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1 \documentclass[journal = jpccck, manuscript = article]{achemso}
2 \setkeys{acs}{usetitle = true}
3
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24 \usepackage[version=3]{mhchem} % this is a great package for formatting chemical reactions
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40
41
42 \title{Nitrile vibrations as reporters of field-induced phase
43 transitions in liquid crystals}
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 The behavior of the spectral lineshape of the nitrile group in
62 4-Cyano-4'-pentylbiphenyl (5CB) in response to an applied electric
63 field has been simulated using both classical molecular dynamics
64 simulations and {\it ab initio} quantum mechanical calculations of
65 liquid-like clusters. This nitrile group is a well-known reporter
66 of local field effects in other condensed phase settings, and our
67 simulations suggest that there is a significant response when 5CB
68 liquids are exposed to a relatively large external field. However,
69 this response is due largely to the field-induced phase transition.
70 We observe a peak shift to the red of nearly 40
71 cm\textsuperscript{-1}. These results indicate that applied fields
72 can play a role in the observed peak shape and position even if
73 those fields are significantly weaker than the local electric fields
74 that are normally felt within polar liquids.
75 \end{abstract}
76
77 \newpage
78
79 \section{Introduction}
80
81 The fundamental characteristic of liquid crystal mesophases is that
82 they maintain some degree of orientational order while translational
83 order is limited or absent. This orientational order produces a
84 complex direction-dependent response to external perturbations like
85 electric fields and mechanical distortions. The anisotropy of the
86 macroscopic phases originates in the anisotropy of the constituent
87 molecules, which typically have highly non-spherical structures with a
88 significant degree of internal rigidity. In nematic phases, rod-like
89 molecules are orientationally ordered with isotropic distributions of
90 molecular centers of mass, while in smectic phases, the molecules
91 arrange themselves into layers with their long (symmetry) axis normal
92 ($S_{A}$) or tilted ($S_{C}$) with respect to the layer planes.
93
94 The behavior of the $S_{A}$ phase can be partially explained with
95 models mainly based on geometric factors and van der Waals
96 interactions. However, these simple models are insufficient to
97 describe liquid crystal phases which exhibit more complex polymorphic
98 nature. X-ray diffraction studies have shown that the ratio between
99 lamellar spacing ($s$) and molecular length ($l$) can take on a wide
100 range of values.\cite{Gray:1984hc,Leadbetter:1976vf,Hardouin:1980yq}
101 Typical $S_{A}$ phases have $s/l$ ratios on the order of $0.8$, while
102 for some compounds, e.g. the 4-alkyl-4'-cyanobiphenyls, the $s/l$
103 ratio is on the order of $1.4$. Molecules which form $S_{A}$ phases
104 can exhibit a wide variety of subphases like monolayers ($S_{A1}$),
105 uniform bilayers ($S_{A2}$), partial bilayers ($S_{\tilde A}$) as well
106 as interdigitated bilayers ($S_{A_{d}}$), and often have a terminal
107 cyano or nitro group. In particular lyotropic liquid crystals (those
108 exhibiting liquid crystal phase transition as a function of water
109 concentration) often have polar head groups or zwitterionic charge
110 separated groups that result in strong dipolar
111 interactions.\cite{Collings97} Because of their versatile polymorphic
112 nature, polar liquid crystalline materials have important
113 technological applications in addition to their immense relevance to
114 biological systems.\cite{Collings97}
115
116 Experimental studies by Levelut {\it et al.}~\cite{Levelut:1981eu}
117 revealed that terminal cyano or nitro groups usually induce permanent
118 longitudinal dipole moments on the molecules.
119
120 Liquid crystalline materials with dipole moments located at the ends
121 of the molecules have important applications in display technologies
122 in addition to their relevance in biological systems.\cite{LCapp}
123
124 Many of the technological applications of the lyotropic mesogens
125 manipulate the orientation and structuring of the liquid crystal
126 through application of local electric fields.\cite{?}
127 Macroscopically, this restructuring is visible in the interactions the
128 bulk phase has with scattered or transmitted light.\cite{?}
129
130 4-Cyano-4'-pentylbiphenyl (5CB), has been a model for field-induced
131 phase changes due to the known electric field response of the liquid
132 crystal\cite{Hatta:1991ee}. It was discovered (along with three
133 similar compounds) in 1973 in an effort to find a LC that had a
134 melting point near room temperature.\cite{Gray:1973ca} It's known to
135 have a crystalline to nematic phase transition at 18 C and a nematic
136 to isotropic transition at 35 C.\cite{Gray:1973ca}
137
138 Nitrile groups can serve as very precise electric field reporters via
139 their distinctive Raman and IR signatures.\cite{Boxer:2009xw} The
140 triple bond between the nitrogen and the carbon atom is very sensitive
141 to local field changes and is observed to have a direct impact on the
142 peak position within the spectrum. The Stark shift in the spectrum
143 can be quantified and mapped into a field value that is impinging upon
144 the nitrile bond. This has been used extensively in biological systems
145 like proteins and enzymes.\cite{Tucker:2004qq,Webb:2008kn}
146
147 To date, the nitrile electric field response of
148 4-Cyano-4'-n-alkylbiphenyl liquid crystals has not been investigated.
