular dynamics simulations of 5CB that were done in the |
180 |
presence of static electric fields. These simulations were then |
181 |
coupled with both {\it ab intio} calculations of CN-deformations and |
182 |
classical bond-length correlation functions to predict spectral |
183 |
shifts. These predictions made should be easily varifiable with |
184 |
scanning electrochemical microscopy experiments. |
185 |
|
186 |
\section{Computational Details} |
187 |
The force field used for 5CB was taken from Guo {\it et |
188 |
al.}\cite{Zhang:2011hh} However, for most of the simulations, each |
189 |
of the phenyl rings was treated as a rigid body to allow for larger |
190 |
time steps and very long simulation times. The geometries of the |
191 |
rigid bodies were taken from equilibrium bond distances and angles. |
192 |
Although the phenyl rings were held rigid, bonds, bends, torsions and |
193 |
inversion centers that involved atoms in these substructures (but with |
194 |
connectivity to the rest of the molecule) were still included in the |
195 |
potential and force calculations. |
196 |
|
197 |
Periodic simulations cells containing 270 molecules in random |
198 |
orientations were constructed and were locked at experimental |
199 |
densities. Electrostatic interactions were computed using damped |
200 |
shifted force (DSF) electrostatics.\cite{Fennell:2006zl} The molecules |
201 |
were equilibrated for 1~ns at a temperature of 300K. Simulations with |
202 |
applied fields were carried out in the microcanonical (NVE) ensemble |
203 |
with an energy corresponding to the average energy from the canonical |
204 |
(NVT) equilibration runs. Typical applied-field runs were more than |
205 |
60ns in length. |
206 |
|
207 |
Static electric fields with magnitudes similar to what would be |
208 |
available in an experimental setup were applied to the different |
209 |
simulations. With an assumed electrode seperation of 5 nm and an |
210 |
electrostatic potential that is limited by the voltage required to |
211 |
split water (1.23V), the maximum realistic field that could be applied |
212 |
is $\sim 0.024$ V/\AA. Three field environments were investigated: |
213 |
(1) no field applied, (2) partial field = 0.01 V/\AA\ , and (3) full |
214 |
field = 0.024 V/\AA\ . |
215 |
|
216 |
After the systems had come to equilibrium under the applied fields, |
217 |
additional simulations were carried out with a flexible (Morse) |
218 |
nitrile bond, |
219 |
\begin{displaymath} |
220 |
V(r_\ce{CN}) = D_e \left(1 - e^{-\beta (r_\ce{CN}-r_e)}\right)^2 |
221 |
\end{displaymath} |
222 |
where $r_e= 1.157437$ \AA , $D_e = 212.95 \mathrm{~kca~l} / |
223 |
\mathrm{mol}^{-1}$ and $\beta = 2.67566 $\AA~$^{-1}$. These |
224 |
parameters correspond to a vibrational frequency of $2375 |
225 |
\mathrm{~cm}^{-1}$, a bit higher than the experimental frequency. The |
226 |
flexible nitrile moiety required simulation time steps of 1~fs, so the |
227 |
additional flexibility was introducuced only after the rigid systems |
228 |
had come to equilibrium under the applied fields. Whenever time |
229 |
correlation functions were computed from the flexible simulations, |
230 |
statistically-independent configurations were sampled from the last ns |
231 |
of the induced-field runs. These configurations were then |
232 |
equilibrated with the flexible nitrile moiety for 100 ps, and time |
233 |
correlation functions were computed using data sampled from an |
234 |
additional 200 ps of run time carried out in the microcanonical |
235 |
ensemble. |
236 |
|
237 |
\section{Field-induced Nematic Ordering} |
238 |
|
239 |
In order to characterize the orientational ordering of the system, the |
240 |
primary quantity of interest is the nematic (orientational) order |
241 |
parameter. This was determined using the tensor |
242 |
\begin{equation} |
243 |
Q_{\alpha \beta} = \frac{1}{2N} \sum_{i=1}^{N} \left(3 \hat{e}_{i |
244 |
\alpha} \hat{e}_{i \beta} - \delta_{\alpha \beta} \right) |
245 |
\end{equation} |
246 |
where $\alpha, \beta = x, y, z$, and $\hat{e}_i$ is the molecular |
247 |
end-to-end unit vector for molecule $i$. The nematic order parameter |
248 |
