Milan Ambrožič

Memory effects in randomly perturbed systems exhibiting continuous symmetry breaking

We studied pattern characteristics in randomly perturbed structures exhibiting continuous symmetry breaking. A Lebwohl–Lasher‐type lattice model was used which described well the onset of orientational ordering of a system of rod‐like objects. For example, such systems mimic the orientational ordering tendency in liquid crystals or in an ensemble of nanotubes. We set impurities to impose a random anisotropy type of disorder on the objects. Structural characteristics were studied as a function of concentration of impurities, interaction strength w between impurities and rod‐like objects, external ordering strength and history of samples. We showed that the characteristic linear size of patterns and range of ordering strongly depend on the history of samples for weak enough strength w. The two‐dimensional and three‐dimensional simulations yielded qualitatively similar results.

Impact of Nanoparticles on Nematic Ordering in Square Wells

Nematic liquid crystalline structures within square wells are studied numerically using both Lebwohl-Lasher lattice semimicroscopic and the Landau-de Gennes mesoscopic approach. At lateral boundary wall strong planar anchoring is enforced. The cell thickness h along the z Cartesian coordinate is assumed to be smaller than the characteristic square well size R. Using semimicroscopic modelling we restrict to effectively two-dimensional systems which we study in terms of the tensor nematic order parameter. We consider impact of appropriate nanoparticles (NPs) on nematic configuration for cases where R becomes comparable to the biaxial order parameter correlation length. In this case a star-like order reconstruction biaxial profile could be formed in absence of NPs. We demonstrate existence of a rich variety of different nematic structures, including topological defects, which are enabled by presence of appropriate NPs.

Competition between local disordering and global ordering fields in nematic liquid crystals.

Summary We study the influence of external electric or magnetic field B on orientational ordering of nematic liquid crystals or of other rod-like objects (e.g. nanotubes immersed in a liquid) in the presence of random anisotropy field type of disorder. The Lebwohl–Lasher lattice type of semi-microscopic approach is used at zero temperature. Therefore, results are valid well below the transition into the isotropic phase. We calculate the correlation function of systems as a function of B, concentration p of impurities imposing random anisotropy field disorder, the disorder strength W and system dimensionality (2D and 3D systems). In order to probe memory effects we calculate correlation length ξ for random and homogeneous initial configurations. We determine the crossover fields B c(p) separating roughly the ordered and disordered regime. Memory effects are apparent only in the latter case, i.e. for B < B c. PACS numbers: 47.51.+a, 47.54.-r, 07.05.Tp, 61.30.-v

Interference textures of defects in a thin nematic film: an applet presentation

We have developed an applet presentation showing different structures of a nematic liquid crystal confined to a thin transparent plan-parallel cell. The nematic structures possessing single defects or their pairs may be studied. The corresponding interference textures are shown simulating the polarization optic microscopy experiment. Several parameters defining the experimental set-up can be interactively varied enabling observation of subsequent changes in the interference pattern within a reasonable real time. The basic physics of liquid crystal defects necessary for understanding the limitations of the applet presentation is given.

History-Dependent Patterns in Randomly Perturbed Nematic Liquid Crystals

We study the characteristics of nematic structures in a randomly perturbed nematic liquid crystal (LC) phase. We focus on the impact of the samples history on the universal behavior. The obtained results are of interest for every randomly perturbed system exhibiting a continuous symmetry-breaking phase transition. A semimicroscopic lattice simulation is used where the LC molecules are treated as cylindrically symmetric, rod-like objects interacting via a Lebwohl-Lasher (LL) interaction. Pure LC systems exhibit a first order phase transition into the orientationally ordered nematic phase at on lowering the temperature . The orientational ordering of LC molecules is perturbed by the quenched, randomly distributed rod-like impurities of concentration . Their orientation is randomly distributed, and they are coupled with the LC molecules via an LL-type interaction. Only concentrations below the percolation threshold are considered. The key macroscopic characteristics of perturbed LC structures in the symmetry-broken nematic phase are analyzed for two qualitatively different histories at . We demonstrate that, for a weak enough interaction among the LC molecules and impurities, qualitatively different history-dependent states could be obtained. These states could exhibit either short-range, quasi-long-range, or even long-range order.

