| 40 |
|
|
| 41 |
|
|
| 42 |
|
\title{Nitrile vibrations as reporters of field-induced phase |
| 43 |
< |
transitions in liquid crystals} |
| 43 |
> |
transitions in 4-cyano-4'-pentylbiphenyl} |
| 44 |
|
\author{James M. Marr} |
| 45 |
|
\author{J. Daniel Gezelter} |
| 46 |
|
\email{gezelter@nd.edu} |
| 58 |
|
\begin{doublespace} |
| 59 |
|
|
| 60 |
|
\begin{abstract} |
| 61 |
< |
4-Cyano-4'-pentylbiphenyl (5CB) is a liquid-crystal-forming compound |
| 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 various contributions to the Stark shift of the terminal |
| 66 |
< |
nitrile group. A field-induced isotropic-nematic phase transition |
| 67 |
< |
was observed in the simulations, and the effects of this transition |
| 68 |
< |
on the distribution of nitrile frequencies were computed. Classical |
| 69 |
< |
bond displacement correlation functions exhibited a ($\sim 40 |
| 70 |
< |
\mathrm{cm}^{-1}$ red shift of a fraction of the main nitrile peak, |
| 71 |
< |
and this shift was observed only when the fields were large enough |
| 72 |
< |
to induce orientational ordering of the bulk phase. Our simulations |
| 73 |
< |
appear to indicate that phase-induced changes to the local |
| 74 |
< |
surroundings are a larger contribution to the change in the nitrile |
| 75 |
< |
spectrum than the direct field contribution. |
| 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 |
– |
The Stark shift of nitrile groups in response to applied electric |
| 82 |
– |
fields have been used extensively in biology for probing the internal |
| 83 |
– |
fields of structures like proteins and DNA. Integration of these |
| 84 |
– |
probes into different materials is also important for studying local |
| 85 |
– |
structure in confined fluids. This work centers on the vibrational |
| 86 |
– |
response of the terminal nitrile group in 4-Cyano-4'-pentylbiphenyl |
| 87 |
– |
(5CB), a liquid crystalline molecule with an isotropic to nematic |
| 88 |
– |
phase transition that can be triggered by the application of an |
| 89 |
– |
external field. |
| 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 |
| 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 |
| 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, while in smectic phases, the molecules |
| 130 |
< |
arrange themselves into layers with their long (symmetry) axis normal |
| 131 |
< |
($S_{A}$) or tilted ($S_{C}$) with respect to the layer planes. |
| 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 |
< |
The behavior of the $S_{A}$ phase can be partially explained with |
| 134 |
< |
models mainly based on geometric factors and van der Waals |
| 135 |
< |
interactions. However, these simple models are insufficient to |
| 136 |
< |
describe liquid crystal phases which exhibit more complex polymorphic |
| 137 |
< |
nature. X-ray diffraction studies have shown that the ratio between |
| 138 |
< |
lamellar spacing ($s$) and molecular length ($l$) can take on a wide |
| 139 |
< |
range of values.\cite{Gray:1984hc,Leadbetter:1976vf,Hardouin:1980yq} |
| 140 |
< |
Typical $S_{A}$ phases have $s/l$ ratios on the order of $0.8$, while |
| 141 |
< |
for some compounds, e.g. the 4-alkyl-4'-cyanobiphenyls, the $s/l$ |
| 142 |
< |
ratio is on the order of $1.4$. Molecules which form $S_{A}$ phases |
| 143 |
< |
can exhibit a wide variety of subphases like monolayers ($S_{A1}$), |
| 144 |
< |
uniform bilayers ($S_{A2}$), partial bilayers ($S_{\tilde A}$) as well |
| 145 |
< |
as interdigitated bilayers ($S_{A_{d}}$), and often have a terminal |
| 146 |
< |
cyano or nitro group. In particular, lyotropic liquid crystals (those |
| 147 |
< |
exhibiting liquid crystal phase transition as a function of water |
| 148 |
< |
concentration), often have polar head groups or zwitterionic charge |
| 149 |
< |
separated groups that result in strong dipolar |
| 150 |
< |
interactions.\cite{Collings97} Because of their versatile polymorphic |
| 151 |
< |
nature, polar liquid crystalline materials have important |
| 152 |
< |
technological applications in addition to their immense relevance to |
| 124 |
< |
biological systems.\cite{Collings97} |
| 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 |
< |
Experimental studies by Levelut {\it et al.}~\cite{Levelut:1981eu} |
| 155 |
< |
revealed that terminal cyano or nitro groups usually induce permanent |
| 156 |
< |
longitudinal dipole moments on the molecules. Liquid crystalline |
