On spatial variations of nematic ordering

We present a theory of orientational order in nematic liquid crystals which interpolates between several distinct approaches based on the director field (Oseen and Frank), order parameter tensor (Landau and de Gennes), and orientation probability density function (Onsager). As in density-functional theories, the suggested free energy is a functional of spatially-dependent orientation distribution, however, the nonlocal effects are taken into account via phenomenological elastic terms rather than by means of a direct pair-correlation function. In illustration of this approach we consider a simplified model with orientation parameter on a circle and reveal its relation to the complex Ginzburg-Landau theory.     

Embedding atom-jellium model for metal surface

To describe metal surfaces efficiently and accurately, an embedding atom-jellium model is proposed. Within density functional theory, we consider a multiscale scheme that combines jellium and atomistic approaches. We use the former to model layers deep inside a metal surface to reduce the computational cost and the later to maintain the accuracy required for chemical bonding. Work functions of Al(111) and Cu(111) surfaces are studied using this model with comparisons to all-atom and pure jellium models. The much closer results of the embedding atom-jellium model to the all-atom results than to the pure jellium results show a good prospect for our approach in large-scale density functional calculations.     

Novel two-layered zeolite NaA-silicalite-1 membranes

A two-layered zeolite NaA-silicalite-1 membrane has been successfully prepared on a porous α-alumina tube by using seeded hydrothermal synthesis. The procedure involves pre-seeding with nanosized seed and subsequent regrowth by hydrothermal treatment. Single-layered NaA and silicalite-1 membranes were also synthesized for comparison. The membrane was composed of a silicalite-1 layer on top and a NaA layer on the porous support. SEM results of the membrane indicate that both the silicalite-1 layer and the NaA layer are uniform and well-intergrown. The silicalite-1 and NaA layers in the ‘sandwich’ mode have similar thickness of 3-4 μm, whereas the thickness of their respective seed layer is different. The NaA seed layer is much thicker than the silicalite-1seed layer. This may be attributed to the different capillary action on the support and NaA layer during using a slip-casting seeding method. XRD analysis has also proved both zeolite NaA and zeolite silicalite-1 layers coexist in the dual-layered membrane. This method is also suitable for preparing other multi-layer zeolite membranes.     

A core-softened fluid model in disordered porous media. Grand canonical Monte Carlo simulation and integral equations

We have studied the microscopic structure and thermodynamic properties of a core-softened fluid model in disordered matrices of Lennard-Jones particles by using grand canonical Monte Carlo simulation. The dependence of density on the applied chemical potential (adsorption isotherms), pair distribution functions, as well as the heat capacity in different matrices are discussed. The microscopic structure of the model in matrices changes with density similar to the bulk model. Thus one should expect that the structural anomaly persists at least in dilute matrices. The region of densities for the heat capacity anomaly shrinks with increasing matrix density. This behavior is also observed for the diffusion coefficient on density from independent molecular dynamics simulation. Theoretical results for the model have been obtained by using replica Ornstein-Zernike integral equations with hypernetted chain closure. Predictions of the theory generally are in good agreement with simulation data, except for the heat capacity on fluid density. However, possible anomalies of thermodynamic properties for the model in disordered matrices are not captured adequately by the present theory. It seems necessary to develop and apply more elaborated, thermodynamically self-consistent closures to capture these features.     

Nonequilibrium sedimentation of colloids on the particle scale

We investigate sedimentation of model hard-sphere-like colloidal dispersions confined in horizontal capillaries using laser scanning confocal microscopy, dynamical density functional theory, and Brownian dynamics computer simulations. For homogenized initial states we obtain quantitative agreement of the results from the respective approaches for the time evolution of the one-body density distribution and the osmotic pressure on the walls. We demonstrate that single-particle information can be obtained experimentally in systems that were initialized further out of equilibrium such that complex lateral patterns form.     

