Light scattering by optically anisotropic scatterers II: T--matrix computations for radially and uniformly anisotropic droplets

This is the second paper in a series on light scattering from optically anisotropic scatterers embedded in an isotropic medium. The apparently complex T-matrix theory involving mixing of angular momentum components turns out to be an efficient approach to calculating scattering in these systems. We present preliminary results of numerical calculations of the scattering by spherical droplets in some simple cases. The droplets contain optically anisotropic material with local radial or uniform anisotropy. We concentrate on cases in which the scattering is due only to the local optical anisotropy within the scatterer. For radial anisotropy we find non-monotonic dependence of the scattering cross-section on the degree of anisotropy can occur in a regime for which both the Rayleigh and semi-classical theories are inapplicable. For uniform anisotropy the cross-section is strongly dependent on the angle between the incident light and the optical axis, and for larger droplets this dependence is non-monotonic.Comment: 14 pages, 6 figures, uses RevTex

Computational studies of history-dependence in nematic liquid crystals in random environments

Glassy liquid crystalline systems are expected to show significant history-dependent effects. Two model glassy systems are the RAN and SSS (sprinkled silica spin) lattice models. The RAN model is a Lebwohl-Lasher lattice model with locally coupled nematic spins, together with uncorrelated random anisotropy fields at each site, while the SSS model has a finite concentration of impurity spins frozen in random directions. Here Brownian simulation is used to study the effect of different sample histories in the low temperature regime in a three-dimensional (d=3) model intermediate between SSS and RAN, in which a finite concentration p<pc (pc the percolation threshold) of frozen spins interacts with neighboring nematic spins with coupling W. Simulations were performed at temperature T?TNI/2 (TNI the bulk nematic-isotropic transition temperature) for temperature-quenched and field-quenched histories (TQH and FQH, respectively), as well as for temperature-annealed histories (AH). The first two of these limits represent extreme histories encountered in typical experimental studies. Using long-time averages for equilibrated systems, we calculate orientational order parameters and two-point correlation functions. Finite-size scaling was used to determine the range of the orientational ordering, as a function of coupling strength W,p and sample history. Sample history plays a significant role; for given concentration p, as disorder strength W is increased, TQH systems sustain quasi-long-range order (QLRO) and short-range order (SRO). The data are also consistent with a long-range order (LRO) phase at very low disorder strength. By contrast, for FQH and p?0.1, only LRO and QLRO occur within the range of parameters investigated. The crossover between regimes depends on history, but in general, the FQH phase is more ordered than the AH phase, which is more ordered than the TQH phase. However, at temperatures close to the isotropic-nematic phase transition of pure samples we observe SRO for p=0.1 even for FQH. We detect also in the QLRO phase a domain-type structural pattern, consistent with ideas introduced by Giamarchi and Doussal [Phys. Rev. B 52, 1242 (1995)] on superconducting flux lattices. In the weak-disorder limit the orientational correlation length obeys the Larkin-Imry-Ma scaling ??D?2/(4?d)

Liquid crystal anchoring transitions on aligning substrates processed by plasma beam

We observe a sequence of the anchoring transitions in nematic liquid crystals (NLC) sandwiched between the hydrophobic polyimide substrates treated with the plasma beam. There is a pronounced continuous transition from homeotropic to low tilted (nearly planar) alignment with the easy axis parallel to the incidence plane of the plasma beam (the zenithal transition) that takes place as the exposure dose increases. In NLC with positive dielectric anisotropy, a further increase in the exposure dose results in in-plane reorientation of the easy axis by 90 degrees (the azimuthal transition). This transition occurs through the two-fold degenerated alignment characteristic for the second order anchoring transitions. In contrast to critical behavior of anchoring, the contact angle of NLC and water on the treated substrates monotonically declines with the exposure dose. It follows that the surface concentration of hydrophobic chains decreases continuously. The anchoring transitions under consideration are qualitatively interpreted by using a simple phenomenological model of competing easy axes which is studied by analyzing anchoring diagrams of the generalized polar and non-polar anchoring models.Comment: revtex4, 18 pages, 10 figure

Surface alignment and anchoring transitions in nematic lyotropic chromonic liquid crystal

The surface alignment of lyotropic chromonic liquid crystals (LCLCs) can be not only planar (tangential) but also homeotropic, with self-assembled aggregates perpendicular to the substrate, as demonstrated by mapping optical retardation and by three-dimensional imaging of the director field. With time, the homeotropic nematic undergoes a transition into a tangential state. The anchoring transition is discontinuous and can be described by a double-well anchoring potential with two minima corresponding to tangential and homeotropic orientation.Comment: Accepted for publication in Phys. Rev. Lett. (Accepted Wednesday Jun 02, 2010

Influence of Homeotropic Anchoring Walls upon Nematic and Smectic Phases

McMillan liquid crystal model sandwiched between strong homeotropic anchoring walls is studied. Phase transitions between isotropic, nematic, and smectic A phases are investigated for wide ranges of an interaction parameter and of the system thickness. It is confirmed that the anchoring walls induce an increase in transition temperatures, dissappearance of phase transitions, and an appearance of non-spontaneous nematic phase. The similarity between influence of anchoring walls and that of external fields is discussed.Comment: 5 pages, 6 figure

