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\title{Nitrile vibrations as reporters of field-induced phase |
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transitions in liquid crystals} |
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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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\date{\today} |
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\begin{document} |
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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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The behavior of the spectral lineshape of the nitrile group in |
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4-Cyano-4'-pentylbiphenyl (5CB) in response to an applied electric |
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field has been simulated using both classical molecular dynamics |
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simulations and {\it ab initio} quantum mechanical calculations of |
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liquid-like clusters. This nitrile group is a well-known reporter |
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of local field effects in other condensed phase settings, and our |
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simulations suggest that there is a significant response when 5CB |
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liquids are exposed to a relatively large external field. However, |
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this response is due largely to the field-induced phase transition. |
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We observe a peak shift to the red of nearly 40 |
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cm\textsuperscript{-1}. These results indicate that applied fields |
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can play a role in the observed peak shape and position even if |
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those fields are significantly weaker than the local electric fields |
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that are normally felt within polar liquids. |
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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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The fundamental characteristic of liquid crystal mesophases is that |
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they maintain some degree of orientational order while translational |
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order is limited or absent. This orientational order produces a |
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complex direction-dependent response to external perturbations like |
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electric fields and mechanical distortions. The anisotropy of the |
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macroscopic phases originates in the anisotropy of the constituent |
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molecules, which typically have highly non-spherical structures with a |
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significant degree of internal rigidity. In nematic phases, rod-like |
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molecules are orientationally ordered with isotropic distributions of |
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molecular centers of mass, while in smectic phases, the molecules |
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arrange themselves into layers with their long (symmetry) axis normal |
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($S_{A}$) or tilted ($S_{C}$) with respect to the layer planes. |
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|
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The behavior of the $S_{A}$ phase can be partially explained with |
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models mainly based on geometric factors and van der Waals |
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interactions. However, these simple models are insufficient to |
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describe liquid crystal phases which exhibit more complex polymorphic |
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nature. X-ray diffraction studies have shown that the ratio between |
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lamellar spacing ($s$) and molecular length ($l$) can take on a wide |
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range of values.\cite{Gray:1984hc,Leadbetter:1976vf,Hardouin:1980yq} |
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Typical $S_{A}$ phases have $s/l$ ratios on the order of $0.8$, while |
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for some compounds, e.g. the 4-alkyl-4'-cyanobiphenyls, the $s/l$ |
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ratio is on the order of $1.4$. Molecules which form $S_{A}$ phases |
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can exhibit a wide variety of subphases like monolayers ($S_{A1}$), |
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uniform bilayers ($S_{A2}$), partial bilayers ($S_{\tilde A}$) as well |
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as interdigitated bilayers ($S_{A_{d}}$), and often have a terminal |
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cyano or nitro group. In particular lyotropic liquid crystals (those |
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exhibiting liquid crystal phase transition as a function of water |
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concentration) often have polar head groups or zwitterionic charge |
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separated groups that result in strong dipolar |
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interactions.\cite{Collings97} Because of their versatile polymorphic |
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nature, polar liquid crystalline materials have important |
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technological applications in addition to their immense relevance to |
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biological systems.\cite{Collings97} |
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|
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Experimental studies by Levelut {\it et al.}~\cite{Levelut:1981eu} |
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revealed that terminal cyano or nitro groups usually induce permanent |
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longitudinal dipole moments on the molecules. |
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|
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Liquid crystalline materials with dipole moments located at the ends |
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of the molecules have important applications in display technologies |
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in addition to their relevance in biological systems.\cite{LCapp} |
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|
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Many of the technological applications of the lyotropic mesogens |
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manipulate the orientation and structuring of the liquid crystal |
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through application of local electric fields.\cite{?} |
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Macroscopically, this restructuring is visible in the interactions the |
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bulk phase has with scattered or transmitted light.\cite{?} |
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|
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4-Cyano-4'-pentylbiphenyl (5CB), has been a model for field-induced |
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phase changes due to the known electric field response of the liquid |
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crystal\cite{Hatta:1991ee}. It was discovered (along with three |
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similar compounds) in 1973 in an effort to find a LC that had a |
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melting point near room temperature.\cite{Gray:1973ca} It's known to |
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have a crystalline to nematic phase transition at 18 C and a nematic |
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to isotropic transition at 35 C.\cite{Gray:1973ca} |
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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 |
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to local field changes and is observed to have a direct impact on the |
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peak position within the spectrum. The Stark shift in the spectrum |
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can be quantified and mapped into a field value that is impinging upon |
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the nitrile bond. This has been used extensively in biological systems |
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like proteins and enzymes.\cite{Tucker:2004qq,Webb:2008kn} |
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|
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To date, the nitrile electric field response of |
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4-Cyano-4'-n-alkylbiphenyl liquid crystals has not been investigated. |