Tunneling of two interacting electrons in a quantum wire

A model calculation is reported for the tunneling probability of one as well as two interacting electrons from a quantum well within a narrow channel. We discuss the cases when the two electrons are spin polarized or unpolarized by transforming the system to a noninteracting one with the use of quantal density functional theory to obtain an effective single-particle confining potential. A semiclassical approach is used to obtain the tunneling probability from this effective potential. The calculation is motivated by recent measurements of the conductance of an electron gas in a narrow channel but is not meant to explain the anomalous behavior that has been reported since, for example, we deal with a simplified two-level system. Numerical results for the tunneling probability are presented.     

Density functional theory for nonuniform polymer melts: Based on the universality of the free energy density functional

A density functional theory is proposed for nonuniform freely jointed tangential hard sphere polymer melts in which the bonding interaction is treated on the basis of the properties of the Dirac δ-function, thus avoiding the use of the single chain simulation in the theory. The excess free energy is treated by making use of the universality of the free energy density functional and the Verlet-modified (VM) bridge function. To proceed numerically, one of the input parameters, the second-order direct correlation function of a uniform polymer melt is obtained by solving numerically the Polymer-RISM integral equation with the Percus-Yevick (PY) closure. The predictions of the present theory for the site density distribution, the partition coefficient and the adsorption isotherm, near a hard wall or between two hard walls are compared with computer simulation results and with those of previous theories. Comparison indicates that the present approach is more accurate than the previous integral equation theory and the most accurate Monte Carlo density functional theories. The predicted oscillations of the medium-induced force between two hard walls immersed in polymer melts are consistent with the experimental results available in the literature. Received 18 April 2000     

The dielectric constant of barium mono-chalcogenides and their improved band gap results

We have applied Engel-Vosko exchange energy within density functional theory, to calculate the electronic structure and the optical properties of BaX (X = Te, Se, and S) compounds via full potential linearized augmented plane wave method. We have found that this improves the band gap results comparing to our previous work in which we had made use of Perdew et al. exchange energy functional. We have also calculated the dielectric constant of these compounds, using both Perdew et al. and Engel-Vosko schemes. It is shown that Engel-Vosko exchange energy functional leads to a better result. We have also reported the effect of spin-orbit coupling on the results.     

Low-energy band structure very sensitive to the interlayer distance in Bernal-stacked tetralayer graphene

We have investigated Bernal-stacked tetralayer graphene as a function of interlayer distance and perpendicular electric field by using density functional theory calculations. The low-energy band structure was found to be very sensitive to the interlayer distance, undergoing a metal-insulator transition. It can be attributed to the nearest-layer coupling that is more sensitive to the interlayer distance than are the next-nearest-layer couplings. Under a perpendicular electric field above a critical field, six electric-field-induced Dirac cones with mass gaps predicted in tight-binding models were confirmed, however, our density functional theory calculations demonstrate a phase transition to a quantum valley Hall insulator, contrasting to the tight-binding model prediction of an ordinary insulator.     

Specification of Density Functional Approximation by Radial Distribution Function of Bulk Fluid

A systematic methodology is proposed to deal with the weighted density approximation version of classical density functional theory by employing the knowledge of radial distribution function of bulk fluid.The present methodology results from the concept of universality of the free energy density functional combined with the test particle method.It is shown that the new method is very accurate for the predictions of density distribution of a hard sphere fluid at different confining geometries.The physical foundation of the present methodology is also applied to the quantum density functional theory.     

Effect of shape anisotropy on the phase diagram of the Gay-Berne fluid

We have used the density functional theory to study the effect of molecular elongation on the isotropic-nematic, isotropic-smectic A and nematic-smectic A phase transitions of a fluid of molecules interacting via the Gay-Berne intermolecular potential. We have considered a range of length-to-width parameter 3.0 ⩽ x₀ ⩽ 4.0 in steps of 0.2 at different densities and temperatures. Pair correlation functions needed as input information in density functional theory are calculated using the Percus-Yevick integral equation theory. Within the small range of elongation, the phase diagram shows significant changes. The fluid at low temperature is found to freeze directly from isotropic to smectic A phase for all the values of x₀ considered by us on increasing the density while the nematic phase stabilizes in between isotropic and smectic A phases only at high temperatures and densities. Both isotropic-nematic and nematic-smectic A transition density and pressure are found to decrease as we increase x₀. The phase diagram obtained is compared with computer simulation result of the same model potential and is found to be in good qualitative agreement.     

