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\title{Nitrile vibrations as reporters of field-induced phase |
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transitions in 4-cyano-4'-pentylbiphenyl} |
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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 |
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 |
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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} |
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|
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Nitrile groups can serve as very precise electric field reporters via |
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their distinctive Raman and IR signatures.\cite{Boxer:2009xw} The |
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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 |
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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 |
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received.\cite{Lindquist:2008bh,Lindquist:2008qf,Oh:2008fk,Choi:2008cr,Waegele:2010ve} |
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|
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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} |
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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} |
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|
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Macroscopic electric fields applied using electrodes on opposing sides |
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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 |
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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 |
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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 |
|
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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 |
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coupled with both {\it ab intio} calculations of CN-deformations and |
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classical bond-length correlation functions to predict spectral |
183 |
shifts. These predictions made should be easily varifiable with |
184 |
scanning electrochemical microscopy experiments. |
185 |
|
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\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 |
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potential and force calculations. |
196 |
|
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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 |
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 |
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(NVT) equilibration runs. Typical applied-field runs were more than |
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60ns in length. |
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|
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Static electric fields with magnitudes similar to what would be |
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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 |
210 |
electrostatic potential that is limited by the voltage required to |
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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) |
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nitrile bond, |
219 |
\begin{displaymath} |
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V(r_\ce{CN}) = D_e \left(1 - e^{-\beta (r_\ce{CN}-r_e)}\right)^2 |
221 |
\end{displaymath} |
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where $r_e= 1.157437$ \AA , $D_e = 212.95 \mathrm{~kca~l} / |
223 |
\mathrm{mol}^{-1}$ and $\beta = 2.67566 $\AA~$^{-1}$, corresponding to a |
224 |
vibrational frequency of $2375 \mathrm{~cm}^{-1}$, a |
225 |
bit higher than the experimental frequency. The flexible nitrile |
226 |
moiety required simulation time steps of 1~fs, so the additional |
227 |
flexibility was introducuced only after the rigid systems had come to |
228 |
equilibrium under the applied fields. Whenever time correlation |
229 |
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 |
In Figure \ref{fig:orderParameter}, the field-induced phase change can |
258 |
be clearly seen over the course of a 60 ns equilibration run. 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 landed in the nematic-ordered state, it became stable for the |
264 |
remaining 50 ns of simulation time. It is possible that the |
265 |
partial-field simulation is meta-stable and given enough time, it |
266 |
would eventually find a nematic-ordered phase, but the partial-field |
267 |
simulation was stable as an isotropic phase for the full duration of a |
268 |
60 ns simulation. |
269 |
\begin{figure} |
270 |
\includegraphics[trim = 5mm 10mm 3mm 10mm, clip, width=3.25in]{P2} |
271 |
\caption{Ordering of each external field application over the course |
272 |
of 60 ns with a sampling every 100 ps. Each trajectory was started |
273 |
after equilibration with zero field applied.} |
274 |
\label{fig:orderParameter} |
275 |
\end{figure} |
276 |
|
277 |
In figure \ref{fig:Cigars}, the field-induced isotropic-nematic |
278 |
transition is represented using ellipsoids aligned along the long-axis |
279 |
of each molecule. The vector between the nitrogen of the nitrile |
280 |
group and the terminal tail atom is used to orient each |
281 |
ellipsoid. Both the zero field and partial field simulations appear |
282 |
isotropic, while the full field simulations has clearly been |
283 |
orientationally ordered |
284 |
\begin{figure} |
285 |
\includegraphics[width=7in]{Elip_3} |
286 |
\caption{Ellipsoid reprsentation of 5CB at three different |
