--- trunk/5cb/5CB.tex 2014/02/06 23:20:32 4025 +++ trunk/5cb/5CB.tex 2014/02/18 21:48:35 4029 @@ -40,7 +40,7 @@ \title{Nitrile vibrations as reporters of field-induced phase - transitions in liquid crystals} + transitions in 4-cyano-4'-pentylbiphenyl} \author{James M. Marr} \author{J. Daniel Gezelter} \email{gezelter@nd.edu} @@ -58,168 +58,263 @@ Nitrile Stark shift repsonses to electric fields have \begin{doublespace} \begin{abstract} -Nitrile Stark shift repsonses to electric fields have been used -extensively in biology for the probing of local internal fields of -structures like proteins and DNA. Intigration of these probes into -different areas of interest are important for studing local structure -and fields within confined, nanoscopic -systems. 4-Cyano-4'-pentylbiphenyl (5CB) is a liquid crystal with a known -macroscopic structure reordering from the isotropic to nematic -phase with the application of an external -field and as the name suggests has an inherent nitrile group. Through -simulations of this molecule where application of -large, nanoscale external fields were applied, the nitrile was invenstigated -as a local field sensor. It was -found that while most computational methods for nitrile spectral -calculations rely on a correlation between local electric field and -the nitrile bond, 5CB did not have an easily obtained -correlation. Instead classical calculation through correlation of the -cyanide bond displacement in time use enabled to show a spectral -change in the formation of a red -shifted peak from the main peak as an external field was applied. This indicates -that local structure has a larger impact on the nitrile frequency then -does the local electric field. By better understanding how nitrile -groups respond to local and external fields it will help -nitrile groups branch out beyond their biological -applications to uses in electronics and surface sciences. + 4-cyano-4'-pentylbiphenyl (5CB) is a liquid-crystal-forming compound + with a terminal nitrile group aligned with the long axis of the + molecule. Simulations of condensed-phase 5CB were carried out both + with and without applied electric fields to provide an understanding + of the the Stark shift of the terminal nitrile group. A + field-induced isotropic-nematic phase transition was observed in the + simulations, and the effects of this transition on the distribution + of nitrile frequencies were computed. Classical bond displacement + correlation functions exhibit a $\sim 40 \mathrm{~cm}^{-1}$ red + shift of a portion of the main nitrile peak, and this shift was + observed only when the fields were large enough to induce + orientational ordering of the bulk phase. Our simulations appear to + indicate that phase-induced changes to the local surroundings are a + larger contribution to the change in the nitrile spectrum than + direct field contributions. \end{abstract} \newpage \section{Introduction} +Nitrile groups can serve as very precise electric field reporters via +their distinctive Raman and IR signatures.\cite{Boxer:2009xw} The +triple bond between the nitrogen and the carbon atom is very sensitive +to local field changes and has been observed to have a direct impact +on the peak position within the spectrum. The Stark shift in the +spectrum can be quantified and mapped into a field value that is +impinging upon the nitrile bond. This has been used extensively in +biological systems like proteins and +enzymes.\cite{Tucker:2004qq,Webb:2008kn} + +The response of nitrile groups to electric fields has now been +investigated for a number of small molecules,\cite{Andrews:2000qv} as +well as in biochemical settings, where nitrile groups can act as +minimally invasive probes of structure and +dynamics.\cite{Lindquist:2009fk,Fafarman:2010dq} The vibrational Stark +effect has also been used to study the effects of electric fields on +nitrile-containing self-assembled monolayers at metallic +interfaces.\cite{Oklejas:2002uq,Schkolnik:2012ty} + +Recently 4-cyano-4'-pentylbiphenyl (5CB), a liquid crystalline +molecule with a terminal nitrile group, has seen renewed interest as +one way to impart order on the surfactant interfaces of +nanodroplets,\cite{Moreno-Razo:2012rz} or to drive surface-ordering +that can be used to promote particular kinds of +self-assembly.\cite{PhysRevLett.111.227801} The nitrile group in 5CB +is a particularly interesting case for studying electric field +effects, as 5CB exhibits an isotropic to nematic phase transition that +can be triggered by the application of an external field near room +temperature.