$S$ is the largest eigenvalue of $Q_{\alpha \beta}$, and the |
249 |
corresponding eigenvector defines the director axis for the phase. |
250 |
$S$ takes on values close to 1 in highly ordered (smectic A) phases, |
251 |
but falls to zero for isotropic fluids. Note that the nitrogen and |
252 |
the terminal chain atom were used to define the vectors for each |
253 |
molecule, so the typical order parameters are lower than if one |
254 |
defined a vector using only the rigid core of the molecule. In |
255 |
nematic phases, typical values for $S$ are close to 0.5. |
256 |
|
257 |
The field-induced phase transition can be clearly seen over the course |
258 |
of a 60 ns equilibration runs in figure \ref{fig:orderParameter}. All |
259 |
three of the systems started in a random (isotropic) packing, with |
260 |
order parameters near 0.2. Over the course 10 ns, the full field |
261 |
causes an alignment of the molecules (due primarily to the interaction |
262 |
of the nitrile group dipole with the electric field). Once this |
263 |
system started exhibiting nematic ordering, the orientational order |
264 |
parameter became stable for the remaining 50 ns of simulation time. |
265 |
It is possible that the partial-field simulation is meta-stable and |
266 |
given enough time, it would eventually find a nematic-ordered phase, |
267 |
but the partial-field simulation was stable as an isotropic phase for |
268 |
the full duration of a 60 ns simulation. Ellipsoidal renderings of the |
269 |
final configurations of the runs shows that the full-field (0.024 |
270 |
V/\AA\ ) experienced a isotropic-nematic phase transition and has |
271 |
ordered with a director axis that is parallel to the direction of the |
272 |
applied field. |
273 |
|
274 |
\begin{figure}[H] |
275 |
\includegraphics[width=\linewidth]{Figure1} |
276 |
\caption{Evolution of the orientational order parameters for the |
277 |
no-field, partial field, and full field simulations over the |
278 |
course of 60 ns. Each simulation was started from a |
279 |
statistically-independent isotropic configuration. On the right |
280 |
are ellipsoids representing the final configurations at three |
281 |
different field strengths: zero field (bottom), partial field |
282 |
(middle), and full field (top)} |
283 |
\label{fig:orderParameter} |
284 |
\end{figure} |
285 |
|
286 |
|
287 |
\section{Sampling the CN bond frequency} |
288 |
|
289 |
The vibrational frequency of the nitrile bond in 5CB is assumed to |
290 |
depend on features of the local solvent environment of the individual |
291 |
molecules as well as the bond's orientation relative to the applied |
292 |
field. Therefore, the primary quantity of interest is the |
293 |
distribution of vibrational frequencies exhibited by the 5CB nitrile |
294 |
bond under the different electric fields. Three distinct methods for |
295 |
mapping classical simulations onto vibrational spectra were brought to |
296 |
bear on these simulations: |
297 |
\begin{enumerate} |
298 |
\item Isolated 5CB molecules and their immediate surroundings were |
299 |
extracted from the simulations, their nitrile bonds were stretched |
300 |
and single-point {\em ab initio} calculations were used to obtain |
301 |
Morse-oscillator fits for the local vibrational motion along that |
302 |
bond. |
303 |
\item The potential - frequency maps developed by Cho {\it et |
304 |
al.}~\cite{Oh:2008fk} for nitrile moieties in water were |
305 |
investigated. This method involves mapping the electrostatic |
306 |
potential around the bond to the vibrational frequency, and is |
307 |
similar in approach to field-frequency maps that were pioneered by |
308 |
Skinner {\it et al.}\cite{XXXX} |
309 |
\item Classical bond-length autocorrelation functions were Fourier |
310 |
transformed to directly obtain the vibrational spectrum from |
311 |
molecular dynamics simulations. |
312 |
\end{enumerate} |
313 |
|
314 |
\subsection{CN frequencies from isolated clusters} |
315 |
The size of the periodic condensed phase system prevented direct |
316 |
computation of the complete library of nitrile bond frequencies using |
317 |
{\it ab initio} methods. In order to sample the nitrile frequencies |
318 |