287 |
field strengths, Zero Field (Left), Partial Field (Middle), and Full |
288 |
Field (Right) Each image was created by taking the final |
289 |
snapshot of each 60 ns run} |
290 |
\label{fig:Cigars} |
291 |
\end{figure} |
292 |
|
293 |
\section{Analysis} |
294 |
|
295 |
For quantum calculation of the nitrile bond frequency, Gaussian 09 was |
296 |
used. A single 5CB molecule was selected for the center of the |
297 |
cluster. For effects from molecules located near the chosen nitrile |
298 |
group, parts of molecules nearest to the nitrile group were |
299 |
included. For the body not including the tail, any atom within 6~\AA |
300 |
of the midpoint of the nitrile group was included. For the tail |
301 |
structure, the whole tail was included if a tail atom was within 4~\AA |
302 |
of the midpoint. If the tail did not include any atoms from the ring |
303 |
structure, it was considered a propane molecule and included as |
304 |
such. Once the clusters were generated, input files were created that |
305 |
stretched the nitrile bond along its axis from 0.87 to 1.52~\AA at |
306 |
increments of 0.05~\AA. This generated 13 single point energies to be |
307 |
calculated. The Gaussian files were run with B3LYP/6-311++G(d,p) with |
308 |
no other keywords for the zero field simulation. Simulations with |
309 |
fields applied included the keyword ''Field=Z+5'' to match the |
310 |
external field applied in molecular dynamic runs. Once completed, the central nitrile bond frequency |
311 |
was calculated with a Morse fit. Using this fit and the solved energy |
312 |
levels for a Morse oscillator, the frequency was found. Each set of |
313 |
frequencies were then convolved together with a lorezian lineshape |
314 |
function over each value. The width value used was 1.5. For the zero |
315 |
field spectrum, 67 frequencies were used and for the full field, 59 |
316 |
frequencies were used. |
317 |
|
318 |
Classical nitrile bond frequencies were found by replacing the rigid |
319 |
cyanide bond with a flexible Morse oscillator bond |
320 |
($r_0= 1.157437$ \AA , $D_0 = 212.95$ and |
321 |
$\beta = 2.67566$) . Once replaced, the |
322 |
systems were allowed to re-equilibrate in NVT for 100 ps. After |
323 |
re-equilibration, the system was run in NVE for 20 ps with a snapshot |
324 |
spacing of 1 fs. These snapshot were then used in bond correlation |
325 |
calculation to find the decay structure of the bond in time using the |
326 |
average bond displacement in time, |
327 |
\begin{equation} |
328 |
C(t) = \langle \left(r(t) - r_0 \right) \cdot \left(r(0) - r_0 \right) \rangle |
329 |
\end{equation} |
330 |
% |
331 |
where $r_0$ is the equilibrium bond distance and $r(t)$ is the |
332 |
instantaneous bond displacement at time $t$. Once calculated, |
333 |
smoothing was applied by adding an exponential decay on top of the |
334 |
decay with a $\tau$ of 6000. Further smoothing |
335 |
was applied by padding 20,000 zeros on each side of the symmetric |
336 |
data. This was done five times by allowing the systems to run 1 ns |
337 |
with a rigid bond followed by an equilibrium run with the bond |
338 |
switched back to a Morse oscillator and a short production run of 20 ps. |
339 |
|
340 |
\section{Results} |
341 |
|
342 |
This change in phase was followed by two courses of further |
343 |
analysis. First was the replacement of the static nitrile bond with a |
344 |
morse oscillator bond. This was then simulated for a period of time |
345 |
and a classical spetrum was calculated. Second, ab intio calcualtions |
346 |
were performed to investigate if the phase change caused any change |
347 |
spectrum through quantum effects. |
348 |
|
349 |
The classical nitrile spectrum can be seen in Figure 2. Most noticably |
350 |
is the position of the two peaks. Obviously the experimental peak |
351 |
position is near 2226 cm\textsuperscript{-1}. However, in this case |
352 |
the peak position is shifted to the blue at a position of 2375 |
353 |
cm\textsuperscript{-1}. This shift is due solely to the choice of |
354 |
oscillator strength in the Morse oscillator parameters. While this |
355 |
shift makes the two spectra differ, it does not affect the ability to |
356 |
qualitatively compare peak changes to possible experimental changes. |
357 |
With this important fact out of the way, differences between the two |
358 |
states are subtle but are very much present. The first and |
359 |
most notable is the apperance for a strong band near 2300 |
360 |
cm\textsuperscript{-1}. |
361 |
\begin{figure} |
362 |
\includegraphics[width=3.25in]{2Spectra} |
363 |
\caption{The classically calculated nitrile bond spetrum for no |
364 |
external field application (black) and full external field |
365 |
application (red)} |
366 |
\label{fig:twoSpectra} |
367 |
\end{figure} |
368 |
|
369 |
Before Gaussian silumations were carried out, it was attempt to apply |
370 |
the method developed by Cho {\it et al.}~\cite{Oh:2008fk} This method involves the fitting |
371 |
of multiple parameters to Gaussian calculated freuencies to find a |
372 |
correlation between the potential around the bond and the |
373 |
frequency. This is very similar to work done by Skinner {\it et al.}~with |
374 |
water models like SPC/E. The general method is to find the shift in |
375 |
the peak position through, |
376 |
\begin{equation} |
377 |
\delta\tilde{\nu} =\sum^{n}_{a=1} l_{a}\phi^{water}_{a} |
378 |
\end{equation} |
379 |
where $l_{a}$ are the fitting parameters and $\phi^{water}_{a}$ is the |
380 |
potential from the surrounding water cluster. This $\phi^{water}_{a}$ |
381 |
takes the form, |
382 |
\begin{equation} |
383 |
\phi_{a} = \frac{1}{4\pi \epsilon_{0}} \sum_{m} \sum_{j} |
384 |
\frac{C^{H_{2}O}_{j \left(m \right) }}{r_{aj \left(m\right)}} |
385 |
\end{equation} |
386 |
