Self-organisation in two dimensional system involving patchy and isotropic disks

ABSTRACT

We study the phase behaviour and morphology of systems involving mixtures of isotropic and anisotropic particles. The investigations are carried out using Molecular Dynamics technique. For this purpose we have proposed a model suitable for Molecular Dynamic simulations of such systems. The main part of calculations was carried out for two system compositions. At equimolar composition dense systems exhibit a specific structure. Both components form two interwoven lattices. Anisotropic particles are arranged in a honeycomb-like structure, while the bundles of fluid molecules are located inside these hexagons. If the number of isotropic molecules per one anisotropic particle is larger, then dense systems order into lamellar, solid-like structures.     

DNA molecule as an elastic Heisenberg chain

A DNA molecule is simulated by an anisotropic elastic fiber which defines the configuration of the molecule central line and is supplemented with a chain of quantum two-level systems imitating hydrogen bonds between two polynucleotide chains in the DNA double helix. The system Hamiltonian consists of Kirchhoff’s classical elastic energy and the energy of a quantum anisotropic chain of “spins” 1/2. The two-level systems and macroscopic vector variables which determine the conformation of the central line are coupled by a classical vector field q, which is introduced to take into account the existence of two polynucleotide strands. Averaging over fast (microscopic) variables yields an effective potential U(q). In the approximation of weak coupling between the systems, the spectrum of elementary excitations and effective potential U(q) have been calculated in explicit form. The relation between elementary excitations in the “magnetic” subsystem and so-called breathing modes [C. Mandel, N. R. Kallenbach, and S. W. Englander, J. Mol. Biol. 135, 391 (1980); G. Manning, Biopolymers 22, 689 (1983)] corresponding to low-frequency excitations in DNA molecules is discussed. Zh. éksp. Teor. Fiz. 111, 1833–1844 (May 1997)     

DFT - based study of electronic structures and mechanical properties of LiTaO3: ferroelectric and paraelectric phases

Abstract

By applying ab initio calculation within density functional theory (DFT), we study the structure parameters, electronic band structure, elastic coefficients, polycrystalline elastic properties, anisotropy factors and Debye temperature of ferroelectric and paraelectric phases of LiTaO₃ within the generalised gradient approximation at ambient pressure. The atomic structure in both phases is fully relaxed and the lattice constant, angle and atomic positions are well consistent with experimental values. The computed single-crystal elastic coefficients indicate that mechanical stability of LiTaO₃ in both phases is confirmed using the generalised Born criteria. The shear, bulk and Young’s modulus, Poisson’s ratio, and Vickers hardness were computed according to theoretical elastic constants by Voight–Reuss–Hill method. Several anisotropy factors and indexes are computed to illustrate mechanical anisotropy. Both phases are shown to be weakly anisotropic. The Debye temperature is estimated using the longitude and transverse elastic wave velocity of the ideal polycrystalline LiTaO₃ aggregates. We have found that LiTaO₃ in both phases has an indirect energy band gap. The differences in the electronic structure and density of states for both phases are quite small. Our results indicate that the mechanical and bonding properties of both phases are very similar. The obtained results were compared with the available experimental and theoretical values.     

An equation of state of a carbon-fibre epoxy composite under shock loading

An anisotropic equation of state (EOS) is proposed for the accurate extrapolation of high-pressure shock Hugoniot (anisotropic and isotropic) states to other thermodynamic (anisotropic and isotropic) states for a shocked carbon-fibre epoxy composite (CFC) of any symmetry. The proposed EOS, using a generalised decomposition of a stress tensor [A.A. Lukyanov, Int. J. Plasticity 24, 140 (2008)], represents a mathematical and physical generalisation of the Mie-Grüneisen EOS for isotropic material and reduces to this equation in the limit of isotropy. Although a linear relation between the generalised anisotropic bulk shock velocity U_s ^A and particle velocity u_p was adequate in the through-thickness orientation, damage softening process produces discontinuities both in value and slope in the U_s ^A-u_p relation. Therefore, the two-wave structure (non-linear anisotropic and isotropic elastic waves) that accompanies damage softening process was proposed for describing CFC behaviour under shock loading. The linear relationship U_s ^A-u_p over the range of measurements corresponding to non-linear anisotropic elastic wave shows a value of c₀ ^A (the intercept of the U_s ^A-u_p curve) that is in the range between first and second generalised anisotropic bulk speed of sound [A.A. Lukyanov, Eur. Phys. J. B 64, 159 (2008)]. An analytical calculation showed that Hugoniot Stress Levels (HSLs) in different directions for a CFC composite subject to the two-wave structure (non-linear anisotropic elastic and isotropic elastic waves) agree with experimental measurements at low and at high shock intensities. The results are presented, discussed and future studies are outlined.     