Domain Patterns in Homogeneous and Random Perturbed Nematic Liquid Crystals: A Simulation Study

We have simulated lattice models of homogenous and randomly perturbed systems exhibiting continuous symmetry breaking, concentrating on domain sizes and configuration character. The system consists of rod-like objects within a cubic lattice interacting via a Lebwohl–Lasher-type interaction at temperature T, but including impurities at concentration p imposing a random anisotropy field-type disorder, coupled with anchoring strength W to neighboring host director molecules. An example of such systems represents nematic LC or nanotubes. We study molecular domain patterns as a function of p, W, T, and sample history. Histories are defined either by a temperature-quenched history (TQH), a field-quenched history (FQH) or from an annealed history (AH). Finite size-scaling is used to determine the nature of the orientational ordering correlations. We distinguish three different kinds of phase. Short ranged order (SRO) implies exponential decay of orientational correlations. Quasi-long-range order (QLRO) sustains algebraic decay of orientational correlations. True long-range order (LRO) implies a non-zero order parameter in the thermodynamic limit in the absence of an external field. In the TQH case for particular values of p and W, we find SRO or QLRO, with possible LRO at very low W and p. For FQH, in the limit of very low W and p, we observe LRO, which gives way to an SRO regime with increasing p and W. Comparing FQH and TQH histories at particular values of T, we saw QLRO and SRO respectively. The crossover between regimes depends on history, but in general, the FQH yields a more ordered phase than the AH, which in turn yields a more ordered phase than the TQH. In phases in which SRO occurs, the orientational correlation length in the weak-disorder limit obeys universal Imry-Ma scaling ξd ∼ W− 2/(4 − d).

Field Induced Memory Effects in Random Nematics

We studied numerically external field induced memory effects in randomly perturbed nematic liquid crystals. Random anisotropy nematic-type lattice model was used. The impurities imposing orientational disorder were randomly spatially distributed with the concentration below the percolation threshold. Simulations were carried for finite temperatures, where we varied , interaction strength between LC molecules, and impurities and external field . In the plane we determined lines separating short range—quasi long range and quasi long range—long range order. Furthermore, crossover regime separating external field and random field dominated regime was estimated. We calculated remanent nematic ordering in samples at as a function of the previously experienced external field strength .

Visualization of Nematic Director Field With the RGB Color System

The two-dimensional presentation of the three-dimensional nematic liquid crystal structure can be visualized in various ways: by oriented rotational ellipsoids, bricks, cylinders, or sticks, representing either individual molecules or nematic director field. Here, we give a different approach: the three axes of Cartesian coordinate system are assigned with three colors (red for x-axis, green for y-axis and blue for z-axis). We use the proportional mixing of these colors for various directions of the nematic director. Using this technique, different structures of nematic liquid crystals can be visualized clearly, particularly when combined with representation of nematic director field with sticks.

Higher Mathematics in Physics

In physics all the laws and theorems connected with the physical quantities which vary in space and time, can be written with differential equations. These can be ordinary or partial, scalar or vector, but in several cases there is a system of a few or many coupled differential equations, depending on the dimension and complexity of the physical problem. While the differential equations are the local form of writing physical laws, the integral equations contain the whole space or time, or a definite space and time area. A typical example of writing equations in both forms is a set of Maxwell equations in electromagnetism or variational calculus connected with the minimization of the free energy. By setting and solving (analytically or numerically) these equation we can capture all the areas of physics, from mechanics and movement of point-like bodies, where the special physical branch called analytical mechanics introduces the concepts of generalized coordinates and impulses, Lagrangian and Hamiltonian, up to treatment of scalar and vector fields in electromagnetism and wave optics, quantum physics, thermodynamics, physics of fluids, probability theory etc.

Random nematic structures in the absence of inherent frustrations

We study the impact of anisotropic nanoparticles (NPs) on the nematic liquid crystal (LC) order. Within a mesoscopic Flory–Huggins-type approach we have estimated regimes where LC–NP mixtures are essentially homogenous. Using a lattice Lebwohl–Lasher type approach we have also studied the impact of anisotropic NPs on LC ordering. We analysed the cases where the orientations of NPs are either frozen-in or could be varied, to which we refer as random field mixtures and annealed mixtures, respectively. In the latter case we have demonstrated the existence of qualitatively different regimes. In particular, we determined the concentration regime, where LC configurations resembling a transparent nematic phase could be observed. Such domain patterns are stabilised by NPs hindering the annihilation of topological defects in LC order.