where $C^{H_{2}O}_{j \left(m \right) }$ indicates the partial charge |
387 |
on the $j$th site of the $m$th water molecule and $r_{aj \left(m\right)}$ |
388 |
is the distance between the site $a$ of the nitrile molecule and the $j$th |
389 |
site of the $m$th water molecule. However, since these simulations |
390 |
are done under the presence of external fields and in the |
391 |
absence of water, the equations need a correction factor for the shift |
392 |
caused by the external field. The equation is also reworked to use |
393 |
electric field site data instead of partial charges from surrounding |
394 |
atoms. So by modifing the original |
395 |
$\phi^{water}_{a}$ to $\phi^{5CB}_{a}$ we get, |
396 |
\begin{equation} |
397 |
\phi^{5CB}_{a} = \frac{1}{4\pi \epsilon_{0}} \left( \vec{E}\bullet |
398 |
\left(\vec{r}_{a}-\vec{r}_{CN}\right) \right) + \phi^{5CB}_{0} |
399 |
\end{equation} |
400 |
where $\vec{E}$ is the electric field at each atom, $\left( \vec{r}_{a} - |
401 |
\vec{r}_{CN} \right)$ is the vector between the nitrile bond and the |
402 |
cooridinates described by Cho around the bond and $\phi^{5CB}_{0}$ is |
403 |
the correction factor for the system of parameters. After these |
404 |
changes, the correction factor was found for multiple values of an |
405 |
external field being applied. However, the factor was no linear and |
406 |
was overly large due to the fitting parameters being so small. |
407 |
|
408 |
Due to this, Gaussian calculations were performed in lieu of this |
409 |
method. A set of snapshots for the zero and full field simualtions, |
410 |
they were first investigated for any dependence on the local, with |
411 |
external field included, electric field. This was to see if a linear |
412 |
or non-linear relationship between the two could be utilized for |
413 |
generating spectra. This was done in part because of previous studies |
414 |
showing the frequency dependence of nitrile bonds to the electric |
415 |
fields generated locally between solvating water. It was seen that |
416 |
little to no dependence could be directly shown. This data is not |
417 |
shown. |
418 |
|
419 |
Since no explicit dependence was observed between the calculated |
420 |
frequency and the electric field, it was not a viable route for the |
421 |
calculation of a nitrile spectrum. Instead, the frequencies were taken |
422 |
and convolved together with a lorentzian line shape applied around the |
423 |
frequency value. These spectra are seen below in Figure |
424 |
4. While the spectrum without a field is lower in intensity and is |
425 |
almost bimodel in distrobution, the external field spectrum is much |
426 |
more unimodel. This tighter clustering has the affect of increasing the |
427 |
intensity around 2226 cm\textsuperscript{-1} where the peak is |
428 |
centered. The external field also has fewer frequencies of higher |
429 |
energy in the spectrum. Unlike the the zero field, where some frequencies |
430 |
reach as high as 2280 cm\textsuperscript{-1}. |
431 |
\begin{figure} |
432 |
\includegraphics[width=3.25in]{Convolved} |
433 |
\caption{Lorentzian convolved Gaussian frequencies of the zero field |
434 |
system (black) and the full field system (red)} |
435 |
\label{fig:Con} |
436 |
\end{figure} |
437 |
\section{Discussion} |
438 |
Interestingly, the field that is needed to switch the phase of 5CB |
439 |
macroscopically is larger than 1 V. However, in this case, only a |
440 |
voltage of 1.2 V was need to induce a phase change. This is impart due |
441 |
to the short distance of 5 nm the field is being applied across. At such a small |
442 |
distance, the field is much larger than the macroscopic and thus |
443 |
easily induces a field dependent phase change. However, this field |
444 |
will not cause a breakdown of the 5CB since electrochemistry studies |
445 |
have shown that it can be used in the presence of fields as high as |
446 |
500 V macroscopically. This large of a field near the surface of the |
447 |
elctrode would cause breakdown of 5CB if it could happen. |
448 |
|
449 |
The absence of any electric field dependency of the freuquency with |
450 |
the Gaussian simulations is interesting. A large base of research has been |
451 |
built upon the known tuning of the nitrile bond as the local field |
452 |
changes. This difference may be due to the absence of water or a |
453 |
molecule that induces a large internal field. Liquid water is known to have a very high internal field which |
454 |
is much larger than the internal fields of neat 5CB. Even though the |
455 |
application of Gaussian simulations followed by mapping it to |
456 |
some classical parameter is easy and straight forward, this system |
457 |
illistrates how that 'go to' method can break down. |
458 |
|
459 |
While this makes the application of nitrile Stark effects in |
460 |
simulations without water harder, these data show |
461 |
that it is not a deal breaker. The classically calculated nitrile |
462 |
spectrum shows changes in the spectra that will be easily seen through |
463 |
experimental routes. It indicates a shifted peak lower in energy |
464 |
should arise. This peak is a few wavenumbers from the leading edge of |
465 |
the larger peak and almost 75 wavenumbers from the center. This |
466 |
seperation between the two peaks means experimental results will show |
467 |
an easily resolved peak. |
468 |
|
469 |
The Gaussian derived spectra do indicate an applied field |
470 |
and subsiquent phase change does cause a narrowing of freuency |
471 |
distrobution. With narrowing, it would indicate an increased |
472 |
homogeneous distrobution of the local field near the nitrile. |
473 |
\section{Conclusions} |
474 |
Field dependent changes |
475 |
\newpage |
476 |
|
477 |
\bibliography{5CB} |
478 |
|
479 |
\end{doublespace} |
480 |
\end{document} |