Simulation of nanopowder compaction in terms of granular dynamics

The uniaxial compaction of nanopowders is simulated using the granular dynamics in the 2D geometry. The initial arrangement of particles is represented by (i) a layer of particles executing Brownian motion (isotropic structures) and (ii) particles falling in the gravity field (anisotropic structures). The influence of size effects and the size of a model cell on the properties of the structures are studied. The compaction of the model cell is simulated with regard to Hertz elastic forces between particles, Cattaneo-Mindlin-Deresiewicz shear friction forces, and van der Waals-Hamaker dispersion forces of attraction. Computation is performed for monodisperse powders with particle sizes ranging from 10 to 400 nm and for “cohesionless” powder, in which attractive forces are absent. It is shown that taking into account dispersion forces makes it possible to simulate the size effect in the nanopowder compaction: the compressibility of the nanopowder drops as the particles get finer. The mean coordination number and the axial and lateral pressures in the powder systems are found, and the effect of the density and isotropy of the initial structure on the compressibility is analyzed. The applicability of well-known Rumpf’s formula for the size effect is discussed.     

Lattice dynamics of crystalline In4Se3

Calculations of the phonon spectrum of crystalline In₄Se₃ in a model of central-pair interactions with neglect of the long-range forces are presented. The model developed contains five unknown parameters, which are determined from experimental values of the elastic moduli without consideration of the internal displacement of the sublattices. The phonon spectrum obtained contains a large number of low-frequency modes, which deform the acoustic branches. Some common features are discovered in the dispersion curves of the electron and phonon spectra. Fiz. Tverd. Tela (St. Petersburg) 40, 2103–2108 (November 1998)     

Pseudo-molecular approach for the elastic constants of nematic liquid crystals interacting via anisotropic dispersion forces

The bulk and the surface-like elastic constants of a nematic liquid crystal are calculated for an ensemble of particles interacting via anisotropic dispersion forces using the pseudo-molecular method. The geometrical anisotropy of the molecules is also taken into account in the calculations by choosing a molecular volume of ellipsoidal shape. Analytical expressions for the elastic constants are obtained as a function of the eccentricity in the molecular volume shape. The method allows one to explore the dependence on the molecular orientation with respect to the intermolecular vector by analyzing the magnitude and the behaviour of macroscopic elastic parameters defining the nematic phase.     

Non-orthogonal tight-binding model for tellurium and selenium

Abstract

The twofold coordinated heavier group-VI elements tellurium and selenium with the trigonal crystal structure have unshared electron pairs (lone pairs) which control the interplay of the intra- and inter-chain interactions and their sensitivity on pressure and temperature. We have developed tight-binding (TB) parameters for the helical structures of tellurium and selenium using the Naval Research Laboratory Tight-Binding (NRL-TB) method. The TB parameters were derived by fitting to the band structures and total energies of density functional theory (DFT) calculations. We have applied the TB parameters to study the phase stabilities of different structures under hydrostatic pressure. We have predicted (without fitting) the volume dependence of the rhombohedral and diamond structures, the bcc to rhombohedral and rhombohedral to simple cubic phase transitions and the elastic constants of the trigonal structures, all in agreement with ab initio and experimental results. While the results for the unrelaxed vacancy formation energies and surface energies are in good agreement with the DFT values, we find large discrepancies for the relaxed values indicating that the present set of TB parameters cannot accurately capture the inter-chain interactions.     

A chiral axial next nearest neighbour xy-model for antiferroelectric liquid crystals

We describe a chiral axial next nearest neighbour xy-model to account for the various subphases exhibited by antiferroelectric liquid crystals made of chiral rod-like molecules. The assumed form of the interlayer interactions is based on physical processes which are discussed. Using a discrete model, the predicted sequence of transitions is SmA-SmC-SmC-FI_H-FI_I-FI_L-SmC ^* A, where FI stands for a ferriphase, as seen in many compounds. The ferri and SmC phases are characterized by relatively large angles between the c-vectors of successive layers and occur only when the compounds have high optical purity. The calculated field induced structures exhibit a plateau of the apparent tilt angle at , where is the tilt angle of the molecules in the ferriphase. The conoscopic figures in the presence of a field and ellipsometric parameters in the absence of a field have also been generated, which agree extremely well with the experimental results. Recent anomalous X-ray scattering studies prove the xy-character of the configurations, though the commensurate structures that are found in the ferriphase require an extension of the model to include lock-in terms. Received 23 August 1999     

DNA condensation and size effects of DNA condensation agent

Based on the model of the strong correlation of counterions condensed on DNA molecule, by tailoring interaction potential, interduplex spacing and correlation spacing between condensed counterions on DNA molecule and interduplex spacing fluctuation strength, toroidal configuration, rod-like configuration and two-hole configurations are possible. The size effects of counterion structure on the toroidal structure can be detected by this model. The autocorrelation function of the tangent vectors is found as an effective way to detect the structure of toroidal conformations and the generic pathway of the process of DNA condensation. The generic pathway of all of the configurations involves an initial nucleation loop, and the next part of the DNA chain is folded on the top of the initial nucleation loop with different manners, in agreement with the recent experimental results.     

