Dimer structures formed in smectic films by inclusions with parallel and antiparallel topological dipole moments

Self-organization of cholesteric and nematic droplets in smectic free-standing films is investigated. Strong tangential anchoring at the droplet boundary leads to nucleation of a topological defect and formation of a topological dipole from the droplet and the defect. The interaction between droplets results in assembly of the droplets in dimers and line chains. Topological dipoles of the droplet-defect pairs can be oriented in dimers with polar (ferroelectric) and nonpolar (antiferroelectric) ordering. In this paper we found novel dimer structures formed by droplets with different handedness of the c-director field near the droplets. Depending on the relative magnitude of the droplet dipoles the resulting structure may be dipolar or quadrupolar. Formation of antiferroelectric dimers is discussed on the basis of electromagnetic analogy.     

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

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 .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. Received 11 December 1998     

Different mechanisms of nucleation and self-organization of droplets in ferroelectric smectic membranes

New mechanisms of droplet nucleation and self-organization in ferroelectric membranes are described. The droplets may be accompanied by different number of topological defects (zero, one, two) whose location may be on the droplet boundary or in the membrane. Nucleation and self-organization of droplets with total topological charge S = 0 , S = + 1 and S = - 1 were investigated. We found that an S = - 1 topological defect may be the center of both droplet nucleation and chain formation. This mechanism of chaining drastically differs from the droplet self-organization described earlier which is realized by attraction of droplet-defect pairs. Our observations demonstrate new possibilities for manipulating the inclusions and their self-organization in smectic membranes.     

Chain structures and clusters of particles with the mixed dipole–quadrupole interaction in smectic freely suspended nanofilms

The formation of unusual chain structures and clusters of particles with the mixed dipole–quadrupole interaction has been found in smectic nanofilms. Unlike topological dipoles and quadrupoles, the interaction between which leads to the formation of structures with finite interparticle distances, the particles with the mixed interaction touch each other and form stable chains and two-dimensional clusters. The orientation of particles in chains is intermediate between dipole and quadrupole chains. The variation of the interparticle distance and orientation of chains is explained qualitatively on the basis of the calculation of the с-director (field lines) near particles and the mutual arrangement of particles providing the minimum distortion of field lines.     

Morphologies of Fe-66.7 at.%Si alloy solidified in a drop tube

Solidification of 0.1–1.0 mm diameter droplets of Fe-66.7 at.%Si alloy was achieved in a 3 m drop tube. The XRD, EDS, and SEM measurements reveal that all the droplets are composed of the primary phase α and the α+ε eutectic. With decreasing droplet diameter, the growth mode of the primary phase α changes from faceted to nonfaceted growth and the eutectic changes from needle-like to anomalous eutectic. In addition, the width of the primary phase α decreases with decreasing droplet size. The different cooling rates and undercooling levels corresponding to the samples with different sizes are responsible for the morphology changes. The cooling rates of the samples with different diameters during free fall were calculated and their effects on the microstructure formation were discussed. This kind of transition is also found inside the same sample, which is due to the larger cooling rate on the surface than at the center.     

Field dependent shape variation of magnetic fluid droplets on magnetic dots

The morphology of magnetic fluid droplets on magnetic thin film dots is studied experimentally, including the aspect ratio and the contact angle variation of the droplets. Under a uniform external magnetic field, the droplet's aspect ratio increases with the external field and with the diameter of the magnetic dot due to the concentrated magnetic flux inside the magnetic fluid droplet. Similar to the electrical wetting phenomenon, the induced magnetic dipoles in the magnetic film and in the magnetic fluid near the solid–liquid interface change the solid–liquid interfacial tension, and in consequence reduce the apparent contact angle of the magnetic fluid droplet.     

Smectic islands in antiferroelectric nanofilms

Heterochiral islands, in which topological dipoles are oppositely directed, are observed in freestanding antiferroelectric (SmC _A ^*) films. The topological dipoles in films with a transverse electric polarization and a planar molecule orientation at island boundaries are coplanar with an electric field. The topological dipoles in films with a longitudinal polarization and a planar orientation at island boundaries are perpendicular to an electric field. For a radial director orientation at island boundaries, the topological dipoles in films with a longitudinal polarization are coplanar with a field. Changing the orientation of an electric field, we can control the position of a topological defect at an island boundary and the orientation of a topological dipole. Heterochiral islands can form dimers with an anomalously small interisland distance.     