149 While macroscopic electric fields applied across macro electrodes show
150 the phase change of the molecule as a function of electric
151 field,\cite{Lim:2006xq} the effect of a microscopic field application
152 has not been probed. These previous studies have shown the nitrile
153 group serves as an excellent indicator of the molecular orientation
154 within the field applied. Blank showed the 180 degree change in field
155 direction could be probed with the nitrile peak intensity as it
156 decreased and increased with molecule alignment in the
157 field.\cite{Lee:2006qd,Leyte:97}
158
159 While these macroscopic fields worked well at showing the bulk
160 response, the atomic scale response has not been studied. With the
161 advent of nano-electrodes and coupling them with atomic force
162 microscopy, control of electric fields applied across nanometer
163 distances is now possible\cite{citation1}. This application of
164 nanometer length is interesting in the case of a nitrile group on the
165 molecule. While macroscopic fields are insufficient to cause a Stark
166 effect, small fields across nanometer-sized gaps are of sufficient
167 strength. If one were to assume a gap of 5 nm between a lower
168 electrode having a nanoelectrode placed near it via an atomic force
169 microscope, a field of 1 V applied across the electrodes would
170 translate into a field of 2x10\textsuperscript{8} $\frac{V}{M}$. This
171 field is theoretically strong enough to cause a phase change from
172 isotropic to nematic, as well as Stark tuning of the nitrile
173 bond. This should be readily visible experimentally through Raman or
174 IR spectroscopy.
175
176 Herein, we show the computational investigation of these electric field effects through atomistic simulations. These are then coupled with ab intio and classical spectrum calculations to predict changes experiments should be able to replicate.
177
178 \section{Computational Details}
179 The force field was mainly taken from Guo et al.\cite{Zhang:2011hh} A
180 deviation from this force field was made to create a rigid body from
181 the phenyl rings. Bond distances within the rigid body were taken from
182 equilibrium bond distances. While the phenyl rings were held rigid,
183 bonds, bends, torsions and inversion centers still included the rings.
184
185 Simulations were with boxes of 270 molecules locked at experimental
186 densities with periodic boundaries. The molecules were thermalized
187 from 0 kelvin to 300 kelvin. To equilibrate, each was first run in NVT
188 for 1 ns. This was followed by NVE for simulations used in the data
189 collection.
190
191 External electric fields were applied in a simplistic charge-field
192 interaction. Forces were calculated by multiplying the electric field
193 being applied by the charge at each atom. For the potential, the
194 origin of the box was used as a point of reference. This allows for a
195 potential value to be added to each atom as the molecule move in space
196 within the box. Fields values were applied in a manner representing
197 those that would be applable in an experimental set-up. The assumed
198 electrode seperation was 5 nm and the field was input as
199 $\frac{V}{\text{\AA}}$. The three field environments were, 1) no field
200 applied, 2) 0.01 $\frac{V}{\text{\AA}}$ (0.5 V) and 3) 0.024
201 $\frac{V}{\text{\AA}}$ (1.2 V). Each field was applied in the
202 Z-axis of the simulation box. For the simplicity of this paper,
203 each field will be called zero, partial and full, respectively.
204
205 For quantum calculation of the nitrile bond frequency, Gaussian 09 was
206 used. A single 5CB molecule was selected for the center of the
207 cluster. For effects from molecules located near the chosen nitrile
208 group, parts of molecules nearest to the nitrile group were
209 included. For the body not including the tail, any atom within 6~\AA
210 of the midpoint of the nitrile group was included. For the tail
211 structure, the whole tail was included if a tail atom was within 4~\AA
212 of the midpoint. If the tail did not include any atoms from the ring
213 structure, it was considered a propane molecule and included as
214 such. Once the clusters were generated, input files were created that
215 stretched the nitrile bond along its axis from 0.87 to 1.52~\AA at
216 increments of 0.05~\AA. This generated 13 single point energies to be
217 calculated. The Gaussian files were run with B3LYP/6-311++G(d,p) with
218 no other keywords for the zero field simulation. Simulations with
219 fields applied included the keyword ''Field=Z+5'' to match the
220 external field applied in molecular dynamic runs. Once completed, the central nitrile bond frequency
221 was calculated with a Morse fit. Using this fit and the solved energy
222 levels for a Morse oscillator, the frequency was found. Each set of
223 frequencies were then convolved together with a lorezian lineshape
224 function over each value. The width value used was 1.5. For the zero
225 field spectrum, 67 frequencies were used and for the full field, 59
226 frequencies were used.