Study of the broadening of the rotational Raman lines of CO2 perturbed by rare gases

This paper presents the results of an experimental and theoretical study of the broadening of the rotational Raman lines of the linear molecule CO₂ perturbed by rare gases: helium, neon and argon. In the first part, the experimental set-up and the method to deduce linewidths from the spectra are presented. This method is similar to that used by Welsh et al. although we take into account the contribution of the molecules in the (01¹0) vibrational state for which the rotational quantum number J can be odd. The results for the pressure broadening coefficient are then given for several values of J. We then briefly recall how one can derive collision cross sections from the measured linewidths. The second part is devoted to an attempt to interpret the experimental results in terms of the theory of the Raman linewidths developed by Van Kranendonk. After recalling briefly the assumptions used in that theory and discussing the intermolecular potentials that are used, we present the results of numerical calculations performed with several types of anisotropic interaction potentials between CO₂ and the atom of rare gas. We reach the conclusion that the approximate methods used by Van Kranendonk (matrix elements of the evolution operator S computed by second order perturbation theory) are probably inadequate to calculate the effect of elastic collisions that disorient the molecule. It is suggested that it might be advantageous to consider anisotropic forces of shorter range than the anisotropic London dispersion forces derived from an r^-6 potential.     

Effects of a self-assembled monolayer on the sliding friction and adhesion of an Au surface

The friction and adhesion mechanisms with and without a self-assembled monolayer (SAM) in nanotribology were studied using molecular dynamics (MD) simulation. The MD model consisted of two gold planes with and without n-hexadecanethiol SAM chemisorbed to the substrate, respectively. The molecular trajectories, tilt angles, normal forces, and frictional forces of the SAM and gold molecules were evaluated during the frictional and relaxation processes for various parameters, including the number of CH₂ molecules, the interference magnitude, and whether or not the SAM lubricant was used. The various parameters are discussed with regard to frictional and adhesion forces, mechanisms, and molecular or atomic structural transitions. The stick–slip behavior of SAM chains can be completely attributed to the van der Waals forces of the chain/chain interaction. When the number of CH₂ molecules was increased, the SAM chains appeared to have bigger tilt angles at deformation. The magnitude of the strain energy that was saved and relaxed is proportional to the elastic deformable extent of the SAM molecules. The frictional force was higher for long chain molecules. With shorter SAM molecules, the adhesion force behavior was more stable during the compression and relaxation processes. A surface coated with a SAM can increase nano-device lifetimes by avoiding interface effects like friction and adhesion. PACS 52.65.Yy; 81.40.Pq; 81.16; 68.35.-p     

Elastic response of single DNA molecules exhibits a reentrant collapsing transition

We measured the elastic response of single DNA molecules at various concentrations of the trivalent cation, spermidine. When added spermidine caused the DNA to collapse, the force-extension curves showed either plateaus or stick-release patterns depending on the concentration. The periodic stick-release response determines a characteristic length, which may reflect toroidal supercoiling. At high concentrations of spermidine, we observed the reelongation of single molecules of collapsed DNA. Thus condensation occurs between lower and upper critical concentrations, verifying that the transition is reentrant as theoretically predicted.     

First-principles investigation of the structural,dynamical, electronic,and elastic properties of WGe2 and W5Ge3

ABSTRACT

We have investigated the structural, dynamical, elastic, and electronic properties of WGe₂ and W₅Ge₃ compounds in different phases. We have considered the C11_b (tetragonal, space group I4/mmm) and C23 (orthorhombic, space group Pnma) strukturbericht phases for WGe₂ compound and D8₁ (tetragonal, space group I4/mcm), D8_m (tetragonal space group I4/mcm) strukturbericht phases for W₅Ge₃ compound. The structural parameters, formation enthalpies, phonon dispersion curves, elastic constants, mechanical modulus, anisotropic factors, thermal conductivities, and electronic structures have been investigated using generalised gradient approximation within in the plane wave pseudopotential density functional theory. The calculated lattice constants are in a good agreement with the experimental data. The considered phases for WGe₂ and W₅Ge₃ compounds have a metallic character. The results indicated that all phases for compounds are both mechanically stable and dynamically stable except for W₅Ge₃-D8₁. The anisotropy in some mechanical modulus has been investigated using several elastic anisotropy indexes and directional dependence of compressibility, Young’s moduli, shear moduli, and Poisson’s ratio.     

