A. Bródka

Coulomb interactions in a computer simulation of a system periodic in two directions

The integral representation of the gamma function and the Poisson summation formula are used to calculate the interaction energy of charged particles in a 3-dimensional system periodic in two directions. A parallelogram shape simulation box is considered. Calculations are carried out for interactions described by any inverse power, and analytical continuation of the energy function leads to the final expression for the Coulomb interaction energy. Summation over the simulation box replica along one or the other side of the box base is replaced by summation in reciprocal space. Therefore there are two equivalent formulas for the potential energy that offer the possibility of avoiding slowly convergent series. The energy expressions are identical to those obtained from the Lekner method. The special case is considered where the functions defining the energy are infinite, i.e. when two charges lie on a line parallel to the simulation box side that was chosen to convert real space summation into reciprocal space.

Molecular dynamics simulation study of a liquid crystal model: Gay-Berne particles with transverse dipole moments

Abstract Molecular dynamics simulations for molecules represented by Gay-Berne ellipsoidal particles and transverse point dipoles are reported. The system is compressed at constant temperature, and the thermodynamic and structural properties of the system are studied and compared with the results for a non-polar Gay-Berne fluid. Both systems reach a smectic phase at the same point, however, the polar molecules exhibit partial orientational order at lower densities. Moreover, the polar system shows three well separated tilted phases, and positional order of the particles in the smectic layers is better than in the case of the non-polar system.

Methane in carbon nanotube: molecular dynamics simulation

The behaviour of methane molecules inside carbon nanotubes at room temperature is studied using classical molecular dynamics simulations. A methane molecule is represented either by a shapeless super-atom or by a rigid set of five interaction centres localized on atoms. Different loadings of methane molecules ranging from the dense gas density to the liquid density, and the influence of flexibility of the CNT on structural and dynamic properties of confined molecules are considered. The simulation results show the decreases of the diffusion coefficient of methane molecules with density. At higher densities diffusion coefficient values are almost independent of molecular shape, but at low densities one observes faster motion of the super-atom molecule than that for the tetrahedral model of the molecule. For loadings of methane considered here the nanotube flexibility, introduced by the reactive empirical bond order (REBO) potential for interactions between carbon atoms of nanotube, does not have an effect on diffusivity of methane molecules, and its impact on the molecular structure is weak. It is found that methane molecules in the vicinity of the nanotube wall show tripod orientation with respect to the nanotube surface.

Structural studies of disordered carbons by high-energy X-ray diffraction

X-ray diffraction measurements were carried out on three samples of disordered, commercially produced carbons, AX21, CXV and BP71, on the ID15B beam-line at the European Synchrotron Radiation Facility (ESRF), Grenoble. Intensity data were converted to pair correlation functions via the Fourier transform. The results obtained show that the structure of the studied samples consists of one–four graphite-like layers, stacked without spatial correlations. The size of the ordered regions is in the range of 9–16 Å. The atomic arrangement within an individual layer can be described in terms of the paracrystalline ordering, in which lattice distortions propagate proportionally to the square root of interatomic distances. The paracrystalline structure was simulated by introducing the Stone–Wales defects (pair of two pentagons and two heptagons), randomly distributed in the network. The resulting structures were relaxed using the reactive empirical bond order potential for carbon–carbon interaction and the Lennard-Jones potential with parameters for interlayer interactions. Such defects lead to curvature of individual layers.

Electrostatic interactions in molecular dynamics simulation of a three-dimensional system with periodicity in one direction

The Mellin transform and Poisson summation formula are used to derive an expression for the Coulomb interaction energy of a three-dimensional system with periodicity in one direction. Initially, calculations are performed for interactions characterized by any inverse power and, using the analytical continuation of the energy function, one obtains the final expression for the interaction energy of charges. We consider also a special case when two different charges are located on a line parallel to the periodicity direction. The energy and force expressions are identical to those obtained from the Lekner summation which is simply a sum over reciprocal lattice terms. The convergence behaviour of the Lekner summation is compared with that based on the Ewald type approach.

Structural modeling of dahlia-type single-walled carbon nanohorn aggregates by molecular dynamics.

The structure of dahlia-type single-walled carbon nanohorn aggregates has been modeled by classical molecular dynamics simulations, and the validity of the model has been verified by neutron diffraction. Computer-generated models consisted of an outer part formed from single-walled carbon nanohorns with diameters of 20-50 Å and a length of 400 Å and an inner turbostratic graphite-like core with a diameter of 130 Å. The diffracted intensity and the pair correlation function computed for such a constructed model are in good agreement with the neutron diffraction experimental data. The proposed turbostratic inner core explains the occurrence of the additional (002) and (004) graphitic peaks in the diffraction pattern of the studied sample and provides information about the interior structure of the dahlia-type aggregates.

Ewald type summation method for electrostatic interactions in computer simulations of a three-dimensional system periodic in one direction

Abstract The energy expressions for the Coulomb and dipole–dipole interactions in systems with one-dimensional periodicity are derived. In the calculations we used the integral representation of the gamma function, the one-dimensional Poisson summation formula, and two-dimensional Fourier transforms of the functions depending on position components perpendicular to the periodicity direction. In this method the reciprocal-space summation can be expressed as a sum of structure factors, containing charge or dipole positions, multiplied by coefficients depending on the reciprocal-space vector, however, in a general case two parameters must be introduced.

Diffusion in restricted volume

The usually assumed anisotropy of the diffusion coefficient for molecules in a bounded region is questioned. The mean-square displacements of molecules are calculated from results of a molecular dynamics simulation of a C60/C6H12 mixture in a cylindrical pore. On the basis of the diffusion equation it is shown that the mean-square displacements parallel and perpendicular to the pore axis are reproduced using one diffusion coefficient.

High pressure Raman study of fermi resonance spectrum in gaseous carbon dioxide

Abstract The Raman spectra of Fermi diads in gaseous carbon dioxide were measured up to 2155 bars at 50°C. The perturbed frequencies and the intensity ratio of the bands in resonance have been obtained by fitting the isotropic spectra to the theoretical function obtained on the basis of projection-operator formalism. These results enable us to calculate the Fermi coupling and uncoupled frequencies.

Computationally efficient method for summing interactions of point dipoles in three dimensions with two-dimensional periodicity

Abstract A modification of the Ewald type summation of the dipole–dipole interactions in computer simulation of a system periodic in two directions is presented. Using Fourier transforms of the functions appearing in the reciprocal-space term the energy expression has a simple form, which is similar to that in the conventional three-dimensional Ewald method. The modified method is applied in the molecular dynamics simulations of two systems composed of polar ellipsoidal particles, and it is much faster than the traditional two-dimensional Ewald method.