Stability of cellulose lyotropic liquid crystal emulsions

We studied a new kind of W/O emulsions based on a lyotropic liquid crystal as the aqueous droplet phase. The cholesteric phase, a solution hydroxypropyl cellulose in water was dispersed in the continuous oil matrix, paraffin oil or heptane. We made a specific choice of surfactant in order to impose director anchoring conditions at the oil-water interface and orient the liquid crystal inside the droplet. The strong anchoring conditions resulted in a topological defect inside the droplets of size above the critical value R^*. The defect elastic energy creates a barrier against droplet coalescence, the effect of topological size selection. We have studied the orientation of the director inside the droplets and their size distribution.     

Structure of connections of single-walled carbon nanotubes with the use of the combined 5–7 and 4–8 topological defects

The structures of zigzag-zigzag, armchair-zigzag, zigzag-chiral, armchair-armchair, armchair-chiral, and chiral-chiral pair connections produced by single-walled carbon nanotubes 1.5–5.0 diameter with the use of the combined 5–7 and 4–8 topological defects have been calculated by molecular mechanics methods. It has been established that the use of the combined 5–7 topological defect makes it possible to produce connections between pairs of single-walled carbon nanotubes with any conductivities, chiralities, and diameters, whereas the use of the combined 4–8 topological defect provides a means for forming connections between nanotubes only with the same type of conductivity. The angles between the axes of nanotubes connected by the combined 5–7 and 4–8 topological defects lie in the ranges 145°–180° and 112°–178°, respectively. It has been revealed that there are correlations between structural parameters of the connections and the relative arrangement of the simple topological defects in the combined topological defects.     

Lattice defects in natural α-spodumene

Summary Experiments on the thermoluminescent emission of samples of natural α-spodumene show the presence of a large density of defects. Comparison with defect density in synthetic β-spodumene indicates that in natural α-spodumene defects are not in thermodynamic equilibrium.     

Coexistence of two colloidal crystals at the nematic-liquid-crystal-air interface

Glycerol droplets at a nematic-liquid-crystal-air interface form two different lattices--hexagonal and dense quasihexagonal--which are separated by the energy barrier and can coexist. Director distortions around each droplet form an elastic dipole. The first order transition between the two lattices is driven by a reduction of the dipole-dipole repulsion through reorientation of these dipoles. The elastic-capillary attraction is essential for the both lattices. The effect has a many-body origin.     

铁磁绝缘体间的极薄Bi2Se3薄膜的相变研究

研究一个极薄三维拓扑绝缘体Bi₂Se₃薄膜处于两个铁磁绝缘体层之间, 其铁磁层的磁化方向都处于竖直平面, 系统拓扑性质随磁化方向夹角的变化. 从表面态电子低能有效哈密顿量出发计算系统的Chern 数, 和运用一个具有Armchair边界的单层六角晶格带的紧束缚模型模拟系统的体能带和边缘态, 来确定系统所处的拓扑相. 发现两个铁磁层的磁化方式从平行转到反平行的某一临界角度, 系统经历从反常量子霍尔相到普通绝缘相的转变.     

Colloidal dipolar interactions in 2D smectic-C films

We use a two-dimensional (2D) elastic free energy to calculate the effective interaction between two circular disks immersed in smectic-C films. For strong homeotropic anchoring, the distortion of the director field caused by the disks generates topological defects that induce an effective interaction between the disks. We use finite elements, with adaptive meshing, to minimize the 2D elastic free energy. The method is shown to be accurate and efficient for inhomogeneities on the length scales set by the disks and the defects, that differ by up to 3 orders of magnitude. We compute the effective interaction between two disk-defect pairs in a simple (linear) configuration. For large disk separations, D, the elastic free energy scales as ∼D ^-2, confirming the dipolar character of the long-range effective interaction. For small D the energy exhibits a pronounced minimum. The lowest energy corresponds to a symmetrical configuration of the disk-defect pairs, with the inner defect at the mid-point between the disks. The disks are separated by a distance that is twice the distance of the outer defect from the nearest disk. The latter is identical to the equilibrium distance of a defect nucleated by an isolated disk. Received 26 October 2001 and Received in final form 14 December 2001     

Macroscopic vortex droplets in Bi2Sr2CaCu2O8 crystals pumped by an ac magnetic field

The formation of droplets (or breathers) of vortex matter in Bi(2)Sr(2)CaCu(2)O(8) crystals pumped by the low-frequency ac magnetic field is observed by magneto-optic imaging. The droplets nucleate at the points of crossing the planar defects. The magnetic flux in the droplet and the droplet size increase with time. When the flux in the droplet exceeds a critical value, the droplet shifts along the defect to the sample bulk and a new droplet with the opposite flux direction starts to nucleate at the same point. As a result, a beadlike structure of the droplets arises along the defect. A possible explanation of the phenomenon is proposed.     