Electronic structure of substitutional defects and vacancies in GaSe

We have investigated the nature of defect states associated with substitutional impurities (Cd, In, Sn) and both Ga and Se vacancies in GaSe using ab initio electronic structure methods within density functional theory. These calculations were done using supercell model allowing for internal atomic relaxation. Binding energies (BEs) of defects obtained in this model are compared with effective mass approximation results. Significant central cell corrections are present for most of the defects. This is consistent with charge densities associated with the defect states that show clearly their strongly localized nature. Because of the difficulties associated with LDA/GGA in giving the correct band gap in semiconductors, we have only compared the acceptor BEs with available experiments. Our theoretical results agree well with the experiment for Cd_Ga and V_Ga. The fundamental role played by the Ga dimers in the formation of defect states is discussed.     

Aluminum Hugoniot from model calculations including semicore electrons based on density functional theory

We present a method to obtain Hugoniot from model calculations based on density functional theory, and apply the method to aluminum Hugoniot. Technological advances have extended the experimental research of high energy density physics, and call for quantitative theoretical analysis. However, direct computation of Hugoniot from density functional theory is very difficult. We propose two step calculations of Hugoniot from density functional theory. The first step is molecular dynamics simulations with an ambient temperature for electrons. The second step is total energy calculations of a crystal with desired high temperatures for electrons and with the ambient temperature for electrons. We treated the semicore 2s and 2p electrons of aluminum as valence electrons only for the total energy calculations of the aluminum crystal. The aluminum Hugoniot from our model calculations is in excellent agreement with available experimental data and the previous density functional theory calculations in the literature.     

A density-functional-theory-based finite element model to study the mechanical properties of zigzag phosphorene nanotubes

In this paper, the density functional theory calculations are used to obtain the elastic properties of zigzag phosphorene nanotubes. Besides, based on the similarity between phosphorene nanotubes and a space-frame structure, a three-dimensional finite element model is proposed in which the atomic bonds are simulated by beam elements. The results of density functional theory are employed to compute the properties of the beam elements. Finally, using the proposed finite element model, the elastic modulus of the zigzag phosphorene nanotubes is computed. It is shown that phosphorene nanotubes with larger radii have larger Young's modulus. Comparing the results of finite element model with those of density functional theory, it is concluded that the proposed model can predict the elastic modulus of phosphorene nanotubes with a good accuracy.     

Magnetic hysteresis in the microwave surface resistance of Nb samples in the critical state

We discuss the hysteretic behavior of the field-induced variations of the microwave surface resistance in superconductors in the critical state. Measurements have been performed in a bulk sample of Nb and a powdered one at different values of the temperature. We discuss a model, based on the Coffey and Clem theory, in which we take into account the flux distribution inside the sample, due to the critical state. The experimental results are quite well justified in the framework of our model. We show that by fitting the experimental data it is possible to determine the value of the critical current density and its field dependence.     

First principles study of barium chalcogenides

In this study, ab initio calculation results of the vibrational properties and elastic parameters as well as characteristic Debye temperature and Poisson's ratios of two barium chalcogenides, BaSe and BaS, which crystallize in NaCl-type structure, were presented. Calculations were based on plane wave basis sets together with ultrasoft pseudopotentials in the framework of density functional theory (DFT) with generalized gradient approximation. Phonon dispersion spectra were obtained using the first principles linear response approach of the density functional perturbation theory (DFPT). The detailed total energy calculations were performed in order to obtain elastic constants using distortions on cubic phase. The calculated structural, elastic, and thermal parameters of BaSe and BaS systems agree well with the available experimental data and theoretical calculations.