The interaction between a disclination in a nematic liquid crystal and a rubbed surface

For the case of a rubbed surface with a finite anisotropic surface tension, a model is developed for the structure and energy of a surface disclination and of an edge disclination near the surface. It is found that there is an energy barrier against detaching a disclination from the surface, and also that there is a critical distance within which a disclination is attracted, and beyond which it is repelled, by the surface. These properties may provide a measurement of the anisotropy of the surface tension.     

Twist disclination loops in chiral smectic C liquid crystals

The notion of an infinitesimal twist disclination loop known from solids is introduced into a chiral smectic C liquid crystal with parallel layers. Finite rectangular and straight twist disclinations are described as a synthesis of a planar distribution of infinitesimal loops. Then a small impurity which disturbs only the molecular arrangement in one smectic layer is modelled by a pair of infinitesimal twist disclination loops. The interaction between a 2π-twist disclination and a small impurity is estimated using the interaction energy between a straight 2π-twist disclination and an infinitesimal twist disclination loop.     

The solution of a wedge disclination dipole interacting with an annular inclusion and the force acting on the disclination dipole

The interaction between a wedge disclination dipole and an elastic annular inclusion is investigated. Utilizing the Muskhelishvili complex variable method, the explicit series form solutions of the complex potentials in the matrix and the inclusion region are derived. The image force acting on the disclination dipole centre is also calculated. The influence of the location of the disclination dipole and the thickness of the annular inclusion as well as the elastic dissimilarity of materials upon the equilibrium position of the disclination dipole is discussed in detail. The results show that a stable equilibrium point of the disclination dipole near the inclusion is found for certain combinations of material constant. Moreover, the force on the disclination dipole is strongly affected by the position of the disclination dipole and the thickness of annular inclusion. The repulsion force increases （or the attraction force reduces） with the increase of the thickness of the annular inclusion. An appropriate critical value of the thickness of the annular inclusion may be found to change the direction of the force on the disclination dipole. The present solutions include previous results as special eases.     

Elastic behaviour of a wedge disclination dipole near a sharp crack emanating from a semi-elliptical blunt crack

The interaction between a wedge disclination dipole and a crack emanating from a semi-elliptic hole is investigated. Utilising the complex variable method, the closed form solutions are derived for complex potentials and stress fields. The stress intensity factor at the tip of the crack and the image force acting on the disclination dipole center are also calculated. The influence of the morphology of the blunt crack and the position of the disclination dipole on the shielding effect to the crack and the image force is examined in detail. The results indicate that the shielding or anti-shielding effect to the stress intensity factor increases when the wedge disclination dipole approaches the tip of the crack. The effects of the morphology of the blunt crack on the stress intensity factor of the crack and the image force are very significant.     

Screening of the elastic field of disclinations by a dislocation ensemble

A self-consistent dynamics of a dislocation ensemble in the disclination field is analyzed within the kinetic approach. The effective Airy stress functions for the wedge disclination and the disclination dipole with due regard for the screening effect of the system of distributed dislocation charges are determined. The coordinate dependences of the stress tensor components and dislocation charge density for the screened disclination systems are found. The elastic energies of the screened disclination systems are calculated.     

Anchoring screening of defects interaction in a nematic liquid crystal

The relaxation dynamic of a dipole of +1/2 and -1/2 parallel disclination lines in a confined geometry is measured. The confinement and the planar anchoring conditions force the disclinations to be normal to the glass plates. In a first asymptotic regime, the direct elastic interaction between disclination is completely screened out by the anchoring energy. In a second regime, corresponding to the final annihilation steps, the dynamic follows the square-root law predicted by de Gennes for two isolated and parallel disclinations. The annihilation dynamic, in the asymptotic regime, is in good agreement with an elastic model based on an electrostatic analogy.     

Magnetic-field-induced motion of disclinations in a twisted nematic layer

In a twisted nematic layer oppositely twisted regions can exist, separated by a disclination line, as demonstrated by the orientation of Williams domains. The disclination line can move under the influence of a magnetic field. Measurements of the velocity as a function of magnetic field strength and sample thickness lead to an estimate of the size of the disclination core.     

Competing relaxation mechanisms in a disclinated nanowire: temperature and size effects

This Letter reports a molecular dynamics study of the temperature and size dependence of disclination relaxation in a bicrystalline titanium nanowire. The simulations show that an unstable disclination may relax via crack nucleation and/or structural transformation. The critical disclination strength to nucleate a crack decreases with the nanowire diameter at 0 K, but an inverse relation may exist at higher temperatures. Similar relaxation mechanisms are operative in other hcp materials. The results suggest that grain boundaries in nanostructured materials can be disordered through disclinations which relax via amorphization.     

Continuous description of a grain boundary in forsterite from atomic scale simulations: the role of disclinations

We present continuous modelling at inter-atomic scale of a high-angle symmetric tilt boundary in forsterite. The model is grounded in periodic arrays of dislocation and disclination dipoles built on information gathered from discrete atomistic configurations generated by molecular dynamics simulations. The displacement, distortion (strain and rotation), curvature, dislocation and disclination density fields are determined in the boundary area using finite difference and interpolation techniques between atomic sites. The distortion fields of the O, Si and Mg sub-lattices are detailed to compare their roles in the accommodation of lattice incompatibility along the boundary. It is shown that the strain and curvature fields associated with the dislocation and disclination fields in the ‘skeleton’ O and Si sub-lattices accommodate the tilt incompatibility, whereas the elastic strain and rotation fields of the Mg sub-lattice are essentially compatible and induce stresses balancing the incompatibility stresses in the overall equilibrium.     