| 157 |
< |
materials with dipole moments located at the ends of the molecules |
| 158 |
< |
have important applications in display technologies in addition to |
| 159 |
< |
their relevance in biological systems.\cite{LCapp} |
| 160 |
< |
|
| 161 |
< |
Many of the technological applications of the lyotropic mesogens |
| 134 |
< |
manipulate the orientation and structuring of the liquid crystal |
| 135 |
< |
through application of external electric fields.\cite{?} |
| 136 |
< |
Macroscopically, this restructuring is visible in the interactions the |
| 137 |
< |
bulk phase has with scattered or transmitted light.\cite{?} |
| 138 |
< |
|
| 139 |
< |
4-Cyano-4'-pentylbiphenyl (5CB), has been a model for field-induced |
| 140 |
< |
phase changes due to the well-studied electric field |
| 141 |
< |
response,\cite{Hatta:1991ee} and the fact that it has a set of phase |
| 142 |
< |
transitions near room temperature.\cite{Gray:1973ca} The have a solid |
| 143 |
< |
to nematic phase transition at 18 C and a nematic to isotropic |
| 144 |
< |
transition at 35 C.\cite{Gray:1973ca} Recently there has been renewed |
| 145 |
< |
interest in 5CB in nanodroplets to understand defect sites and |
| 146 |
< |
nanoparticle structuring.\cite{PhysRevLett.111.227801} |
| 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 |
< |
Nitrile groups can serve as very precise electric field reporters via |
| 149 |
< |
their distinctive Raman and IR signatures.\cite{Boxer:2009xw} The |
| 150 |
< |
triple bond between the nitrogen and the carbon atom is very sensitive |
| 151 |
< |
to local field changes and is observed to have a direct impact on the |
| 152 |
< |
peak position within the spectrum. The Stark shift in the spectrum |
| 153 |
< |
can be quantified and mapped into a field value that is impinging upon |
| 154 |
< |
the nitrile bond. This has been used extensively in biological systems |
| 155 |
< |
like proteins and enzymes.\cite{Tucker:2004qq,Webb:2008kn} |
| 156 |
< |
|
| 157 |
< |
To date, the nitrile electric field response of |
| 158 |
< |
4-Cyano-4'-n-alkylbiphenyl liquid crystals has not been investigated. |
| 159 |
< |
While macroscopic electric fields applied across macro electrodes show |
| 160 |
< |
the phase change of the molecule as a function of electric |
| 161 |
< |
field,\cite{Lim:2006xq} the effect of a nanoscopic field application |
| 162 |
< |
has not been probed. These previous studies have shown the nitrile |
| 163 |
< |
group serves as an excellent indicator of the molecular orientation |
| 164 |
< |
within the field applied. Lee {\it et al.}~showed the 180 degree |
| 165 |
< |
change in field direction could be probed with the nitrile peak |
| 166 |
< |
intensity as it decreased and increased with molecule alignment in the |
| 167 |
< |
field.\cite{Lee:2006qd,Leyte:97} |
| 168 |
< |
|
| 169 |
< |
While these macroscopic fields worked well at showing the bulk |
| 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}. This application of |
| 168 |
< |
nanometer length is interesting in the case of a nitrile group on the |
| 169 |
< |
molecule. While macroscopic fields are insufficient to cause a Stark |
| 170 |
< |
effect, small fields across nanometer-sized gaps are of sufficient |
| 171 |
< |
strength. If one were to assume a gap of 5 nm between a lower |
| 172 |
< |
electrode having a nanoelectrode placed near it via an atomic force |
| 173 |
< |
microscope, a field of 1 V applied across the electrodes would |
| 174 |
< |
translate into a field of 2x10\textsuperscript{8} $\frac{V}{M}$. This |
| 175 |
< |
field is theoretically strong enough to cause a phase change from |
| 176 |
< |
isotropic to nematic, as well as Stark tuning of the nitrile |
| 183 |
< |
bond. This should be readily visible experimentally through Raman or |
| 184 |
< |
IR spectroscopy. |
| 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 rest of this paper, we outline a series of classical molecular |
| 179 |
< |
dynamics simulations of 5CB that were done in the presence of static |
| 180 |
< |
electric fields. These simulations were then coupled with both {\it ab |
| 181 |
< |
intio} calculations of CN-deformations and classical correlation |
| 182 |
< |
functions to predict spectral shifts. These predictions should be |
| 183 |
< |
easily varifiable with scanning electrochemical microscopy |
| 184 |
< |
experiments. |
| 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 |