present in the condensed-phase, individual molecules were selected |
319 |
randomly to serve as the center of a local (gas phase) cluster. To |
320 |
include steric, electrostatic, and other effects from molecules |
321 |
located near the targeted nitrile group, portions of other molecules |
322 |
nearest to the nitrile group were included in the quantum mechanical |
323 |
calculations. The surrounding solvent molecules were divided into |
324 |
``body'' (the two phenyl rings and the nitrile bond) and ``tail'' (the |
325 |
alkyl chain). Any molecule which had a body atom within 6~\AA of the |
326 |
midpoint of the target nitrile bond had its own molecular body (the |
327 |
4-cyano-4'-pentylbiphenyl moiety) included in the configuration. For |
328 |
the alkyl tail, the entire tail was included if any tail atom was |
329 |
within 4~\AA of the target nitrile bond. If tail atoms (but no body |
330 |
atoms) were included within these distances, only the tail was |
331 |
included as a capped propane molecule. |
332 |
|
333 |
\begin{figure}[H] |
334 |
\includegraphics[width=\linewidth]{Figure2} |
335 |
\caption{Cluster calculations were performed on randomly sampled 5CB |
336 |
molecules from each of the simualtions. Surrounding molecular |
337 |
bodies were included if any body atoms were within 6 \AA\ of the |
338 |
target nitrile bond, and tails were included if they were within 4 |
339 |
\AA. The CN bond on the target molecule was stretched and |
340 |
compressed (left), and the resulting single point energies were |
341 |
fit to Morse oscillators to obtain frequency distributions.} |
342 |
\label{fig:cluster} |
343 |
\end{figure} |
344 |
|
345 |
Inferred hydrogen atom locations were generated, and cluster |
346 |
geometries were created that stretched the nitrile bond along from |
347 |
0.87 to 1.52~\AA at increments of 0.05~\AA. This generated 13 single |
348 |
point energies to be calculated per gas phase cluster. Energies were |
349 |
computed with the B3LYP functional and 6-311++G(d,p) basis set. For |
350 |
the cluster configurations that had been generated with applied |
351 |
fields, a field strength of 5 atomic units in the $z$ direction was |
352 |
applied to match the molecular dynamics runs. |
353 |
|
354 |
The relative energies for the stretched and compressed nitrile bond |
355 |
were used to fit a Morse oscillator, and the frequencies were obtained |
356 |
from the $0 \rightarrow 1$ transition for the exact energies. To |
357 |
obtain a spectrum, each of the frequencies was convoluted with a |
358 |
Lorentzian lineshape with a width of 1.5 $\mathrm{cm}^{-1}$. Our |
359 |
available computing resources limited us to 67 clusters for the |
360 |
zero-field spectrum, and 59 for the full field. |
361 |
|
362 |
\subsection{CN frequencies from potential-frequency maps} |
363 |
Before Gaussian silumations were carried out, it was attempt to apply |
364 |
the method developed by Cho {\it et al.}~\cite{Oh:2008fk} This method involves the fitting |
365 |
of multiple parameters to Gaussian calculated freuencies to find a |
366 |
correlation between the potential around the bond and the |
367 |
frequency. This is very similar to work done by Skinner {\it et al.}~with |
368 |
water models like SPC/E. The general method is to find the shift in |
369 |
the peak position through, |
370 |
\begin{equation} |
371 |
\delta\tilde{\nu} =\sum^{n}_{a=1} l_{a}\phi^{water}_{a} |
372 |
\end{equation} |
373 |
where $l_{a}$ are the fitting parameters and $\phi^{water}_{a}$ is the |
374 |
potential from the surrounding water cluster. This $\phi^{water}_{a}$ |
375 |
takes the form, |
376 |
\begin{equation} |
377 |
\phi_{a} = \frac{1}{4\pi \epsilon_{0}} \sum_{m} \sum_{j} |
378 |
\frac{C^{H_{2}O}_{j \left(m \right) }}{r_{aj \left(m\right)}} |
379 |
\end{equation} |
380 |
where $C^{H_{2}O}_{j \left(m \right) }$ indicates the partial charge |
381 |
on the $j$th site of the $m$th water molecule and $r_{aj \left(m\right)}$ |
382 |
is the distance between the site $a$ of the nitrile molecule and the $j$th |
383 |
site of the $m$th water molecule. However, since these simulations |
384 |
are done under the presence of external fields and in the |
385 |