Line defect dynamics around a colloidal particle

We study experimentally the dynamics of a topological defect located around a colloidal particle suspended in a thermotropic nematic liquid crystal. The considered defect consists of a disclination loop encircling the particle at the equator. Under specific conditions, it is shown that this disclination continuously shrinks to a hedgehog defect located in the immediate vicinity of the particle. This phenomenon corresponds to a transition between an elastic quadrupolar configuration and an elastic dipolar configuration. We performed a basic numerical calculation to get an estimate of the dissipated energy during the transition; we compare the results with theoretical predictions that describe the elastic energy of particles surrounded by defects. Received 21 December 2001     

Atomistic simulations of the tensile strength of a disclinated bicrystalline nanofilm

The tensile strength of a metallic bicrystalline nanofilm containing a wedge disclination in the middle of a grain boundary (GB) terminating at the film surfaces was studied via atomistic simulations. The results show that an increase in the disclination power strengthens the film, which is contrary to intuition, if a crack initiates at one end of the terminated GB, whereas it weakens the film if a crack initiates at the disclination core. Both the strengthening and weakening demonstrate a size effect for film thickness in the range 10–20 nm, and are also significantly influenced by the GB misorientation. It is further shown that the strength can be increased to ～80% of the theoretical strength of a defect-free film by introducing a disclination of moderate power in the GB.     

Defects in smectic C* liquid crystals

We consider the structure and properties of various topological defects that can occur in smectic C* liquid crystals. The polarization field associated with disclinations, the effect of incommensuration on the structure of dispirations, some interesting situations in the interaction between dispiration and disclination and between dispirations themselves have been discussed in detail. The properties of cholesteric type disclinations and a possible model for the core structure of a wedge disclination have also been dealt with. The author felicitates Prof. D S Kothari on his eightieth birthday and dedicates this paper to him on this occasion.     

Twist disclination system in a planar sample of chiral smectic C* liquid crystal

In thick samples of Sm C^* liquid crystals the helicoidal structure in the sample centre is connected to the unwound structure near sample surfaces by a regular system of (?2π) and (+2π)-twist disclinations associated in rows near the upper and lower sample surfaces. The geometry and stability of such a disclination system in a high electric field is investigated and the critical electric field causing the disclination annihilation is estimated. The mutual disclination annihilation is the proposed mechanism for the field induced transition from helicoidal Sm C^* structure to unwound Sm C^* structure with the twist along the sample thickness.     

Disclination motion in liquid crystalline films

We theoretically study a single disclination motion in a thin free-standing liquid crystalline film. Backflow effects and the own dynamics of the orientational degree of freedom (bond or director angle) are taken into account. We find the orientation field and the hydrodynamic velocity distribution around the moving disclination, which allows us to relate the disclination velocity to the angle gradient far from the disclination. Different cases are examined depending on the ratio of the rotational and shear viscosity coefficients.     

Misfit dislocations in thin films on plastically deformed substrates

A theoretical model describing the nucleation of misfit dislocations (MD) in interfaces between films and plastically deformed substrates with disclinations is proposed. The ranges of the parameters (disclination strength, density of the disclination ensemble, film thickness, and degree of misfit) within which MD nucleation is energetically favorable are found. It is shown that at certain strengths of disclinations and densities of their ensemble the critical thickness of the film on a plastically deformed substrate with disclinations can exceed that on an undeformed defect-free substrate by a few times.     

On the annealing of junction disclinations in deformed polycrystals

The kinetics of relaxation of disclination quadrupoles formed within triple junctions of grains during plastic deformation are studied. The calculations are made using the discrete dislocation model for disclinations by simulating the climb of dislocations. Exponential relationships are obtained for the relaxation of the strength and elastic energy of disclination quadrupoles with a characteristic time proportional to the cube of grain size. The distribution of vacancy fluxes along grain boundaries (GBs) during the relaxation of a disclination quadrupole is studied in detail. The relation between continuum and discrete dislocation approaches to a study of the GB recovery process is considered. Characteristics of each relaxation stage are studied. A hierarchy of characteristic relaxation times for dimerent grain size ranges is constructed and it is show that in nanocrystalline materials the spreading time of trapped lattice dislocations can depend on the grain size.     

Elastic behaviour of a wedge sharp crack emanating from a disclination dipole near a semi-elliptical blunt crack

The interaction between a wedge disclination dipole and a crack emanating from a semi-elliptic hole is investigated. Utilising the complex variable method, the closed form solutions are derived for complex potentials and stress fields. The stress intensity factor at the tip of the crack and the image force acting on the disclination dipole center are also calculated. The influence of the morphology of the blunt crack and the position of the disclination dipole on the shielding effect to the crack and the image force is examined in detail. The results indicate that the shielding or anti-shielding effect to the stress intensity factor increases when the wedge disclination dipole approaches the tip of the crack. The effects of the morphology of the blunt crack on the stress intensity factor of the crack and the image force are very significant.     

Controlled nucleation of point defects on a disclination line near a free surface during smectic-A-to-nematic directional melting

A disclination line populated with point defects that break the translational symmetry forms near a free nematic (N) interface in a confined geometry. The disclination line is, however, absent in the smectic-A phase (SmA). We use this fact to control the formation of point defect distributions on a disclination line by directional melting of the SmA phase in a temperature gradient. A threshold velocity ( v _th) exists below which a defect-free disclination line is formed. The frequency of nucleation of point defects increases steadily for v > v _th and exhibits a remarkable regularity. We derive an empirical scaling for v _th in terms of the experimental tuning parameters. We propose a simple model that allows to understand the formation of the point defects. Received 1 October 2002 / Published online: 15 April 2003 RID="a" ID="a"Permanent address: Departament de Quımica Fısica, Universitat de Barcelona, Martı i Franquès 1, Barcelona 08028, Spain; e-mail: jignes@qf.ub.es