\cite{Gray:1973ca,Hatta:1991ee} This presents the +possiblity that the field-induced changes in the local environment +could have dramatic effects on the vibrations of this particular CN +bond. Although the infrared spectroscopy of 5CB has been +well-investigated, particularly as a measure of the kinetics of the +phase transition,\cite{Leyte:1997zl} the 5CB nitrile group has not yet +seen the detailed theoretical treatment that biologically-relevant +small molecules have +received.\cite{Lindquist:2008bh,Lindquist:2008qf,Oh:2008fk,Choi:2008cr,Waegele:2010ve} + The fundamental characteristic of liquid crystal mesophases is that they maintain some degree of orientational order while translational order is limited or absent. This orientational order produces a complex direction-dependent response to external perturbations like -electric fields and mechanical distortions. The anisotropy of the +electric fields and mechanical distortions. The anisotropy of the macroscopic phases originates in the anisotropy of the constituent molecules, which typically have highly non-spherical structures with a -significant degree of internal rigidity. In nematic phases, rod-like +significant degree of internal rigidity. In nematic phases, rod-like molecules are orientationally ordered with isotropic distributions of -molecular centers of mass, while in smectic phases, the molecules -arrange themselves into layers with their long (symmetry) axis normal -($S_{A}$) or tilted ($S_{C}$) with respect to the layer planes. +molecular centers of mass. For example, 5CB has a solid to nematic +phase transition at 18C and a nematic to isotropic transition at +35C.\cite{Gray:1973ca} -The behavior of the $S_{A}$ phase can be partially explained with -models mainly based on geometric factors and van der Waals -interactions. However, these simple models are insufficient to -describe liquid crystal phases which exhibit more complex polymorphic -nature. X-ray diffraction studies have shown that the ratio between -lamellar spacing ($s$) and molecular length ($l$) can take on a wide -range of values.\cite{Gray:1984hc,Leadbetter:1976vf,Hardouin:1980yq} -Typical $S_{A}$ phases have $s/l$ ratios on the order of $0.8$, while -for some compounds, e.g. the 4-alkyl-4'-cyanobiphenyls, the $s/l$ -ratio is on the order of $1.4$. Molecules which form $S_{A}$ phases -can exhibit a wide variety of subphases like monolayers ($S_{A1}$), -uniform bilayers ($S_{A2}$), partial bilayers ($S_{\tilde A}$) as well -as interdigitated bilayers ($S_{A_{d}}$), and often have a terminal -cyano or nitro group. In particular lyotropic liquid crystals (those -exhibiting liquid crystal phase transition as a function of water -concentration) often have polar head groups or zwitterionic charge -separated groups that result in strong dipolar -interactions.\cite{Collings97} Because of their versatile polymorphic -nature, polar liquid crystalline materials have important -technological applications in addition to their immense relevance to -biological systems.\cite{Collings97} +In smectic phases, the molecules arrange themselves into layers with +their long (symmetry) axis normal ($S_{A}$) or tilted ($S_{C}$) with +respect to the layer planes. The behavior of the $S_{A}$ phase can be +partially explained with models mainly based on geometric factors and +van der Waals interactions. The Gay-Berne potential, in particular, +has been widely used in the liquid crystal community to describe this +anisotropic phase +behavior.~\cite{Gay:1981yu,Berne72,Kushick:1976xy,Luckhurst90,Cleaver:1996rt} +However, these simple models are insufficient to describe liquid +crystal phases which exhibit more complex polymorphic nature. +Molecules which form $S_{A}$ phases can exhibit a wide variety of +subphases like monolayers ($S_{A1}$), uniform bilayers ($S_{A2}$), +partial bilayers ($S_{\tilde A}$) as well as interdigitated bilayers +($S_{A_{d}}$), and often have a terminal cyano or nitro group. In +particular, lyotropic liquid crystals (those exhibiting liquid crystal +phase transition as a function of water concentration), often have +polar head groups or zwitterionic charge separated groups that result +in strong dipolar interactions,\cite{Collings:1997rz} and terminal cyano +groups (like the one in 5CB) can induce permanent longitudinal +dipoles.\cite{Levelut:1981eu} -Experimental studies by Levelut {\it et al.