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While macroscopic electric fields applied across macro electrodes show |
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the phase change of the molecule as a function of electric |
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field,\cite{Lim:2006xq} the effect of a microscopic field application |
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has not been probed. These previous studies have shown the nitrile |
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group serves as an excellent indicator of the molecular orientation |
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within the field applied. Blank showed the 180 degree change in field |
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direction could be probed with the nitrile peak intensity as it |
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decreased and increased with molecule alignment in the |
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field.\cite{Lee:2006qd,Leyte:97} |
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|
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While these macroscopic fields worked well at showing the bulk |
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response, the atomic scale response has not been studied. With the |
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advent of nano-electrodes and coupling them with atomic force |
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microscopy, control of electric fields applied across nanometer |
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distances is now possible\cite{citation1}. This application of |
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nanometer length is interesting in the case of a nitrile group on the |
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molecule. While macroscopic fields are insufficient to cause a Stark |
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effect, small fields across nanometer-sized gaps are of sufficient |
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strength. If one were to assume a gap of 5 nm between a lower |
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electrode having a nanoelectrode placed near it via an atomic force |
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microscope, a field of 1 V applied across the electrodes would |
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translate into a field of 2x10\textsuperscript{8} $\frac{V}{M}$. This |
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field is theoretically strong enough to cause a phase change from |
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isotropic to nematic, as well as Stark tuning of the nitrile |
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bond. This should be readily visible experimentally through Raman or |
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IR spectroscopy. |
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|
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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. |
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|
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\section{Computational Details} |
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The force field was mainly taken from Guo et al.\cite{Zhang:2011hh} A |
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deviation from this force field was made to create a rigid body from |
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the phenyl rings. Bond distances within the rigid body were taken from |
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equilibrium bond distances. While the phenyl rings were held rigid, |
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bonds, bends, torsions and inversion centers still included the rings. |
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|
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Simulations were with boxes of 270 molecules locked at experimental |
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densities with periodic boundaries. The molecules were thermalized |
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from 0 kelvin to 300 kelvin. To equilibrate, each was first run in NVT |
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for 1 ns. This was followed by NVE for simulations used in the data |
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collection. |
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|
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External electric fields were applied in a simplistic charge-field |
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interaction. Forces were calculated by multiplying the electric field |
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being applied by the charge at each atom. For the potential, the |
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origin of the box was used as a point of reference. This allows for a |
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potential value to be added to each atom as the molecule move in space |
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within the box. Fields values were applied in a manner representing |
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those that would be applable in an experimental set-up. The assumed |
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electrode seperation was 5 nm and the field was input as |
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$\frac{V}{\text{\AA}}$. The three field environments were, 1) no field |
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applied, 2) 0.01 $\frac{V}{\text{\AA}}$ (0.5 V) and 3) 0.024 |
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$\frac{V}{\text{\AA}}$ (1.2 V). Each field was applied in the |
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Z-axis of the simulation box. For the simplicity of this paper, |
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each field will be called zero, partial and full, respectively. |
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|
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For quantum calculation of the nitrile bond frequency, Gaussian 09 was |
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used. A single 5CB molecule was selected for the center of the |
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cluster. For effects from molecules located near the chosen nitrile |
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group, parts of molecules nearest to the nitrile group were |
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included. For the body not including the tail, any atom within 6~\AA |
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of the midpoint of the nitrile group was included. For the tail |
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structure, the whole tail was included if a tail atom was within 4~\AA |
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of the midpoint. If the tail did not include any atoms from the ring |
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structure, it was considered a propane molecule and included as |
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such. Once the clusters were generated, input files were created that |
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stretched the nitrile bond along its axis from 0.87 to 1.52~\AA at |
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increments of 0.05~\AA. This generated 13 single point energies to be |
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calculated. The Gaussian files were run with B3LYP/6-311++G(d,p) with |
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no other keywords for the zero field simulation. Simulations with |
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fields applied included the keyword ''Field=Z+5'' to match the |
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external field applied in molecular dynamic runs. Once completed, the central nitrile bond frequency |
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was calculated with a Morse fit. Using this fit and the solved energy |
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levels for a Morse oscillator, the frequency was found. Each set of |
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frequencies were then convolved together with a guassian spread |
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function over each value. The width value used was 1.5. For the zero |
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field spectrum, 67 frequencies were used and for the full field, 59 |
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frequencies were used. |
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|
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Classical nitrile bond frequencies were found by replacing the rigid |
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cyanide bond with a flexible Morse oscillator bond |
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($r_0= 1.157437$ \AA , $D_0 = 212.95$ and |
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$\beta = 2.67566$) . Once replaced, the |
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systems were allowed to re-equilibrate in NVT for 100 ps. After |
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re-equilibration, the system was run in NVE for 20 ps with a snapshot |
