The intramolecular interaction
potential employed harmonic bond stretching, valence angle bending, and
out-of-plane bending interactions, with torsional potentials described
by a power series in the cosine of the dihedral angle. Generic force constants
from the Dreiding force field  were used for the bond stretching and
bending interactions as well as for ring torsions and out-of-plane bending
interactions. Equilibrium bond lengths, bond angles, and conformational
energy profiles for rotations about backbone dihedrals were obtained from
ab initio calculations at the MP2/6-31G*//HF/6-31G* level, using Gaussian
Van der Waals intermolecular
interactions were described by a Lennard-Jones (LJ) functional form, and
electrostatic interactions were computed with fixed atomic partial charges.
The LJ parameters were taken from the literature [4-8]. In general, these
parameters were optimized to reproduce the thermophysical properties of
low molecular weight organic liquids. We calculated partial charges via
electrostatic potential (ESP) fits to quantum chemical results, using
AM1 electron densities obtained from Gaussian 94 .
We carried out simulations
of neat HOPDOB systems consisting of 90 molecules, and simulations of
mixtures of 90 HOPDOB molecules and 18 HDDA molecules (about 10% monomer
by volume). Simulations of neat HOPDOB were performed at 1 atm pressure
and temperatures of 355 K (in the smectic A phase) and 334 K (in the smectic
C phase). Simulations of HOPDOB/HDDA mixtures were carried out at 355
K and 1 atm, with two different initial conditions (described below).
All runs were of at least 1 ns duration.
To determine whether the smectic phase is thermodynamically stable, we also carried out a 3060 ps simulation of HOPDOB at 355 K, starting from a nematic-like initial condition at a mass density of 0.7 gm/cc. Molecules were initially perfectly aligned, with liquid-like ordering of molecular centers of mass. The initial and final configurations from this simulation are shown in Figure 5. A reduced representation of the final state is shown in Figure 6. Although there is some evidence of local smectic ordering, the final configuration does not exhibit well-developed smectic A ordering. Thus it is not possible to draw any firm conclusions as to the stability of the smectic A phase at this temperature, although the smectic A phase appears to be at least metastable.
Figure 5: Initial and final (after 3060 ps) states of the 355 K (smectic A) simulation with nematic initial condition. Left: initial configuration. Right: final configuration.
Figure 6: Final state (after 3060 ps) of the 355 K (smectic A) simulation with nematic initial condition, with molecular long axes represented by lines andmolecular centers of mass by spheres. Left: projection into X-Z plane. Right: projection into Y-Z plane.Smectic C Phase
Starting from the final configuration of the smectic A simulation described above, we carried out a further 1060 ps simulation at a lower temperature, 334 K, which is in the middle of the smectic C phase range for HOPDOB. The smectic C phase is a tilted lamellar phase in which molecular long axes are inclined with respect to the layer normal direction, and the layer spacing is correspondingly decreased. Our 334 K simulation, on the contrary, showed no indication of molecular tilt, nor was the layer spacing observed to decrease from its smectic A value. Apparently, the factors responsible for producing molecular tilt in the smectic C phase of HOPDOB are not properly taken into account by our model. An obvious possibility is that molecular tilt in the smectic C phase of HOPDOB is driven by induction (dipole-induced dipole) interactions, which are not included in our model. Because many LC molecules contain both polar and highly polarizable functional groups, such interactions could be important. We are planning a future study using explicitly polarizable models to investigate such effects. The initial and final configurations from this simulation are shown in Figure 7. A reduced representation of the final state is shown in Figure 8.
Figure 7: Final state (after 1060 ps) of the 334 K (smectic C) simulation.
Figure 8: Final state (after 1060 ps) of the 334 K (smectic C) simulation, with molecular long axes represented by lines and molecular centers of mass by spheres. Left: projection into X-Z plane. Right: projection into Y-Z plane.