}~\cite{Levelut:1981eu} -revealed that terminal cyano or nitro groups usually induce permanent -longitudinal dipole moments on the molecules. +Macroscopic electric fields applied using electrodes on opposing sides +of a sample of 5CB have demonstrated the phase change of the molecule +as a function of electric field.\cite{Lim:2006xq} These previous +studies have shown the nitrile group serves as an excellent indicator +of the molecular orientation within the applied field. Lee {\it et + al.}~showed a 180 degree change in field direction could be probed +with the nitrile peak intensity as it changed along with molecular +alignment in the field.\cite{Lee:2006qd,Leyte:1997zl} -Liquid crystalline materials with dipole moments located at the ends -of the molecules have important applications in display technologies -in addition to their relevance in biological systems.\cite{LCapp} - -Many of the technological applications of the lyotropic mesogens -manipulate the orientation and structuring of the liquid crystal -through application of external electric fields.\cite{?} -Macroscopically, this restructuring is visible in the interactions the -bulk phase has with scattered or transmitted light.\cite{?} - -4-Cyano-4'-pentylbiphenyl (5CB), has been a model for field-induced -phase changes due to the known electric field response of the liquid -crystal\cite{Hatta:1991ee}. It was discovered (along with three -similar compounds) in 1973 in an effort to find a LC that had a -melting point near room temperature.\cite{Gray:1973ca} It's known to -have a crystalline to nematic phase transition at 18 C and a nematic -to isotropic transition at 35 C.\cite{Gray:1973ca} Recently it has -seen new life with the application of droplets of the molecule in -water being used to study defect sites and nanoparticle -strcuturing.\cite{PhysRevLett.111.227801} - -Nitrile groups can serve as very precise electric field reporters via -their distinctive Raman and IR signatures.\cite{Boxer:2009xw} The -triple bond between the nitrogen and the carbon atom is very sensitive -to local field changes and is observed to have a direct impact on the -peak position within the spectrum. The Stark shift in the spectrum -can be quantified and mapped into a field value that is impinging upon -the nitrile bond. This has been used extensively in biological systems -like proteins and enzymes.\cite{Tucker:2004qq,Webb:2008kn} - -To date, the nitrile electric field response of -4-Cyano-4'-n-alkylbiphenyl liquid crystals has not been investigated. -While macroscopic electric fields applied across macro electrodes show -the phase change of the molecule as a function of electric -field,\cite{Lim:2006xq} the effect of a nanoscopic field application -has not been probed. These previous studies have shown the nitrile -group serves as an excellent indicator of the molecular orientation -within the field applied. Lee {\it et al.}~showed the 180 degree change in field -direction could be probed with the nitrile peak intensity as it -decreased and increased with molecule alignment in the -field.\cite{Lee:2006qd,Leyte:97} - -While these macroscopic fields worked well at showing the bulk +While these macroscopic fields work well at indicating the bulk response, the atomic scale response has not been studied. With the advent of nano-electrodes and coupling them with atomic force microscopy, control of electric fields applied across nanometer -distances is now possible\cite{citation1}. This application of -nanometer length is interesting in the case of a nitrile group on the -molecule. While macroscopic fields are insufficient to cause a Stark -effect, small fields across nanometer-sized gaps are of sufficient -strength. If one were to assume a gap of 5 nm between a lower -electrode having a nanoelectrode placed near it via an atomic force -microscope, a field of 1 V applied across the electrodes would -translate into a field of 2x10\textsuperscript{8} $\frac{V}{M}$. This -field is theoretically strong enough to cause a phase change from -isotropic to nematic, as well as Stark tuning of the nitrile -bond. This should be readily visible experimentally through Raman or -IR spectroscopy. +distances is now possible.