227
228 Classical nitrile bond frequencies were found by replacing the rigid
229 cyanide bond with a flexible Morse oscillator bond
230 ($r_0= 1.157437$ \AA , $D_0 = 212.95$ and
231 $\beta = 2.67566$) . Once replaced, the
232 systems were allowed to re-equilibrate in NVT for 100 ps. After
233 re-equilibration, the system was run in NVE for 20 ps with a snapshot
234 spacing of 1 fs. These snapshot were then used in bond correlation
235 calculation to find the decay structure of the bond in time using the
236 average bond displacement in time,
237 \begin{equation}
238 C(t) = \langle \left(r(t) - r_0 \right) \cdot \left(r(0) - r_0 \right) \rangle
239 \end{equation}
240 %
241 where $r_0$ is the equilibrium bond distance and $r(t)$ is the
242 instantaneous bond displacement at time $t$. Once calculated,
243 smoothing was applied by adding an exponential decay on top of the
244 decay with a $\tau$ of 3000 (have to check this). Further smoothing
245 was applied by padding 20,000 zeros on each side of the symmetric
246 data. This was done five times by allowing the systems to run 1 ns
247 with a rigid bond followed by an equilibrium run with the bond
248 switched back on and the short production run.
249
250 \section{Results}
251
252 In order to characterize the orientational ordering of the system, the
253 primary quantity of interest is the nematic (orientational) order
254 parameter. This is determined using the tensor
255 \begin{equation}
256 Q_{\alpha \beta} = \frac{1}{2N} \sum_{i=1}^{N} \left(3 \hat{e}_{i
257 \alpha} \hat{e}_{i \beta} - \delta_{\alpha \beta} \right)
258 \end{equation}
259 where $\alpha, \beta = x, y, z$, and $\hat{e}_i$ is the molecular
260 end-to-end unit vector for molecule $i$. The nematic order parameter
261 $S$ is the largest eigenvalue of $Q_{\alpha \beta}$, and the
262 corresponding eigenvector defines the director axis for the phase.
263 $S$ takes on values close to 1 in highly ordered phases, but falls to
264 zero for isotropic fluids. In the context of 5CB, this value would be
265 close to zero for its isotropic phase and raise closer to one as it
266 moved to the nematic and crystalline phases.
267
268 This value indicates phases changes at temperature boundaries but also
269 when a phase changes occurs due to external field applications. In
270 Figure 1, this phase change can be clearly seen over the course of 60
271 ns. Each system starts with an ordering paramter near 0.1 to 0.2,
272 which is an isotropic phase. Over the course 10 ns, the full external field
273 causes a shift in the ordering of the system to 0.5, the nematic phase
274 of the liquid crystal. This change is consistent over the full 50 ns
275 with no drop back into the isotropic phase. This change is clearly
276 field induced and stable over a long period of simulation time.
277 \begin{figure}
278 \includegraphics[trim = 5mm 10mm 3mm 10mm, clip, width=3.25in]{P2}
279 \caption{Ordering of each external field application over the course
280 of 60 ns with a sampling every 100 ps. Each trajectory was started
281 after equilibration with zero field applied.}
282 \label{fig:orderParameter}
283 \end{figure}
284
285 Interestingly, the field that is needed to switch the phase of 5CB
286 macroscopically is larger than 1 V. However, in this case, only a
287 voltage of 1.2 V was need to induce a phase change. This is impart due
288 to the distance the field is being applied across. At such a small
289 distance, the field is much larger than the macroscopic and thus
290 easily induces a field dependent phase change.
291
292 In the figure below, this phase change is represented nicely as
293 ellipsoids that are created by the vector formed between the nitrogen
294 of the nitrile group and the tail terminal carbon atom. These
295 illistrate the change from isotropic phase to nematic change. Both the
296 zero field and partial field images look mostly disordered. The
297 partial field does look somewhat orded but without any overall order
298 of the entire system. This is most likely a high point in the ordering
299 for the trajectory. The full field image on the other hand looks much
300 more ordered when compared to the two lower field simulations.
