Joachim Stelzer

MOLECULAR DYNAMICS SIMULATIONS OF A GAY-BERNE NEMATIC LIQUID CRYSTAL : ELASTIC PROPERTIES FROM DIRECT CORRELATION FUNCTIONS

We report molecular dynamics simulations of a Gay–Berne nematic liquid crystal at constant temperature and density/pressure using the generalization of an algorithm recently proposed by Toxvaerd [Phys. Rev. E 47, 343 (1993)]. On the basis of these simulations the absolute values of the Oseen–Zocher–Frank elastic constants K11, K22, and K33 as well as the surface constants K13 and K24 have been calculated ab initio within the framework of the direct correlation function approach of Lipkin et al. [J. Chem. Phys. 82, 472 (1985)]. The angular coefficients of the direct pair correlation function, which enter the final equations, have been determined from the computer simulation data for the pair correlation function of the nematic by combining the Ornstein–Zernike relation and the Wiener–Hopf factorization scheme. The unoriented nematic approximation has been assumed when constructing the reference state of Lipkin et al. By an extensive study of the model over a wide range of temperatures, densities and pressu...

Water droplets in a spherically confined nematic solvent: A numerical investigation

Abstract:Recently, it was observed that water droplets suspended in a nematic liquid crystal form linear chains [Poulin et al., Science 275, 1770 (1997)]. The chaining occurs, e.g., in a large nematic drop with homeotropic boundary conditions at all the surfaces. Between each pair of water droplets a point defect in the liquid crystalline order was found in accordance with topological constraints. This point defect causes a repulsion between the water droplets. In our numerical investigation we limit ourselves to a chain of two droplets. For such a complex geometry we use the method of finite elements to minimize the Frank free energy. We confirm an experimental observation that the distance d of the point defect from the surface of a water droplet scales with the radius r of the droplet like

Density functional approach to study the elastic constants of biaxial nematic liquid crystals

d \approx 0.3r

FLEXOELECTRIC EFFECTS IN LIQUID CRYSTALS FORMED BY PEAR-SHAPED MOLECULES. A COMPUTER SIMULATION STUDY

.When the water droplets are moved apart, we find that the point defect does not stay in the middle between the droplets, but rather forms a dipole with one of them. This confirms a theoretical model for the chaining. Analogies to a second order phase transition are drawn. We also find the dipole when one water droplet is suspended in a bipolar nematic drop with two boojums, i.e., surface defects at the outer boundary. Finally, we present a configuration where two droplets repel each other without a defect between them.

Influence of surface anchoring and viscosity upon the switching behavior of twisted nematic cells

Monte Carlo simulations have been performed for a discotic liquid crystal composed of Gay–Berne particles. On the basis of these simulations for the nematic phase, a subset of the spherical harmonic expansion coefficients of the direct pair correlation function (DPCF) were determined from the pair distribution function (PDF) by solving the Ornstein–Zernike (OZ) equation. This was achieved by generalizing the Wiener–Hopf factorization scheme for the numerical solution of the OZ equation. Only the expansion coefficients gl1,l2,l(r) (lα⩽4) of the PDF in the laboratory frame were used when solving the OZ equation; this means that the DPCF so obtained is equivalent to that for a nematic in which the director is randomly distributed. From the DPCF, the scaled Oseen–Zocher–Frank elastic constants K11*, K22*, and K33*, as well as the surface constant K13*, have been calculated from the subset of expansion coefficients. Generally, we find that K33*

DIRECTOR CONFIGURATION OF PLANAR SOLITONS IN NEMATIC LIQUID CRYSTALS

A density functional theory for bulk and surface elastic constants of biaxial nematic liquid crystals is developed. It is based on a functional Taylor expansion of the free energy of a distorted biaxial nematic with respect to the one-particle distribution function. Detailed microscopic expressions for the biaxial elastic constants of bulk and surface deformations are derived by expanding further the distribution functions into symmetry-adapted Wigner matrices. The final expressions depend on generalized orientational order parameters characterizing the biaxial nematic and on expansion coefficients of the direct pair correlation function. The case where the expansions are truncated at the lowest nontrivial order with respect to the momentum index of the Wigner matrices is analyzed in detail. It gives only six distinct, nonzero bulk elastic constants. The mixed elastic constants, which measure distortions of more than one director, vanish within this approximation. As in the uniaxial case, a splay-bend deg...

Motion, creation, and annihilation of disclinations in multidomain structured nematic liquid crystal cells

Abstract The Frank-Oseen elastic constants K 11, K 22 and K 33 as well as the surface constants K 13 and K 24 have been calculated for Gay-Berne nematic liquid crystal with anisotropy parameters k = 3 and k′ = 5. In deriving the elastic constants a direct correlation function approach of Poniewierski and Stecki1 in a version proposed by Lipkin et al. 5 was choosen. The final formulas have been expressed in terms of the orientational order parameters and of the angular coefficients of the direct correlation function of an unoriented nematic. The latter have been determined exactly from the molecular dynamics simulations in the NVT ensemble. Results for the surface elastic constants, qualitatively different than those obtained from all previous treatments, clearly show that the surface deformations are strongly sensitive to details of the direct correlation function. Obtained values of surface elastic constants are partly negative and an order of magnitude smaller than bulk elastic constants.

Flexoelectric Coefficients for Model Pear Shaped Molecules from Monte Carlo Simulations

Abstract The flexoelectric effect in liquid crystals is investigated by means of Monte Carlo simulations for model pear-shaped molecules that interact through a combination of Gay–Berne and Lennard-Jones potentials. Flexoelectric coefficients are evaluated from microscopic expressions derived on the basis of a density functional approach.