Surface energy of biaxial nematics

In this paper, a form of surface energy for biaxial nematics is derived. The methods follow those for deriving Landau elastic energy Frank elastic energy for bulk nematics. The surface energy can also be derived in rotation matrix expansion. The result shows that in the first order approximation, there are four independent coefficients in the surface energy. When each of the three orthogonal directors of biaxial nematics coincides with its corresponding easy axis, the surface energy is linearly proportional to the order parameters. An application of this surface energy is discussed and possible experimental measurements of three linear combinations of the four coefficients are explored.     

Surface energy of biaxial nematics

In this paper, a form of surface energy for biaxial nematics is derived. The methods follow those for deriving Landau elastic energy Frank elastic energy for bulk nematics. The surface energy can also be derived in rotation matrix expansion. The result shows that in the first order approximation, there are four independent coefficients in the surface energy. When each of the three orthogonal directors of biaxial nematics coincides with its corresponding easy axis, the surface energy is linearly proportional to the order parameters. An application of this surface energy is discussed and possible experimental measurements of three linear combinations of the four coefficients are explored.     

Field response and switching times in biaxial nematics

We study by means of virtual molecular dynamics computer experiments the response of a bulk biaxial nematic to an applied external field and, in particular, the relative speed of reorientation of the principal director axis and of the secondary one, typical of these new materials, upon a pi2 field switch. We perform the simulations setting up and integrating the equations of motion for biaxial Gay-Berne particles using quaternions and a suitable time reversible symplectic integrator. We find that switching of the secondary axis is up to an order of magnitude faster than that of the principal axis, and that under fields above a certain strength a reorganization of local domains, temporarily disrupting the nematic and biaxial ordering, rather than a collective concerted reorientation occurs.     

Linear analysis of pattern formation in nematics in oblique magnetic fields

The dynamics of nematic director field reorientation in non-Freedericksz geometries, after a magnetic field H is applied at an oblique angle relatively to the initial homogeneous director n 0 ( H not normal to n 0), is studied considering a magnetic reorientation driven by hydrodynamic instabilities (with backflow). This study is carried out for bounded samples between two parallel plates with planar boundary conditions and with rigid anchoring. Linear stability and wave vector selection analysis predict that, when the angle of the magnetic to the initial director field is increased, for a given magnetic field intensity, two transitions from a homogeneous to a transient distorted director field reorientation can occur: a transition at a first critical angle to an aperiodic distorted director field and a transition at a second critical angle to a periodic distorted director field. It is shown that the periodic mode is cut off at a higher reduced field when the magnetic field acts away from the normal direction.     

Orientational order parameters in biaxial nematics: Polymorphic notation

In this paper, a wealth of notations introduced in the past 30 years to denote second-rank orientational order parameters for biaxial nematics are compared, stressing sources of possible confusion. A unifying, intrinsic treatment of the second-rank orientational order parameters is also presented, which does not suffer from the redundancy of the Saupe matrix and is independent of the way in which rotations are parametrized.     

Nematic reorientation in electric and magnetic fields

Homogeneous reorientation processes of two nematic liquid crystals in electric and magnetic fields have been observed using proton nuclear magnetic resonance spectroscopy (NMR). Using a recently developed experimental set-up, it is possible to study reorientation processes in liquid crystals by means of NMR experiments in a very flexible way. The time constant τ describing these processes has been determined as a function of the applied electric field. It emerges that the electric field cannot only be used to increase the reorientation time but also to slow the director reorientation by approximately one order of magnitude. Experimental data for 5CB and a fluorinated liquid crystal (BCH-5 FFF) are presented. The reorientation time measured as a function of the electric field can be used to calculate the rotational viscosity γ ₁. By repeating these experiments at different temperatures it was possible to investigate the temperature behaviour of γ ₁.     

Stability of the Rydberg atom in the crossed magnetic and electric fields

The stability of equilibrium positions of the Rydberg atom exposed to the uniform crossed electric and magnetic fields is analyzed. The dynamics of the system is described by an autonomous Hamiltonian depending on parameters a and f. By the normalization of the quadratic part of the Hamiltonian expansion in the neighborhood of the equilibrium position it is proved that for any f < 0 and ${1 \over 2} < a < {1 \over 2} + {{( - f)^{3/2} } \over {3\sqrt 3 }}$ , the equilibrium solution of the equations of motion is stable in Liapunov sense, while for f > 0 and a < 1/2, there is a domain of instability in the plain of parameters Ofa bounded by the curve d₃ = 0. In the domain of linear stability, it is proved that there are two curves in the plane Ofa, where the resonance conditions of third (ω₁ = 2ω₂) and fourth (ω₁ = 3ω₂) order are fulfilled. Moreover, by the normalization of the third‐ and fourth‐order terms in the Hamiltonian expansion it is proved that in the case of the third‐order resonance, the equilibrium position is unstable for all f > 0 different from f = 0.111572 and f = 0.281144, for which the stability takes place. In the case of the fourth‐order resonance, there are two intervals of parameters for which the equilibrium position is unstable. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Perturbation calculation on the hydrogen atom in electric and magnetic fields

A generalization of a perturbation theory without wave function is developed which applies to a hydrogen atom perturbed by magnetic and electric fields. A double perturbation expansion for the Stark–Zeeman effect for parallel fields is considered and results for the states obeying |m| = l = n ? 1 in the zero field limit are presented. Other problems that can be treated this way are discussed.     

