ViewVC Help
View File | Revision Log | Show Annotations | View Changeset | Root Listing
root/group/trunk/5cb/5CB.tex
Revision: 4033
Committed: Wed Feb 19 19:48:47 2014 UTC (10 years, 6 months ago) by gezelter
Content type: application/x-tex
File size: 26827 byte(s)
Log Message:
edits

File Contents

# Content
1 \documentclass[journal = jpccck, manuscript = article]{achemso}
2 \setkeys{acs}{usetitle = true}
3
4 \usepackage{caption}
5 \usepackage{float}
6 \usepackage{geometry}
7 \usepackage{natbib}
8 \usepackage{setspace}
9 \usepackage{xkeyval}
10 \usepackage{amsmath}
11 \usepackage{amssymb}
12 \usepackage{times}
13 \usepackage{mathptm}
14 \usepackage{setspace}
15 %\usepackage{endfloat}
16 \usepackage{tabularx}
17 \usepackage{longtable}
18 \usepackage{graphicx}
19 \usepackage{multirow}
20 \usepackage{multicol}
21 \usepackage{achemso}
22 \usepackage{subcaption}
23 \usepackage[colorinlistoftodos]{todonotes}
24 \usepackage[version=3]{mhchem} % this is a great package for formatting chemical reactions
25 % \usepackage[square, comma, sort&compress]{natbib}
26 \usepackage{url}
27 \pagestyle{plain} \pagenumbering{arabic} \oddsidemargin 0.0cm
28 \evensidemargin 0.0cm \topmargin -21pt \headsep 10pt \textheight
29 9.0in \textwidth 6.5in \brokenpenalty=10000
30
31 % double space list of tables and figures
32 %\AtBeginDelayedFloats{\renewcomand{\baselinestretch}{1.66}}
33 \setlength{\abovecaptionskip}{20 pt}
34 \setlength{\belowcaptionskip}{30 pt}
35
36 % \bibpunct{}{}{,}{s}{}{;}
37
38 %\citestyle{nature}
39 % \bibliographystyle{achemso}
40
41
42 \title{Nitrile vibrations as reporters of field-induced phase
43 transitions in 4-cyano-4'-pentylbiphenyl (5CB)}
44 \author{James M. Marr}
45 \author{J. Daniel Gezelter}
46 \email{gezelter@nd.edu}
47 \affiliation[University of Notre Dame]{251 Nieuwland Science Hall\\
48 Department of Chemistry and Biochemistry\\
49 University of Notre Dame\\
50 Notre Dame, Indiana 46556}
51
52 \date{\today}
53
54 \begin{document}
55
56 \maketitle
57
58 \begin{doublespace}
59
60 \begin{abstract}
61 4-cyano-4'-pentylbiphenyl (5CB) is a liquid-crystal-forming compound
62 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
75 direct field contributions.
76 \end{abstract}
77
78 \newpage
79
80 \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}