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spacing of 1 fs. These snapshot were then used in bond correlation |
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calculation to find the decay structure of the bond in time using the |
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average bond displacement in time, |
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\begin{equation} |
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C(t) = \langle \left(r(t) - r_0 \right) \cdot \left(r(0) - r_0 \right) \rangle |
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\end{equation} |
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% |
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where $r_0$ is the equilibrium bond distance and $r(t)$ is the |
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instantaneous bond displacement at time $t$. Once calculated, |
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smoothing was applied by adding an exponential decay on top of the |
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decay with a $\tau$ of 3000 (have to check this). Further smoothing |
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was applied by padding 20,000 zeros on each side of the symmetric |
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data. This was done five times by allowing the systems to run 1 ns |
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with a rigid bond followed by an equilibrium run with the bond |
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switched back on and the short production run. |
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|
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\section{Results} |
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|
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In order to characterize the orientational ordering of the system, the |
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primary quantity of interest is the nematic (orientational) order |
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parameter. This is determined using the tensor |
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\begin{equation} |
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Q_{\alpha \beta} = \frac{1}{2N} \sum_{i=1}^{N} \left(3 \hat{e}_{i |
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\alpha} \hat{e}_{i \beta} - \delta_{\alpha \beta} \right) |
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\end{equation} |
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where $\alpha, \beta = x, y, z$, and $\hat{e}_i$ is the molecular |
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end-to-end unit vector for molecule $i$. The nematic order parameter |
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$S$ is the largest eigenvalue of $Q_{\alpha \beta}$, and the |
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corresponding eigenvector defines the director axis for the phase. |
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$S$ takes on values close to 1 in highly ordered phases, but falls to |
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zero for isotropic fluids. In the context of 5CB, this value would be |
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close to zero for its isotropic phase and raise closer to one as it |
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moved to the nematic and crystalline phases. |
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|
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This value indicates phases changes at temperature boundaries but also |
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when a phase changes occurs due to external field applications. In |
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Figure 1, this phase change can be clearly seen over the course of 60 |
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ns. Each system starts with an ordering paramter near 0.1 to 0.2, |
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which is an isotropic phase. Over the course 10 ns, the full external field |
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causes a shift in the ordering of the system to 0.5, the nematic phase |
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of the liquid crystal. This change is consistent over the full 50 ns |
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with no drop back into the isotropic phase. This change is clearly |
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field induced and stable over a long period of simulation time. |
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|
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Interestingly, the field that is needed to switch the phase of 5CB |
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macroscopically is larger than 1 V. However, in this case, only a |
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voltage of 1.2 V was need to induce a phase change. This is impart due |
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to the distance the field is being applied across. At such a small |
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distance, the field is much larger than the macroscopic and thus |
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easily induces a field dependent phase change. |
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|
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This change in phase was followed by two courses of further |
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simulation. First, was replacement of the static nitrile bond with a |
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morse oscillator bond. This was then simulated for a period of time |
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and a classical spetrum was calculated. Second, ab intio calcualtions were performe to investigate |
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if the phase change caused any change spectrum from quantum |
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effects. |
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|
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In respect to the classical calculations, it was first seen if previous |
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studies of nitriles within water and neat simulation done by Cho |
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et. al. could be used for the spectrum. |
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|
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After Gaussian calculations were performed on a set of snapshots, any |
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\begin{figure} |
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\includegraphics[trim = 5mm 10mm 3mm 10mm, clip, width=3.25in]{P2} |
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\caption{Ordering of each external field application over the course |
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of 60 ns with a sampling every 100 ps. Each trajectory was started |
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after equilibration with zero field applied.} |
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\label{fig:orderParameter} |
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\end{figure} |
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\begin{figure} |
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\includegraphics[width=3.25in]{2Spectra} |
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\caption{The classically calculated nitrile bond spetrum for no |
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external field application (black) and full external field |
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application (red)} |
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\label{fig:twoSpectra} |
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\end{figure} |
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\begin{figure} |
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\includegraphics[width=3.25in]{Convolved} |
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\caption{Gaussian frequencies added together with gaussian } |
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\label{fig:Con} |
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\end{figure} |
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\begin{figure} |
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\includegraphics[width=7in]{Elip_3} |
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\caption{Ellipsoid reprsentation of 5CB at three different |
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field strengths, Zero Field (Left), Partial Field (Middle), and Full |
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Field (Right)} |
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\label{fig:Cigars} |
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\end{figure} |
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|
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\section{Discussion} |
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|
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\section{Conclusions} |
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\newpage |
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|
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\bibliography{5CB} |
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\end{doublespace} |
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\end{document} |