Deformation of magnetosensitive emulsion microdroplets in magnetic and electric fields

A magnetosensitive emulsion comprising an ensemble of nonmagnetic oil droplets suspended in a kerosene-based magnetic fluid is studied. It is found that the droplets of such an emulsion are deformed in both magnetic and electric fields. The character of microdroplet deformation in the electric field depends on the field frequency: at low frequencies, the droplets are flattened; at high frequencies, the droplets are stretched along the force lines of the field. It is established that the deformation caused by the electric field can be compensated for by the imposition of an additional magnetic field, and the conditions of this compensation are determined. It is revealed that, under the action of a magnetic field directed normal to a thin layer of the emulsion, the droplets “split” into branched structures. The action of a similarly directed alternating electric field leads to the transformation of the droplets into tori followed by their rupture. It is concluded that the structure of the emulsion can be efficiently controlled using the combined action of magnetic and electric fields. Original Russian Text ? Yu.I. Dikanskii, O.A. Nechaeva, A.R. Zakinyan, 2006, published in Kolloidnyi Zhurnal, 2006, Vol. 68, No. 2, pp. 161–165.     

Modification of polymeric composites with electric and magnetic fields

Effect of the component composition and magnetic and electric fields on the structure and dielectric and electromechanical properties of composites constituted by incompatible polymers, cellulose acetobutyrate and segmented polyurethane, was studied.     

The sodium D2-line in electric and magnetic fields

The splitting of the hyperfine structure of the D₂ line of the sodium atom was investigated under the influence of simultaneously acting parallel magnetic and electric fields of comparable strength. The experimental spectra were taken by laser-atomic-beam spectroscopy. Theoretical spectra obtained by quantum mechanical calculations agree very well with the experimentally observed spectra, therefore allowing their clear interpretation, especially at anticrossing regions.     

The sodium D2-line in electric and magnetic fields

The influence of perpendicularly crossed electric and magnetic fields of comparable strength on the hyperfine components of the sodium D₂-line was studied by means of laser-atomic-beam spectroscopy. The observed spectra show changes in the polarization type (, ) when one of the fields becomes dominant relative to the other. Theoretical calculations confirm the experimental observations.     

Differential scattering of cold molecules in superimposed electric and magnetic fields

We present a detailed theoretical study of differential cross sections for inelastic collisions of (2)Sigma molecules in the presence of superimposed electric and magnetic fields. Using rigorous quantum dynamical calculations, we show that the angular dependence of cross sections for Zeeman relaxation in collisions of CaD molecules with He atoms at low temperatures can be significantly modified by electric fields of less than 100 kVcm. Our results suggest that the differential scattering cross sections are more sensitive to the electric field than the averaged integral cross sections. We show that the integral cross sections corresponding to a fixed orientation of the incoming collision flux may exhibit interference effects induced by electric fields.     

Behaviour of polymer dispersed cholesteric droplets with negative dielectric anisotropy in electric fields

The behaviour of chiral, polymer dispersed cholesteric liquid crystals with negative dielectric anisotropy in electric fields has been studied for a system with large cholesteric pitch (several μm) using polarizing microscopy. A uniformly oriented region appears in the centre of the droplets for voltages above a threshold voltage. We find that the radius of this region increases exponentially with increasing field strength, while the threshold voltage decreases with increasing drop diameter and with increasing pitch. Investigation of the dynamics reveals a single step mechanism with a time constant of a few seconds when a field is suddenly switched on. The switch-off process is more complex and much slower.     

Deceleration of supersonic beams using inhomogeneous electric and magnetic fields

Methods for the production of cold atomic and molecular samples relying on the deceleration of pulsed supersonic beams are described and a review of the corresponding literature is presented. These methods include multistage Stark deceleration, multistage Zeeman deceleration, and Rydberg-Stark deceleration. Recent applications of the cold samples produced with these techniques are summarized.     

Light scattering in colloidal solution of magnetite in electric and magnetic fields

Light scattering by magnetite particles in kerosene under the simultaneous action of crossed electric and magnetic fields was studied. Decreasing of variation of light scattering intensity at some values of electric and magnetic fields have been found. Values of fields at which a minimum of light scattering intensity occur depend on the angle between laser beam and the plane of crossed fields.     

The sodium D2-line in crossed electric and magnetic fields

The influence of perpendicularly crossed electric and magnetic fields on the sodium D₂-line was studied using laser-atomic-beam spectroscopy. The observed spectra show changes in the polarization type when one of the fields becomes dominant relative to the other.     

The sodium D2-line in parallel electric and magnetic fields

The first time the sodium D₂-line could be investigated under the influence of simultaneousely acting parallel magnetic and electric fields of comparable “strengths”. The observed spectra show anticrossings and can be interpreted by quantum mechanical calculations.     

Inelastic collisions of cold polar molecules in nonparallel electric and magnetic fields

The authors present a detailed study of low-temperature collisions between CaD molecules and He atoms in superimposed electric and magnetic fields with arbitrary orientations. Electric fields do not interact with the electron spin of the molecules directly but modify their rotational structure and, consequently, the spin-rotation interactions. The authors examine molecular Stark and Zeeman energy levels as functions of the angle between the fields and show that rotating fields may induce and shift avoided crossings between the Zeeman levels of the rotationally ground and rotationally excited states of the molecule. The dynamics of molecular collisions are extremely sensitive to external fields near these avoided crossings and it is shown that molecular collisions may be controlled by varying both the strength and the relative orientation of the fields. The effects observed in this study are due to interactions of the isolated molecules with external fields so the conclusions should be relevant for collisions of molecules with other atoms or collisions of molecules with each other. This study demonstrates that electric fields may be used to enhance or suppress spin-rotation interactions in molecules. The spin-rotation interactions induce nonadiabatic couplings between states of different total spins in systems of two open-shell species and it is suggested that electric fields might be used for controlling nonadiabatic spin transitions and spin-forbidden chemical reactions of cold molecules in a magnetic trap.