\cite{citation1} While macroscopic fields +are insufficient to cause a Stark effect without dielectric breakdown +of the material, small fields across nanometer-sized gaps may be of +sufficient strength. For a gap of 5 nm between a lower electrode +having a nanoelectrode placed near it via an atomic force microscope, +a potential of 1 V applied across the electrodes is equivalent to a +field of 2x10\textsuperscript{8} $\frac{V}{M}$. This field is +certainly strong enough to cause the isotropic-nematic phase change +and as well as Stark tuning of the nitrile bond. This should be +readily visible experimentally through Raman or IR spectroscopy. -Herein, we show the computational investigation of these electric -field effects through atomistic simulations of 5CB with external -fields applied. These simulations are then coupled with ab intio and -classical spectrum calculations to predict changes. These changes are -easily varifiable with experiments and should be able to replicated -experimentally. +In the sections that follow, we outline a series of coarse-grained +classical molecular dynamics simulations of 5CB that were done in the +presence of static electric fields. These simulations were then +coupled with both {\it ab intio} calculations of CN-deformations and +classical bond-length correlation functions to predict spectral +shifts. These predictions made should be easily varifiable with +scanning electrochemical microscopy experiments. \section{Computational Details} -The force field was mainly taken from Guo et al.\cite{Zhang:2011hh} A -deviation from this force field was made to create a rigid body from -the phenyl rings. Bond distances within the rigid body were taken from -equilibrium bond distances. While the phenyl rings were held rigid, -bonds, bends, torsions and inversion centers still included the rings. +The force field used for 5CB was taken from Guo {\it et + al.}\cite{Zhang:2011hh} However, for most of the simulations, each +of the phenyl rings was treated as a rigid body to allow for larger +time steps and very long simulation times. The geometries of the +rigid bodies were taken from equilibrium bond distances and angles. +Although the phenyl rings were held rigid, bonds, bends, torsions and +inversion centers that involved atoms in these substructures (but with +connectivity to the rest of the molecule) were still included in the +potential and force calculations. -Simulations were with boxes of 270 molecules locked at experimental -densities with periodic boundaries. The molecules were thermalized -from 0 kelvin to 300 kelvin. To equilibrate, each was first run in NVT -for 1 ns. This was followed by NVE for simulations used in the data -collection. +Periodic simulations cells containing 270 molecules in random +orientations were constructed and were locked at experimental +densities. Electrostatic interactions were computed using damped +shifted force (DSF) electrostatics.\cite{Fennell:2006zl} The molecules +were equilibrated for 1~ns at a temperature of 300K. Simulations with +applied fields were carried out in the microcanonical (NVE) ensemble +with an energy corresponding to the average energy from the canonical +(NVT) equilibration runs. Typical applied-field runs were more than +60ns in length. -External electric fields were applied in a simplistic charge-field -interaction. Forces were calculated by multiplying the electric field -being applied by the charge at each atom. For the potential, the -origin of the box was used as a point of reference. This allows for a -potential value to be added to each atom as the molecule move in space -within the box. Fields values were applied in a manner representing -those that would be applable in an experimental set-up. The assumed -electrode seperation was 5 nm and the field was input as -$\frac{V}{\text{\AA}}$. The three field environments were, 1) no field - applied, 2) 0.01 $\frac{V}{\text{\AA}}$ (0.5 V) and 3) 0.024 - $\frac{V}{\text{\AA}}$ (1.2 V). Each field was applied in the - Z-axis of the simulation box. For the simplicity of this paper, - each field will be called zero, partial and full, respectively. +Static electric fields with magnitudes similar to what would be +available in an experimental setup were applied to the different +simulations. With an assumed electrode seperation of 5 nm and an +electrostatic potential that is limited by the voltage required to +split water (1.23V), the maximum realistic field that could be applied +is $\sim 0.024$ V/\AA. Three field environments were investigated: +(1) no field applied, (2) partial field = 0.01 V/\AA\ , and (3) full +field = 0.024 V/\AA\ . +After the systems had come to equilibrium under the applied fields, +additional simulations were carried out with a flexible (Morse) +nitrile