Figure 9 shows the initial
configuration for the interlamellar simulation, with LC and monomer molecules
displayed separately. Figure 10 shows the same system after 2060 ps of
simulation. Clearly, the interlamellar segregation of HDDA monomers persists
over this time period, and the average layer spacing for the last 500
ps of the run (33.1 angstroms) is 5% larger than that of the neat LC.
This degree of layer swelling is somewhat smaller than that observed experimentally
(nearly 10% for this monomer concentration), even though the monomer segregation
is apparently quite strong. This discrepancy is at least in part due to
the fact that the LC molecules in one (or two) of the layers are significantly
tilted with respect to the layer normal direction (see Figure 11), leading
to a somewhat reduced average layer spacing. The origin of this apparent
monomer-induced tilt is discussed below.
The initial configuration for
the intralamellar simulation is shown in Figure 12, while the state of
the system after 2060 ps is shown in Figure 13. Clearly, the distribution
of monomers in this simulation still differs significantly from that of
the interlamellar simulation, although there is evidence that several
monomers have migrated to the interlamellar region. The average layer
spacing for the last 500 ps of the run is 30.1 angstroms, which is nearly
5% less than that of the neat LC system. Again, this can be attributed
to the significant tilt of LC molecules in one (or two) of the smectic
layers (see Figure 14).
A few words are in order regarding the apparent monomer-induced tilt observed in both simulations. We believe that this is essentially an artifact arising from the initial conditions and boundary conditions employed. Initially, each layer is constrained to contain the same number (30) of LC molecules, and slow interlayer diffusion of LC molecules guarantees that this condition is maintained for the duration of the simulation. On the other hand, monomers are inserted at random irrespective of position, so some layers start out containing more monomers than others (some monomers are initially inside the smectic layers even in the interlamellar case). Thus, all layers are effectively constrained to have the same areal density of LC molecules. On the other hand, there is a strong tendency for the system to maintain a specific mass density, both globally and within each layer. Layers containing relatively few monomers can only achieve the desired mass density within an areal density constraint by thinning, which is accomplished through molecular tilt. This artificial behavior can be overcome by working with shifted periodic boundary conditions or by tilting the layers with respect to the computational cell so that there is effectively only one layer present in the system, so that an inhomogenous distribution of monomers over layers cannot occur.
Figure 9: Interlamellar initial condition for HDDA/HOPDOB mixture. Left: LC molecules. Right: monomer molecules.
Figure 10: Final state (after 2060 ps) of the interlamellar HDDA/HOPDOB mixture. Left: LC molecules. Right: monomer molecules.
Figure 11: Final state (after 2060 ps) of liquid crystal molecules in the interlamellar HDDA/HOPDOB mixture, with molecular long axes represented by lines and molecular centers of mass by spheres. Left: projection into X-Z plane. Right: projection into Y-Z plane.
Figure 12: Intralamellar initial condition for HDDA/HOPDOB mixture. Left: LC molecules. Right: monomer molecules.
Figure 13: Final state (after 2060 ps) of the intralamellar HDDA/HOPDOB mixture. Left: LC molecules. Right: monomer molecules.
Figure 14: Final state (after 2060 ps) of liquid crystal molecules in the intralamellar HDDA/HOPDOB mixture, with molecular long axes represented by lines and molecular centers of mass by spheres. Left: projection into X-Z plane. Right: projection into Y-Z plane.
The stability of the interlamellar
configuration of the HOPDOB/HDDA system is in agreement with experiment,
which indicates a strong segregation of HDDA molecules to the interlamellar
regions of a smectic liquid crystal host. The failure of the HDDA molecules
to completely segregate to the interlamellar regions in the intralamellar
HOPDOB/HDDA system is, on the other hand, contrary to the experimental
findings. This discrepancy clearly shows that much longer simulation times
(on the order of several ns) are needed for the equilibrium monomer distribution
to be established.
For more information on this project, contact Matt Glaser.