Molecular organization of nematic liquid crystals between concentric cylinders: Role of the elastic anisotropy

The orientational order in a nematic liquid crystal sample confined to an annular region between two concentric cylinders is investigated by means of lattice Monte Carlo simulations. Strong anchoring and homeotropic orientations, parallel to the radial direction, are implemented at the confining surfaces. The elastic anisotropy is taken into account in the bulk interactions by using the pair potential introduced by Gruhn and Hess [T. Gruhn and S. Hess, Z. Naturforsch. A 51, 1 (1996)] and parametrized by Romano and Luckhurst [S. Romano, Int. J. Mod. Phys. B 12, 2305 (1998)IJPBEV0217-979210.1142/S0217979298001344; Phys. Lett. A 302, 203 (2002)PYLAAG0375-960110.1016/S0375-9601(02)01042-3; G. R. Luckhurst and S. Romano, Liq. Cryst. 26, 871 (1999)LICRE60267-829210.1080/026782999204561], i.e., the so-called GHRL potential. In the case of equal elastic constants, a small but appreciable deformation along the cylinder axis direction is observed, whereas when the values of K11/K33 if K22=K33 are low enough, all the spins in the bulk follow the orientation imposed by the surfaces. For larger values of K11/K33, spontaneous deformations, perpendicular to the polar plane, increase significantly. Our findings indicate that the onset of these deformations also depends on the ratio K22/K33 and on the radius of the cylindrical surfaces. Although expected from the elastic theory, no tangential component of the deformations was observed in the simulations for the set of parameters analyzed

Concerning some integrals of the generalized exponential-integral function

AbstractThis paper deals with some integrals involving the generalized exponential integral, Eν(x), which are of interest for applications. New relations have been derived by generalizing known expressions valid for ν = n integer. Numerical results are also given, which extend existing tables to the entire real domain

A numerical method for generalized exponential integrals

Abstract We present a method for evaluation of the exponential integral, E s ( x ), generalized to an arbitrary order s > 0. The algorithm is valid whatever s > 0 and x > 0. In the region x ⩾ 1, we start from a proper initial value, obtained by asymptotic calculation, and then compute the required E s ( x ) by means of a suitable combination of Taylor's expansions and recurrences, whatever s > 0. When x s 0 ( x ) (0 s 0 ⩽ 1), which is obtained by the means of suitable expansions. A forward recursion finally yields the required E s ( x ). Numerical stability and accuracy of the proposed algorithm are discussed and some results given

Hybridly Aligned Liquid Crystal Films. A Monte Carlo Study of Molecular Organization and Thermodynamics

Abstract A Monte Cario simulation of a nematic Lebwohl-Lasher hybrid liquid crystal film, confined between two surfaces with antagonistic anchoring alignment, is presented. We have calculated the ordering and the molecular organization inside the film for different lateral sizes. The influence of these boundary conditions on the nematic isotropic phase transition is also investigated

Recent results for generalized exponential integrals

Abstract Basic properties of the exponential-integral function of real order, Ev(x), and relevant expressions for evaluating this special function are presented. The mathematical results have been essentially obtained by generalizing known formulae valid for the usual exponential-integral, En(x)

Computer simulations of nematic droplets with toroidal boundary conditions

We present Monte Carlo simulations of nematic droplets with toroidal boundary conditions (TBC) and various anchoring strengths and we investigate the orientational order and the molecular organizations in these systems that mimic polymer dispersed liquid crystals (PDLC). PACS: 02.50 Monte Carlo studies PACS: 61.30.Jf Defects in liquid crystals PACS: 61.30.Gd Orientational order of liquid crystals PACS: 64.70.M Liquid Crystals phase transition

Method of Monte Carlo grid for data analysis

This paper presents an analysis procedure for experimental data using theoretical functions generated by Monte Carlo. Applying the classical chi-square fitting procedure for some multiparameter systems is extremely difficult due to a lack of an analytical expression for the theoretical functions describing the system. The proposed algorithm is based on the least square method using a grid of Monte Carlo generated functions each corresponding to definite values of the minimization parameters. It is used for the E742 experiment (TRIUMF, Vancouver, Canada) data analysis with the aim to extract muonic atom scattering parameters on solid hydrogen.Comment: 16 pages, 10 figures, submitted to NI

Monte Carlo Simulations of Model Nematic Droplets

Abstract We present Monte Carlo computer simulations of model nematic droplets with radial boundary conditions and various anchoring strengths and we investigate the orientational order and the molecular organizations in these systems that mimic polymer dispersed liquid crystals (PDLC). We find a hedgehog organization at high anchoring strengths and that an ordered domain is created in the droplet center at lower strengths

NMR spectra from Monte Carlo simulations of polymer dispersed liquid crystals

We present the calculation of NMR line shapes, including dynamical effects, of polymer dispersed liquid crystals starting from the Monte Carlo configurations simulated for a lattice spin model. We consider droplets with radial, bipolar, and random boundary conditions and examine to what extent their predicted deuterium NMR spectra differ in the presence of molecular motion

Dynamical and field effects in polymer-dispersed liquid crystals: monte carlo simulations of NMR spectra

We analyze the dynamical aspects of molecular ordering in nematic droplets with radial and bipolar boundary conditions---as encountered in polymer-dispersed liquid crystals---by calculating and interpreting the corresponding ${}^{2}\mathrm{H}$ NMR spectra. In particular, we focus on effects of molecular motion such as fluctuations of molecular long axes and translational diffusion, and on external field ordering effects. As in our previous paper [Phys. Rev. E 60, 4219 (1999)], where field effects were not considered, equilibrium configurations inside nematic droplets are obtained from Monte Carlo simulations of the Lebwohl-Lasher lattice spin model