Spiral patterns in the packing of flexible structures

Spiral patterns are found to be a generic feature in close-packed elastic structures. We describe model experiments of compaction of quasi-1D sheets into quasi-2D containers that allow simultaneous quantitative measurements of mechanical forces and observation of folded configurations. Our theoretical approach shows how the interplay between elasticity and geometry leads to a succession of bifurcations responsible for the emergence of such patterns. Both experimental forces and shapes are also reproduced without any adjustable parameters.     

A first-principles study on structural stability and mechanical properties of polar intermetallic phases CaZn2 and SrZn2

Structural stability and electronic properties of polar intermetallic CaZn₂ and SrZn₂ in both CeCu₂-type and MgZn₂-type structures have been investigated using first-principles method. The calculated equilibrium lattice parameters agree closely with the available experimental and other theoretical results. In terms of formation enthalpy, it is discovered that the present compounds with CeCu₂-type structure are energetically more stable than that with MgZn₂-type. They are all mechanically stable according to the criteria of elastic stability. In particular, we have investigated the pressure effect on the compressive behaviour and structural stability of each compound. Subsequently, the bulk modulus, shear modulus, Young’s modulus, theoretical hardness, Poisson’s ratio and Debye temperature in the ground state can be estimated using Voigt–Reuss–Hill homogenization method. Mechanical anisotropy is characterized by the anisotropic factors and direction-dependent Young’s modulus. Finally, the electronic structures are determined to reveal the bonding characteristics of considered phases.     

Physical Approaches to the Study of DNA

New micromanipulation techniques now enable physicists and biologists to study the behavior of single biomolecules such as DNA. In particular, it is possible to measure the elastic response of individual DNA molecules to changes in the double helix's supercoiling. The force versus extension diagram for torsionally relaxed DNA is continuous and allows one to evaluate the persistence length of the polymer. When the molecule is supercoiled, however, stretching leads to the buildup of torsional stress in the double helix's axis. When the twist energy thus generated increases beyond a critical value, the molecule is locally destabilized and changes conformation. This structural transition occurs at stretching forces which can be exerted in vivo by molecular motors and at degrees of supercoiling found in the cell, and may have implications for DNA structure and function within the nucleus.     

A geometrical template for toroidal aggregates of chiral macromolecules

The formation of toroidal aggregates by long chiral molecules of biological origin, as collagen, f-actin and DNA, or by chiral synthetic polypeptides has been observed in specific ionic environments. Such aggregates have received considerable attention in order to identify the various physical factors susceptible to contribute to this original morphogenesis, particularly in the case of those formed by DNA. We consider here the eventual role of a spontaneous uniform twist of micrometric pitch whose possible occurrence is suggested by some observations and by recent studies of DNA dense phases exhibiting cholesteric and “blue” phase structures. Following an approach inspired by the geometry and topology of fiber bundles, we show that the necessity to propagate such a twist in a dense bundle of fibers leads to the formation of aggregates having a toroidal shape and, in the case of the nanometric aggregates of DNA, characteristic sizes similar to those observed.     

Study of high-pressure phase transition of CeTe and EuTe through three-body interaction potential approach

The high pressure phase transition of lanthanum monotellurides having NaCl-type (B₁) structure have been studied using three-body interaction potential (TBIP) approach. The potential model consists of long-range Coulombic, three-body interaction forces, short-range overlap repulsive forces operative up to next nearest neighbor ions, van der Walls interactions and zero point energy effects. To understand the effect of pressure on elastic constant and their combinations, they have also been studied. The Born stability criterion was also found to be fulfiled in the present study. Our calculated results of phase transitions, volume collapses and elastic behavior of these monotellurides are found to be close to the experimental results. This shows that the inclusion of three-body interaction effects makes the present model suitable for high-pressure studies.     

An ab initio study of the electronic structure and elastic properties of the newly discovered ternary carbide

The electronic structure and elastic properties of the newly discovered ternary layered carbide Ti₄GaC₃ were investigated by means of the first-principle plane-wave pseudopotential total energy calculation method based on density functional theory. The computed results, including lattice constants and internal coordinates, are in good agreement with experimental values. The elastic moduli of ideal polycrystalline Ti₄GaC₃ were predicted from the individual elastic constants by Voigt approximation. The band structure shows that the electrical conductivity is metallic and anisotropic, with a high density of states at the Fermi energy. The elastic properties are anisotropic, related to the Ti–Ga bonds being relatively weaker than the Ti–C bonds.