Collective effects accompanying magnetization of two-dimensional lattices of nanosize magnetic particles

Collective effects arising in a two-dimensional lattice of nanosize magnetic particles as a result of the dipole interparticle interaction are investigated by Hall magnetometry. The experimental system consists of 10⁵ permalloy particles having a diameter of ∼40 nm and a height of ∼40 nm and forming a lattice with a rectangular unit cell (90 nm×180 nm). We attribute the characteristic features observed in the magnetization curves to quasi-one-dimensionality of the experimental lattice of particles and to the formation of solitons in chains of dipoles. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 6, 475–479 (25 September 1998)     

Breathers in the one-dimensional roll structure of twisted nematics

The dynamics of nonsingular defects has been studied experimentally and theoretically in the periodic roll structures arising at electroconvection in nematic liquid crystals twisted by π/2. The presence of an axial component of the velocity of the hydrodynamic flow with the opposite direction in the neighboring rolls is characteristic of roll structures in twisted nematics. The quantitative estimates of the critical frequency of the oscillations of structural defects have been obtained on the basis of the nonlinear equation of motion for the roll displacement. It has been found that the periodic creation and annihilation of a pair of edge dislocations with the topological indices +1 and −1 occur in the process of oscillations of a defect with a nonsingular nucleus. It has been demonstrated that oscillating defects with zero topological indices correspond to the solution of the sine-Gordon equation in the form of standing breathers.     

Studies of linear correlation factor of dielectric polarization and excess dipolar free energies of amides in apolar solvents

The Kirkwood-Frohlich correlation factor (g), Eyring’s parametersG and G^* and the dipolar excess free energies of dilute solutions of formamide, acetamide,N-methyl acetamide,N,N-dimethyl formamide andN,N-dimethyl acetamide in 1,4-dioxan/benzene were obtained from a measurement of their static dielectric permittivities at 308 K. The fluid structure of these amides is discussed. Both in formamide and acetamide a dimeric linear chain with the individual dipoles more or less parallely oriented is preferred. InN-methyl acetamide, the antiparallel orientation of dipoles at lower concentrations turns into a parallel orientation with increase of concentration. In tertiary amides, with increase of concentration, parallel orientation of dipoles with global value ofg tending to unity is observed. The dipolar excess free energy of mixing in a given solvent is of the order primary amide > secondary amide > tertiary amide.     

Energy losses of dipoles traveling relative to a moving medium

We consider the radiation from nonoscillating dipoles traveling with constant velocity directed parallel or antiparallel to the velocity of a homogeneous transparent moving medium. It is assumed that the medium in its rest frame is isotropic and has no spatial dispersion. We obtain expressions for the radiative energy losses and estimate the polarization energy losses of electric and magnetic dipoles of different orientations. In particular, it is shown that the energy loss of a source is negative if it moves in the direction of the medium motion and the source velocity is less than the medium velocity. Estimates for the energy losses of dipoles in the cases of an electron beam and a flow of a weakly dispersive medium are given. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 6, pp. 502–512, June 2006.     

Sliding behavior of water droplets on line-patterned hydrophobic surfaces

We prepared line-patterned hydrophobic surfaces using fluoroalkylsilane (FAS) and octadecyltrimethoxysilane (ODS) then investigated the effect of line direction on sliding behavior of water droplets by direct observation of the actual droplet motion during sliding. Water droplets slide down with a periodic large deformation of the contact line and sliding velocity fluctuation that occurred when they crossed over the 500-μm ODS line regions in FAS regions on a Si surface tilted at 35°. These behaviors are less marked for motion on a 100-μm line surface, or on lines oriented parallel to the slope direction. Smaller droplets slide down with greater displacement in the line direction on 500-μm line patterning when the lines were rotated at 13° in-plane for the slope direction. This sliding behavior depended on the droplet size and rotation angle, and is accountable by the balance between gravitational and retentive forces.     

Hedgehog production in spatially correlated noise

The production of topological defects during a quench in a φ⁴ model is investigated. The influence of a spatially correlated noise on defect production in two and three dimensions is demonstrated. Received 28 August 2001 / Received in final form 11 February 2002 Published online 2 October 2002 RID="a" ID="a"Paper supported in part by ESF “COSLAB” Programme RID="b" ID="b"e-mail: sfdobrow@kinga.cyf-kr.edu.pl