bond, +\begin{displaymath} +V(r_\ce{CN}) = D_e \left(1 - e^{-\beta (r_\ce{CN}-r_e)}\right)^2 +\end{displaymath} +where $r_e= 1.157437$ \AA , $D_e = 212.95 \mathrm{~kca~l} / +\mathrm{mol}^{-1}$ and $\beta = 2.67566 $\AA~$^{-1}$. These +parameters correspond to a vibrational frequency of $2375 +\mathrm{~cm}^{-1}$, a bit higher than the experimental frequency. The +flexible nitrile moiety required simulation time steps of 1~fs, so the +additional flexibility was introducuced only after the rigid systems +had come to equilibrium under the applied fields. Whenever time +correlation functions were computed from the flexible simulations, +statistically-independent configurations were sampled from the last ns +of the induced-field runs. These configurations were then +equilibrated with the flexible nitrile moiety for 100 ps, and time +correlation functions were computed using data sampled from an +additional 200 ps of run time carried out in the microcanonical +ensemble. + +\section{Field-induced Nematic Ordering} + +In order to characterize the orientational ordering of the system, the +primary quantity of interest is the nematic (orientational) order +parameter. This was determined using the tensor +\begin{equation} +Q_{\alpha \beta} = \frac{1}{2N} \sum_{i=1}^{N} \left(3 \hat{e}_{i + \alpha} \hat{e}_{i \beta} - \delta_{\alpha \beta} \right) +\end{equation} +where $\alpha, \beta = x, y, z$, and $\hat{e}_i$ is the molecular +end-to-end unit vector for molecule $i$. The nematic order parameter +$S$ is the largest eigenvalue of $Q_{\alpha \beta}$, and the +corresponding eigenvector defines the director axis for the phase. +$S$ takes on values close to 1 in highly ordered (smectic A) phases, +but falls to zero for isotropic fluids. Note that the nitrogen and +the terminal chain atom were used to define the vectors for each +molecule, so the typical order parameters are lower than if one +defined a vector using only the rigid core of the molecule. In +nematic phases, typical values for $S$ are close to 0.5. + +The field-induced phase transition can be clearly seen over the course +of a 60 ns equilibration runs in figure \ref{fig:orderParameter}. All +three of the systems started in a random (isotropic) packing, with +order parameters near 0.2. Over the course 10 ns, the full field +causes an alignment of the molecules (due primarily to the interaction +of the nitrile group dipole with the electric field). Once this +system started exhibiting nematic ordering, the orientational order +parameter became stable for the remaining 50 ns of simulation time. +It is possible that the partial-field simulation is meta-stable and +given enough time, it would eventually find a nematic-ordered phase, +but the partial-field simulation was stable as an isotropic phase for +the full duration of a 60 ns simulation. +\begin{figure} + \includegraphics[trim = 5mm 10mm 3mm 10mm, clip, width=4in]{P2} + \caption{Evolution of the orientational order parameter for the + no-field, partial field, and full field simulations over the + course of 60 ns. Each simulation was started from a + statistically-independent isotropic configuration.} + \label{fig:orderParameter} +\end{figure} + +The field-induced isotropic-nematic transition can be visualized in +figure \ref{fig:Cigars}, where each molecule has been represented +using and ellipsoids aligned along the long-axis of each molecule. +Both the zero field and partial field simulations appear isotropic, +while the full field simulations has been orientationally ordered +\begin{figure} + \includegraphics[width=7in]{Elip_3} + \caption{Ellipsoid reprsentation of 5CB at three different field + strengths, Zero Field (Left), Partial Field (Middle), and Full + Field (Right) Each image was created from the final configuration + of each 60 ns equilibration run.} + \label{fig:Cigars} +\end{figure} + +\section{Sampling the CN bond frequency} + +The primary quantity of interest is the distribution of vibrational +frequencies exhibited by the 5CB nitrile bond under the different +electric fields. Three distinct methods for mapping classical +simulations onto vibrational spectra were brought to bear on these +simulations: +\begin{enumerate} +\item Isolated 5CB molecules and their immediate surroundings were + extracted from the simulations, their nitrile bonds were stretched + and single-point {\em ab initio} calculations were used to obtain + Morse-oscillator fits for the local vibrational motion along that + bond. +\item The potential - frequency maps developed by Cho {\it et + al.