| 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 included in these bodies (but with connectivity to |
| 194 |
< |
the rest of the molecule) were still included in the potential and |
| 195 |
< |
force calculations. |
| 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 contained 270 molecules and were locked at |
| 198 |
< |
experimental densities. Electrostatic interactions were computed |
| 199 |
< |
using damped shifted force (DSF) electrostatics.\cite{Fennell:2006zl} |
| 200 |
< |
The molecules were equilibrated for 1~ns at a temperature of 300K. |
| 201 |
< |
Simulations with applied fields were carried out in the microcanonical |
| 202 |
< |
(NVE) ensemble with an energy corresponding to the average energy from |
| 203 |
< |
the canonical (NVT) equilibration runs. Typical applied-field runs |
| 204 |
< |
were more than 60ns in length. |
| 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) $0.01 V / \AA$ (0.5 V), and (3) $0.024 V / |
| 214 |
< |
\AA$ (1.2 V). Each field was applied along the $z$-axis of the |
| 222 |
< |
simulation cell. For simplicity, these field strengths will be |
| 223 |
< |
referred to as zero, partial, and full field. |
| 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 (harmonic) |
| 218 |
< |
nitrile bond with an equilibrium bond distance of XXX \AA and a force |
| 219 |
< |
constant of XXX kcal / mol $\AA^2$, corresponding to a vibrational |
| 220 |
< |
frequency of YYYY $\mathrm{cm}^{-1}$. The flexible nitrile moiety |
| 221 |
< |
required simualtion time steps of 1fs, so the additional flexibility |
| 222 |
< |
was introducuced only after the rigid systems had come to equilibrium |
| 223 |
< |
under the applied fields. Whenever time correlation functions were |
| 224 |
< |
computed from the flexible simulations, statistically-independent |
| 225 |
< |
configurations were sampled from the last ns of the induced-field |
| 226 |
< |
runs. These configurations were then equilibrated with the flexible |
| 227 |
< |
nitrile moiety for 100 ps, and time correlation functions were |
| 228 |
< |
computed using data sampled from an additional 200 ps of run time |
| 229 |
< |
carried out in the microcanonical ensemble. |
| 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}$, corresponding to a |
| 224 |
> |
vibrational frequency of $2375 \mathrm{~cm}^{-1}$, a |
| 225 |
> |
bit higher than the experimental frequency. The flexible nitrile |
| 226 |
> |
moiety required simulation time steps of 1~fs, so the additional |
| 227 |
> |
flexibility was introducuced only after the rigid systems had come to |
| 228 |
> |
equilibrium under the applied fields. Whenever time correlation |
| 229 |
> |
functions were computed from the flexible simulations, |
| 230 |
> |
statistically-independent configurations were sampled from the last ns |
| 231 |
> |
of the induced-field runs. These configurations were then |
| 232 |
> |
equilibrated with the flexible nitrile moiety for 100 ps, and time |
| 233 |
> |
correlation functions were computed using data sampled from an |
| 234 |
> |
additional 200 ps of run time carried out in the microcanonical |
| 235 |
> |
ensemble. |
| 236 |
|
|
| 237 |
|
\section{Field-induced Nematic Ordering} |
| 238 |
|
|
| 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. In nematic phases, typical |
| 252 |
< |
values are close to 0.5. |
| 251 |
> |
but falls to zero for isotropic fluids. Note that the nitrogen and |
| 252 |
> |
the terminal chain atom were used to define the vectors for each |
| 253 |
> |
molecule, so the typical order parameters are lower than if one |
| 254 |
> |
defined a vector using only the rigid core of the molecule. In |
| 255 |
> |
nematic phases, typical values for $S$ are close to 0.5. |
| 256 |
|
|
| 257 |
|
In Figure \ref{fig:orderParameter}, the field-induced phase change can |
| 258 |
|
be clearly seen over the course of a 60 ns equilibration run. All |
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\section{Results} |
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| 342 |
– |
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This change in phase was followed by two courses of further |
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analysis. First was the replacement of the static nitrile bond with a |
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morse oscillator bond. This was then simulated for a period of time |