Annihilation of edge dislocations in smectic A liquid crystals

This paper presents a theoretical study of the annihilation of edge dislocations in the same smectic plane in a bulk smectic-A phase. We use a time-dependent Landau-Ginzburg approach where the smectic ordering is described by the complex order parameter psi( r--> ,t) =eta e(iphi) . This quantity allows both the degree of layering and the position of the layers to be monitored. We are able to follow both precollision and postcollision regimes, and distinguish different early and late behaviors within these regimes. The early precollision regime is driven by changes in the phi ( r--> ) configuration. The relative velocity of the defects is approximately inversely proportional to the interdefect separation distance. In the late precollision regime the symmetry changes within the cores of defects also become influential. Following the defect collision, in the early postcollision stage, bulk layer order is approached exponentially in time. At very late times, however, there seems to be a long-time power-law tail in the order parameter fluctuation relaxation

Photoinduced ordering and anchoring properties of azo-dye films

We study both theoretically and experimentally anchoring properties of photoaligning azo-dye films in contact with a nematic liquid crystal depending on photoinduced ordering of azo-dye molecules. In the mean field approximation, we found that the bare surface anchoring energy linearly depends on the azo-dye order parameter and the azimuthal anchoring strength decays to zero in the limit of vanishing photoinduced ordering. From the absorption dichroism spectra measured in the azo-dye films that are prepared from the azo-dye derivative with polymerizable terminal groups (SDA-2) we obtain dependence of the dichroic ratio on the irradiation dose. We also measure the polar and azimuthal anchoring strengths in nematic liquid crystal (NLC) cells aligned by the azo-dye films and derive the anchoring strengths as functions of the dichroic ratio. Though linear fitting of the experimental data for both anchoring strengths gives reasonably well results, it, in contradiction with the theory, predicts vanishing of the azimuthal anchoring strength at certain nonzero value of the azo-dye order parameter. By using a simple phenomenological model we show that this discrepancy can be attributed to the difference between the surface and bulk order parameters in the films.Comment: revtex4, 25 pages, 9 figure

Binary separation in very thin nematic films: thickness and phase coexistence

The behavior as a function of temperature of very thin films (10 to 200 nm) of pentylcyanobiphenyl (5CB) on silicon substrates is reported. In the vicinity of the nematic/isotropic transition we observe a coexistence of two regions of different thicknesses: thick regions are in the nematic state while thin ones are in the isotropic state. Moreover, the transition temperature is shifted downward following a 1/h^2 law (h is the film thickness). Microscope observations and small angle X-ray scattering allowed us to draw a phase diagram which is explained in terms of a binary first order phase transition where thickness plays the role of an order parameter.Comment: 5 pages, 3 figures, submitted to PRL on the 26th of Apri

Polydispersity and ordered phases in solutions of rodlike macromolecules

We apply density functional theory to study the influence of polydispersity on the stability of columnar, smectic and solid ordering in the solutions of rodlike macromolecules. For sufficiently large length polydispersity (standard deviation $\sigma>0.25$) a direct first-order nematic-columnar transition is found, while for smaller $\sigma$ there is a continuous nematic-smectic and first-order smectic-columnar transition. For increasing polydispersity the columnar structure is stabilized with respect to solid perturbations. The length distribution of macromolecules changes neither at the nematic-smectic nor at the nematic-columnar transition, but it does change at the smectic-columnar phase transition. We also study the phase behaviour of binary mixtures, in which the nematic-smectic transition is again found to be continuous. Demixing according to rod length in the smectic phase is always preempted by transitions to solid or columnar ordering.Comment: 13 pages (TeX), 2 Postscript figures uuencode

Beam coupling in hybrid photorefractive inorganic-cholesteric liquid crystal cells: impact of optical rotation

We develop a theoretical model to describe two-beam energy exchange in a hybrid photorefractive inorganic-cholesteric cell. A cholesteric layer is placed between two inorganic substrates. One of the substrates is photorefractive (Ce:SBN). Weak and strong light beams are incident on the hybrid cell. The interfering light beams induce a periodic space-charge field in the photorefractive window. This penetrates into the cholesteric liquid crystal (LC), inducing a diffraction grating written on the LC director. In the theory, the flexoelectric mechanism for electric field-director coupling is more important than the LC static dielectric anisotropy coupling. The LC optics is described in the Bragg regime. Each beam induces two circular polarized waves propagating in the cholesteric cell with different velocities. The model thus includes optical rotation in the cholesteric LC. The incident light beam wavelength can fall above, below, or inside the cholesteric gap. The theory calculates the energy gain of the weak beam, as a result of its interaction with the pump beam within the diffraction grating. Theoretical results for exponential gain coefficients are compared with experimental results for hybrid cells filled with cholesteric mixture BL038/CB15 at different concentrations of chiral agent CB15. Reconciliation between theory and experiment requires the inclusion of a phenomenological multiplier in the magnitude of the director grating. This multiplier is cubic in the space-charge field, and we provide a justification of the q-dependence of the multiplier. Within this paradigm, we are able to fit theory to experimental data for cholesteric mixtures with different spectral position of cholesteric gap relative to the wavelength of incident beams, subject to the use of some fitting parameters