}~\cite{Oh:2008fk} for nitrile moieties in water were + investigated. This method involves mapping the electrostatic + potential around the bond to the vibrational frequency, and is + similar in approach to field-frequency maps that were pioneered by + work done by Skinner {\it et al.}\cite{XXXX} +\item Classical bond-length autocorrelation functions were Fourier + transformed to directly obtain the vibrational spectrum from + molecular dynamics simulations. +\end{enumerate} + +\subsection{CN frequencies from isolated clusters} + For quantum calculation of the nitrile bond frequency, Gaussian 09 was used. A single 5CB molecule was selected for the center of the cluster. For effects from molecules located near the chosen nitrile @@ -243,6 +338,49 @@ Classical nitrile bond frequencies were found by repla field spectrum, 67 frequencies were used and for the full field, 59 frequencies were used. +\subsection{CN frequencies from potential-frequency maps} +Before Gaussian silumations were carried out, it was attempt to apply +the method developed by Cho {\it et al.}~\cite{Oh:2008fk} This method involves the fitting +of multiple parameters to Gaussian calculated freuencies to find a +correlation between the potential around the bond and the +frequency. This is very similar to work done by Skinner {\it et al.}~with +water models like SPC/E. The general method is to find the shift in +the peak position through, +\begin{equation} +\delta\tilde{\nu} =\sum^{n}_{a=1} l_{a}\phi^{water}_{a} +\end{equation} +where $l_{a}$ are the fitting parameters and $\phi^{water}_{a}$ is the +potential from the surrounding water cluster. This $\phi^{water}_{a}$ +takes the form, +\begin{equation} +\phi_{a} = \frac{1}{4\pi \epsilon_{0}} \sum_{m} \sum_{j} +\frac{C^{H_{2}O}_{j \left(m \right) }}{r_{aj \left(m\right)}} +\end{equation} +where $C^{H_{2}O}_{j \left(m \right) }$ indicates the partial charge +on the $j$th site of the $m$th water molecule and $r_{aj \left(m\right)}$ +is the distance between the site $a$ of the nitrile molecule and the $j$th +site of the $m$th water molecule. However, since these simulations +are done under the presence of external fields and in the +absence of water, the equations need a correction factor for the shift +caused by the external field. The equation is also reworked to use +electric field site data instead of partial charges from surrounding +atoms. So by modifing the original +$\phi^{water}_{a}$ to $\phi^{5CB}_{a}$ we get, +\begin{equation} +\phi^{5CB}_{a} = \frac{1}{4\pi \epsilon_{0}} \left( \vec{E}\bullet + \left(\vec{r}_{a}-\vec{r}_{CN}\right) \right) + \phi^{5CB}_{0} +\end{equation} +where $\vec{E}$ is the electric field at each atom, $\left( \vec{r}_{a} - + \vec{r}_{CN} \right)$ is the vector between the nitrile bond and the +cooridinates described by Cho around the bond and $\phi^{5CB}_{0}$ is +the correction factor for the system of parameters. After these +changes, the correction factor was found for multiple values of an +external field being applied. However, the factor was no linear and +was overly large due to the fitting parameters being so small. + + +\subsection{CN frequencies from bond length autocorrelation functions} + Classical nitrile bond frequencies were found by replacing the rigid cyanide bond with a flexible Morse oscillator bond ($r_0= 1.157437$ \AA , $D_0 = 212.95$ and @@ -265,59 +403,7 @@ switched back to a Morse oscillator and a short produc with a rigid bond followed by an equilibrium run with the bond switched back to a Morse oscillator and a short production run of 20 ps. -\section{Results} -In order to characterize the orientational ordering of the system, the -primary quantity of interest is the nematic (orientational) order -parameter. This is determined using the tensor -\begin{equation} -Q_{\alpha \beta} = \frac{1}{2N} \sum_{i=1}^{N} \left(3 \hat{e}_{i - \alpha} \hat{e}_{i \beta} - \delta_{\alpha \beta} \right) -\end{equation} -where $\alpha, \beta = x, y, z$, and $\hat{e}_i$ is the molecular -end-to-end unit vector for molecule $i$. The nematic order parameter -$S$ is the largest eigenvalue of $Q_{\alpha \beta}$, and the -corresponding eigenvector defines the director axis for the phase. -$S$ takes on values close to 1 in highly ordered phases, but falls to -zero for isotropic fluids. In the context of 5CB, this value would be -close to zero for its isotropic phase and raise closer to one as it -moved to the nematic