In this paper, we report a generalized form for the range parameter governing the pair interaction between soft ellipsoidal particles. For nonequivalent uniaxial particles, we extend the Berne-Pechukas Gaussian overlap formalism to obtain an explicit expression for this range parameter. We confirm that this result is identical to that given by an approach that is not widely recognized, based on an approximation to the Perram-Wertheim hard-ellipsoid contact function. We further illustrate the power of the latter route by using it to write down the range parameter for the interaction between two nonequivalent biaxial particles. An explicit interaction potential for nonequivalent uniaxial particles is obtained by importing the uniaxial range parameter result into the standard Gay-Berne form. A parametrization of this potential is investigated for a rod-disk interaction. ͓S1063-651X͑96͒05506-7͔
Molecular dynamics integrators are presented for translational and rotational motion of rigid molecules in microcanonical, canonical, and isothermal-isobaric ensembles. The integrators are all time reversible and are also, in some approaches, symplectic for the microcanonical ensembles. They are developed utilizing the quaternion representation on the basis of the Trotter factorization scheme using a Hamiltonian formalism. The structure is similar to that of the velocity Verlet algorithm. Comparison is made with standard integrators in terms of stability and it is found that a larger time step is stable with the new integrators. The canonical and isothermal-isobaric molecular dynamics simulations are defined by using a chain thermostat approach according to generalized Nosé-Hoover and Andersen methods.
We propose a scaling of an intrinsic molecular chirality index calculated from atomic positions. Its application to the design of chiral molecules through a consideration of atomic or group chiral indices is discussed for a range of molecules from small molecules to liquid crystal molecules. It is found to indicate the trend in change of chirality of a molecule caused by an atom or group substitution. Comparison is made between the method of scaling and an analytic calculation of the index for an orthogonal tetrahedron. We investigate the effect of substitution of atoms and groups in real liquid crystal molecules by application of the generalized chiral index.
Chirality of optically active liquid crystal molecules has become an important research topic and the subject of a number of theoretical and experimental studies. We present here the results of the application of a newly developed scaling method of a chiral index to a range of chiral molecules. Good agreement is found between the scaled chiral index and the helical twisting power for relatively rigid molecules. Two flexible TADDOL (␣,␣,␣Ј,␣Ј-tetraaryl-1,3-dioxolan-4,5-dimethanol͒ molecules are studied to determine which conformations may give rise to their high experimental helical twisting powers. A variety of links between the moment of inertia tensor, the dihedral angles, the scaled chiral indices, the minimum energy of the optimized geometry and the experimental helical twisting power are discussed. The scaled chiral and steric indices and dihedral angles are promising as predictors of experimental helical twisting power, in particular for relatively rigid molecules, in cases where all the relevant interactions are determined by the molecular structure.
Bent-core molecules have received much interest due to their biaxiality and novel phase ordering. It is, therefore, of interest to model the characteristic shape of these molecules and observe the effect on liquid crystal mesophase formation in a computer simulation study. A simple model of the interaction employed a two-site Gay-Berne potential with the sites separated by +/-0.5 reduced units for all models. The angle between the two sites, 180 degrees -gamma, was varied from gamma=0 degrees to gamma=70 degrees and influenced the phase behavior markedly. The rodlike model formed isotropic, nematic, smectic-A, and smectic-B, phases. Results for the bent-core models show that as the angle gamma increases the transition temperature to the ordered phase decreases. As gamma increases the nematic phase is first destabilized then stabilized with respect to the smectic phase and a tilted smectic-B phase is seen at gamma=20 degrees. For gamma=40 degrees a "TGB-like" phase is identified as the system cools whereas for gamma=70 degrees no ordered phase is formed.
Results are presented from molecular dynamics simulations in the NPT ensemble of novel bent-core liquid crystal systems. Following on from a previous study of bent-core steric shape, this study examines the effect the addition of a transverse electric dipole has on the phase diagram of a bent-core liquid crystal model. A simple model of the interaction employed a two-site Gay-Berne potential with the sites separated by +/-0.5 reduced units with a central transverse point dipole, for all models investigated. The angle between the sites 180 degrees -gamma was varied in a range gamma=10 degrees to gamma=70 degrees suggested by real molecules. The addition of the dipole to the model tended to stabilize smectic phases and increase the angle of tilted phases. As the angle gamma increased, the transition temperature to the first ordered phase decreased markedly. Smectic A, tilted smectic B, and a spontaneously polarized smectic B phases were observed in the gamma=10 degrees bent-core model. The gamma=20 degrees model showed smectic A and tilted antiferroelectric smectic B phases. The gamma=40 degrees model showed an antiferroelectric phase that exhibited unusual packing behavior. Both the gamma=20 degrees and gamma=40 degrees models demonstrated a significant phase biaxiality in the smectic B phases.
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