absence of water, the equations need a correction factor for the shift |
386 |
caused by the external field. The equation is also reworked to use |
387 |
electric field site data instead of partial charges from surrounding |
388 |
atoms. So by modifing the original |
389 |
$\phi^{water}_{a}$ to $\phi^{5CB}_{a}$ we get, |
390 |
\begin{equation} |
391 |
\phi^{5CB}_{a} = \frac{1}{4\pi \epsilon_{0}} \left( \vec{E}\bullet |
392 |
\left(\vec{r}_{a}-\vec{r}_{CN}\right) \right) + \phi^{5CB}_{0} |
393 |
\end{equation} |
394 |
where $\vec{E}$ is the electric field at each atom, $\left( \vec{r}_{a} - |
395 |
\vec{r}_{CN} \right)$ is the vector between the nitrile bond and the |
396 |
cooridinates described by Cho around the bond and $\phi^{5CB}_{0}$ is |
397 |
the correction factor for the system of parameters. After these |
398 |
changes, the correction factor was found for multiple values of an |
399 |
external field being applied. However, the factor was no linear and |
400 |
was overly large due to the fitting parameters being so small. |
401 |
|
402 |
|
403 |
\subsection{CN frequencies from bond length autocorrelation functions} |
404 |
|
405 |
Classical nitrile bond frequencies were found by replacing the rigid |
406 |
cyanide bond with a flexible Morse oscillator bond |
407 |
($r_0= 1.157437$ \AA , $D_0 = 212.95$ and |
408 |
$\beta = 2.67566$) . Once replaced, the |
409 |
systems were allowed to re-equilibrate in NVT for 100 ps. After |
410 |
re-equilibration, the system was run in NVE for 20 ps with a snapshot |
411 |
spacing of 1 fs. These snapshot were then used in bond correlation |
412 |
calculation to find the decay structure of the bond in time using the |
413 |
average bond displacement in time, |
414 |
\begin{equation} |
415 |
C(t) = \langle \left(r(t) - r_0 \right) \cdot \left(r(0) - r_0 \right) \rangle |
416 |
\end{equation} |
417 |
% |
418 |
where $r_0$ is the equilibrium bond distance and $r(t)$ is the |
419 |
instantaneous bond displacement at time $t$. Once calculated, |
420 |
smoothing was applied by adding an exponential decay on top of the |
421 |
decay with a $\tau$ of 6000. Further smoothing |
422 |
was applied by padding 20,000 zeros on each side of the symmetric |
423 |
data. This was done five times by allowing the systems to run 1 ns |
424 |
with a rigid bond followed by an equilibrium run with the bond |
425 |
switched back to a Morse oscillator and a short production run of 20 ps. |
426 |
|
427 |
|
428 |
This change in phase was followed by two courses of further |
429 |
analysis. First was the replacement of the static nitrile bond with a |
430 |
morse oscillator bond. This was then simulated for a period of time |
431 |
and a classical spetrum was calculated. Second, ab intio calcualtions |
432 |
were performed to investigate if the phase change caused any change |
433 |
spectrum through quantum effects. |
434 |
|
435 |
The classical nitrile spectrum can be seen in Figure 2. Most noticably |
436 |
is the position of the two peaks. Obviously the experimental peak |
437 |
position is near 2226 cm\textsuperscript{-1}. However, in this case |
438 |
the peak position is shifted to the blue at a position of 2375 |
439 |
cm\textsuperscript{-1}. This shift is due solely to the choice of |
440 |
oscillator strength in the Morse oscillator parameters. While this |
441 |
shift makes the two spectra differ, it does not affect the ability to |
442 |
qualitatively compare peak changes to possible experimental changes. |
443 |
With this important fact out of the way, differences between the two |
444 |
states are subtle but are very much present. The first and |
445 |
most notable is the apperance for a strong band near 2300 |
446 |
cm\textsuperscript{-1}. |
447 |
\begin{figure} |
448 |
\includegraphics[width=3.25in]{2Spectra} |
449 |
\caption{The classically calculated nitrile bond spetrum for no |
450 |
external field application (black) and full external field |
451 |
application (red)} |
452 |
\label{fig:twoSpectra} |
453 |
\end{figure} |
454 |
|
455 |
|
456 |
Due to this, Gaussian calculations were performed in lieu of this |
457 |
method. A set of snapshots for the zero and full field simualtions, |
458 |
they were first investigated for any dependence on the local, with |