301 \begin{figure}
302 \includegraphics[width=7in]{Elip_3}
303 \caption{Ellipsoid reprsentation of 5CB at three different
304 field strengths, Zero Field (Left), Partial Field (Middle), and Full
305 Field (Right) Each image was created by taking the final
306 snapshot of each 60 ns run}
307 \label{fig:Cigars}
308 \end{figure}
309
310 This change in phase was followed by two courses of further
311 analysis. First was the replacement of the static nitrile bond with a
312 morse oscillator bond. This was then simulated for a period of time
313 and a classical spetrum was calculated. Second, ab intio calcualtions were performe to investigate
314 if the phase change caused any change spectrum through quantum
315 effects.
316
317 The classical nitrile spectrum can be seen in Figure 2. Most noticably
318 is the position of the two peaks. Obviously the experimental peak
319 position is near 2226 cm\textsuperscript{-1}. However, in this case
320 the peak position is shifted to the blue at a position of 2375
321 cm\textsuperscript{-1}. This shift is due solely to the choice of
322 oscillator strength in the Mores oscillator parameters. While this
323 shift makes the two spectra differ, it does not affect the ability to
324 compare peak changes to experimental peak changes.
325 With this important fact out of the way, differences between the two
326 states are subtle but are very much present. The first and
327 most notable is the apperance for a strong band near 2300
328 cm\textsuperscript{-1}.
329 \begin{figure}
330 \includegraphics[width=3.25in]{2Spectra}
331 \caption{The classically calculated nitrile bond spetrum for no
332 external field application (black) and full external field
333 application (red)}
334 \label{fig:twoSpectra}
335 \end{figure}
336
337 Before Gaussian silumations were carried out, it was attempt to apply
338 the method developed by Cho et. al. This method involves the fitting
339 of multiple parameters to However, since these simulations
340 are done under the presence of external electric fields and in the
341 absence of water the equations had to be reworked. Originally, the
342 nitrile bond frequency was related to the potential of water around
343 the bond via
344 \begin{equation}
345 \phi_{a} = \frac{1}{4\pi \epsilon_{0}} \sum_{m} \sum_{j}
346 \frac{C^{H_{2}O}_{j \left(m \right) }}{r_{aj \left(m\right)}}
347 \end{equation}
348 After Gaussian calculations were performed on a set of snapshots for
349 the zero and full field simualtions, they were first investigated for
350 any dependence on the local, with external field included, electric
351 field. This was to see if a linear or non-linear relationship between
352 the two could be utilized for generating spectra. This was done in
353 part because of previous studies showing the frequency dependence of
354 nitrile bonds to the electric fields generated locally between
355 solvating water. It was seen that little to no dependence could be
356 directly shown. This data is not shown.
357
358 Since no explicit dependence was observed between the calculated
359 frequency and the electric field, it was not a viable route for the
360 calculation of a nitrile spectrum. Instead, the frequencies were taken
361 and convolved together. These two spectra are seen below in Figure
362 4. While the spectrum without a field is lower in intensity and is
363 almost bimodel in distrobuiton, the external field spectrum is much
364 more unimodel. This narrowing has the affect of increasing the
365 intensity around 2226 cm\textsuperscript{-1} where the peak is
366 centered. The external field also has fewer frequencies higher to the
367 blue of the spectra. Unlike the the zero field, where some frequencies reach as high
368 as 2280 cm\textsuperscript{-1}.
369 \begin{figure}
370 \includegraphics[width=3.25in]{Convolved}
371 \caption{Lorentzian convolved Gaussian frequencies of the zero field
372 system (black) and the full field system (red)}
373 \label{fig:Con}
374 \end{figure}
375 \section{Discussion}
376 The absence of any electric field dependency of the freuquency with
377 the Gaussian simulations is strange. A large base of research has been
378 built upon the known tuning the nitrile bond as local field
379 changes. This differences may be due to the absence of water. Many of
380 the nitrile bond fitting maps are done in the presence of
381 water. Liquid water is known to have a very high internal field which
382 is much larger than the internal fields of neat 5CB. Even though the
383 application of running Gaussian simulations followed by mappying to
384 some classical parameter is easy and straight forward, this system
385 illistrates how that 'go to' method can break down.
386
387 While this makes the application of nitrile Stark effects in
388 simulations of liquid water absent simulations harder, these data show
389 that it is not a deal breaker. The classically calculated nitrile
390 spectrum shows changes in the spectra that will be easily seen through
391 experimental routes. It indicates a shifted peak lower in energy
392 should arise. This peak is a few wavenumbers from the larger peak and
393 almost 75 wavenmubers from the center. This seperation between the two
394 peaks means experimental results will show a well resolved peak.
395
396 The Gaussian derived frequencies and subsiquent spectra also indicate
397 changes that can be observed experimentally.
398 \section{Conclusions}
399 Jonathan K. Whitmer
400 cho stuff
401 \newpage
402
403 \bibliography{5CB}
404
405 \end{doublespace}
406 \end{document}