and crystalline phases. - -This value indicates phases changes at temperature boundaries but also -when a phase change occurs due to external field applications. In -Figure 1, this phase change can be clearly seen over the course of 60 -ns. Each system starts with an ordering paramter near 0.1 to 0.2, -which is an isotropic phase. Over the course 10 ns, the full external field -causes a shift in the ordering of the system to 0.5, the nematic phase -of the liquid crystal. This change is consistent over the full 50 ns -with no drop back into the isotropic phase. This change is clearly -field induced and stable over a long period of simulation time. -\begin{figure} - \includegraphics[trim = 5mm 10mm 3mm 10mm, clip, width=3.25in]{P2} - \caption{Ordering of each external field application over the course - of 60 ns with a sampling every 100 ps. Each trajectory was started - after equilibration with zero field applied.} - \label{fig:orderParameter} -\end{figure} - -In the figure below, this phase change is represented nicely as -ellipsoids that are created by the vector formed between the nitrogen -of the nitrile group and the tail terminal carbon atom. These -illistrate the change from isotropic phase to nematic change. Both the -zero field and partial field images look mostly disordered. The -partial field does look somewhat orded but without any overall order -of the entire system. This is most likely a high point in the ordering -for the trajectory. The full field image on the other hand looks much -more ordered when compared to the two lower field simulations. -\begin{figure} - \includegraphics[width=7in]{Elip_3} - \caption{Ellipsoid reprsentation of 5CB at three different - field strengths, Zero Field (Left), Partial Field (Middle), and Full - Field (Right) Each image was created by taking the final - snapshot of each 60 ns run} - \label{fig:Cigars} -\end{figure} - This change in phase was followed by two courses of further analysis. First was the replacement of the static nitrile bond with a morse oscillator bond. This was then simulated for a period of time @@ -345,44 +431,6 @@ Before Gaussian silumations were carried out, it was a \label{fig:twoSpectra} \end{figure} -Before Gaussian silumations were carried out, it was attempt to apply -the method developed by Cho {\it et al.}~\cite{Oh:2008fk} This method involves the fitting -of multiple parameters to Gaussian calculated freuencies to find a -correlation between the potential around the bond and the -frequency. This is very similar to work done by Skinner {\it et al.}~with -water models like SPC/E. The general method is to find the shift in -the peak position through, -\begin{equation} -\delta\tilde{\nu} =\sum^{n}_{a=1} l_{a}\phi^{water}_{a} -\end{equation} -where $l_{a}$ are the fitting parameters and $\phi^{water}_{a}$ is the -potential from the surrounding water cluster. This $\phi^{water}_{a}$ -takes the form, -\begin{equation} -\phi_{a} = \frac{1}{4\pi \epsilon_{0}} \sum_{m} \sum_{j} -\frac{C^{H_{2}O}_{j \left(m \right) }}{r_{aj \left(m\right)}} -\end{equation} -where $C^{H_{2}O}_{j \left(m \right) }$ indicates the partial charge -on the $j$th site of the $m$th water molecule and $r_{aj \left(m\right)}$ -is the distance between the site $a$ of the nitrile molecule and the $j$th -site of the $m$th water molecule. However, since these simulations -are done under the presence of external fields and in the -absence of water, the equations need a correction factor for the shift -caused by the external field. The equation is also reworked to use -electric field site data instead of partial charges from surrounding -atoms. So by modifing the original -$\phi^{water}_{a}$ to $\phi^{5CB}_{a}$ we get, -\begin{equation} -\phi^{5CB}_{a} = \frac{1}{4\pi \epsilon_{0}} \left( \vec{E}\bullet - \left(\vec{r}_{a}-\vec{r}_{CN}\right) \right) + \phi^{5CB}_{0} -\end{equation} -where $\vec{E}$ is the electric field at each atom, $\left( \vec{r}_{a} - - \vec{r}_{CN} \right)$ is the vector between the nitrile bond and the -cooridinates described by Cho around the bond and $\phi^{5CB}_{0}$ is -the correction factor for the system of parameters. After these -changes, the correction factor was found for multiple values of an -external field being applied. However, the factor was no linear and -was overly large due to the fitting parameters being so small. Due to this, Gaussian calculations were performed in lieu of this method. A set of snapshots for the zero and full field simualtions,