459 |
external field included, electric field. This was to see if a linear |
460 |
or non-linear relationship between the two could be utilized for |
461 |
generating spectra. This was done in part because of previous studies |
462 |
showing the frequency dependence of nitrile bonds to the electric |
463 |
fields generated locally between solvating water. It was seen that |
464 |
little to no dependence could be directly shown. This data is not |
465 |
shown. |
466 |
|
467 |
Since no explicit dependence was observed between the calculated |
468 |
frequency and the electric field, it was not a viable route for the |
469 |
calculation of a nitrile spectrum. Instead, the frequencies were taken |
470 |
and convolved together with a lorentzian line shape applied around the |
471 |
frequency value. These spectra are seen below in Figure |
472 |
4. While the spectrum without a field is lower in intensity and is |
473 |
almost bimodel in distrobution, the external field spectrum is much |
474 |
more unimodel. This tighter clustering has the affect of increasing the |
475 |
intensity around 2226 cm\textsuperscript{-1} where the peak is |
476 |
centered. The external field also has fewer frequencies of higher |
477 |
energy in the spectrum. Unlike the the zero field, where some frequencies |
478 |
reach as high as 2280 cm\textsuperscript{-1}. |
479 |
\begin{figure} |
480 |
\includegraphics[width=3.25in]{Convolved} |
481 |
\caption{Lorentzian convolved Gaussian frequencies of the zero field |
482 |
system (black) and the full field system (red)} |
483 |
\label{fig:Con} |
484 |
\end{figure} |
485 |
\section{Discussion} |
486 |
Interestingly, the field that is needed to switch the phase of 5CB |
487 |
macroscopically is larger than 1 V. However, in this case, only a |
488 |
voltage of 1.2 V was need to induce a phase change. This is impart due |
489 |
to the short distance of 5 nm the field is being applied across. At such a small |
490 |
distance, the field is much larger than the macroscopic and thus |
491 |
easily induces a field dependent phase change. However, this field |
492 |
will not cause a breakdown of the 5CB since electrochemistry studies |
493 |
have shown that it can be used in the presence of fields as high as |
494 |
500 V macroscopically. This large of a field near the surface of the |
495 |
elctrode would cause breakdown of 5CB if it could happen. |
496 |
|
497 |
The absence of any electric field dependency of the freuquency with |
498 |
the Gaussian simulations is interesting. A large base of research has been |
499 |
built upon the known tuning of the nitrile bond as the local field |
500 |
changes. This difference may be due to the absence of water or a |
501 |
molecule that induces a large internal field. Liquid water is known to have a very high internal field which |
502 |
is much larger than the internal fields of neat 5CB. Even though the |
503 |
application of Gaussian simulations followed by mapping it to |
504 |
some classical parameter is easy and straight forward, this system |
505 |
illistrates how that 'go to' method can break down. |
506 |
|
507 |
While this makes the application of nitrile Stark effects in |
508 |
simulations without water harder, these data show |
509 |
that it is not a deal breaker. The classically calculated nitrile |
510 |
spectrum shows changes in the spectra that will be easily seen through |
511 |
experimental routes. It indicates a shifted peak lower in energy |
512 |
should arise. This peak is a few wavenumbers from the leading edge of |
513 |
the larger peak and almost 75 wavenumbers from the center. This |
514 |
seperation between the two peaks means experimental results will show |
515 |
an easily resolved peak. |
516 |
|
517 |
The Gaussian derived spectra do indicate an applied field |
518 |
and subsiquent phase change does cause a narrowing of freuency |
519 |
distrobution. With narrowing, it would indicate an increased |
520 |
homogeneous distrobution of the local field near the nitrile. |
521 |
\section{Conclusions} |
522 |
Field dependent changes |
523 |
\newpage |
524 |
|
525 |
\bibliography{5CB} |
526 |
|
527 |
\end{doublespace} |
528 |
\end{document} |