Free energy of semiflexible polymers and structure of interfaces

The free energy of semiflexible polymers is calculated as a functional of the compositional scalar order parameter and the orientational order parameter of second-rank tensor S_ij on the basis of a microscopic model of wormlike chains with variable segment lengths. We use a density functional theory and a gradient expansion to evaluate the entropic part of the free energy, which is given in a power series of .The interaction term of the free energy is derived with a random phase approximation. For the rigid rod limit, the nematic-isotropic transition point is given by , N and w being the degree of polymerization and the anisotropic interaction parameter, respectively, and the degree of ordering at the transition point is 0.33448. We also find that the contour length of polymer chains becomes larger in a nematic phase than in an isotropic phase. Interface profiles are obtained numerically for some typical cases. In the neighborhood of isotropic-isotropic interfaces, polymer chains tend to align parallel to the interface on the polymer-rich side and perpendicular on the poor side. When an isotropic region and a nematic region coexist, orientational order parallel to the interface is preferred in the nematic region. Received: 28 May 1998 / Revised: 12 August 1998 / Accepted: 8 September 1998     

Quasi Bernoulli fluctuations in random and disordered systems

It is shown that quasi Bernoulli fluctuations, which appear at a morphological phase transition, can be considered as a statistical basis for multifractal processes with constant multifractal specific heat in a wide class of random and disordered systems. This class contains at least following processes: percolation, diffusion-limited aggregation and corrosion, Lorenz like attractors, and mesoscopic systems with Anderson transition. Received: 14 April 1998 / Revised and Accepted: 20 April 1998     

Insulator-metal transition in biased finite polyyne systems

A method for the study of the electronic transport in strongly coupled electron-phonon systems is formalized and applied to a model of polyyne chains biased through metallic Au leads. We derive a stationary non equilibrium polaronic theory in the general framework of a variational formulation. The numerical procedure we propose can be readily applied if the electron-phonon interaction in the device hamiltonian can be approximated as an effective single particle electron hamiltonian. Using this approach, we predict that finite polyyne chains should manifest an insulator-metal transition driven by the non-equilibrium charging which inhibits the Peierls instability characterizing the equilibrium state.     

A study of Peierls instabilities for a two-dimensional t-t' model

In this paper we study Peierls instabilities for a half-filled two-dimensional tight-binding model with nearest-neighbour hopping t and next nearest-neighbour hopping t' at zero and finite temperatures. Two dimerization patterns corresponding to the same phonon vector (π,π) are considered to be realizations of Peierls states. The effect of imperfect nesting introduced by t' on the Peierls instability, the properties of the dimerized ground state, as well as the competition between two dimerized states for each t' and temperature T, are investigated. It is found: (i). The Peierls instability will be frustrated by t' for each of the dimerized states. The Peierls transition itself, as well as its suppression by t', may be of second- or first-order. (ii). When the two dimerized states are considered jointly, one of them will dominate the other depending on parameters t' and T. Two successive Peierls transitions, that is, the system passing from the uniform state to one dimerized state and then to the other may take place with decrease of temperature. Implications of our results to real materials are discussed. Received 31 July 2001     

TiC lattice dynamics from ab initio calculations

Ab initio calculations and a direct method have been applied to derive the phonon dispersion curves and phonon density of states for the TiC crystal. The results are compared and found to be in a good agreement with the experimental neutron scattering data. The force constants have been determined from the Hellmann-Feynman forces induced by atomic displacements in a supercell. The calculated phonon density of states suggests that vibrations of Ti atoms form acoustic branches, whereas the motion of C atoms is confined to optic branches. The elastic constants have been found using the deformation method and compared with the results obtained from acoustic phonon slopes. Received 23 February 1998     

A new simulation method for the determination of forces in polymer/colloid systems

We introduce a new simulation method, which we call the contact-distribution method, for the determination of the Helmholtz potential for polymer/colloid systems from lattice Monte-Carlo simulations. This method allows one to obtain forces between finite or semi-infinite objects of any arbitrary shape and dimensions in the presence of polymer chains in solution or physisorbed or chemisorbed at interfaces. We illustrate the application of the method using two examples: (i) the interaction between the tip of an atomic force microscope (AFM) and a single, end-grafted polymer chain and (ii) the interaction between an AFM tip and a polymer brush. Numerical results for the first two cases illustrate how the method can be used to confirm and extend scaling laws for forces and Helmholtz potentials, to examine the effects of the shapes and sizes of the objects and to examine conformational transitions in the polymer chains. Received: 15 May 1998 / Revised: 11 June 1998 / Accepted: 12 June 1998     

Submillimeter and infrared spectroscopy on La0.85Sr0.15MnO3

The optical conductivity of La_0.85Sr_0.15MnO₃ single crystals was studied by means of submillimeter and infrared spectroscopy for frequencies cm^-1 and temperatures 10 K < T <300 K. The submillimeter conductivity follows the temperature dependence of the dc-data. The phonon spectrum of La_0.85Sr_0.15MnO₃ changes considerably below K revealing a structural phase transition induced by charge or orbital order. At T =10 K a number of phonon modes can be identified in addition to the room-temperature spectrum. The optical conductivity () in the mid-infrared reveals the characteristics of small polaron absorption. Below the magnetic ordering temperature the polaron binding energy is highly reduced, but the onset of charge order interrupts the formation of free charge carriers with a Drude-like behavior. The frequency and temperature dependence of in this regime qualitatively resembles the small polaron predictions by Millis et al. (Phys. Rev. B 54, 5405 (1996)). Received 5 November 1999     

Temperature dependent phonon dynamics in the quasi-one-dimensional systems

The dynamical properties of phonons coupled linearly to the electrons with a planar Fermi surface, are examined at finite temperature. The additional phonon branch, found previously from the T = 0 calculations, should not be observable in the Nb₃Sn-like compounds, which undergo the cubic-to-tetragonal transition. This additional branch exists however in the weak coupling limit, where, unexpectedly, the soft mode becomes well defined only close to the transition temperature for the Peierls instability     

Energy Transport in Weakly Anharmonic Chains

We investigate the energy transport in a one-dimensional lattice of oscillators with a harmonic nearest neighbor coupling and a harmonic plus quartic on-site potential. As numerically observed for particular coupling parameters before, and confirmed by our study, such chains satisfy Fourier’s law: a chain of length N coupled to thermal reservoirs at both ends has an average steady state energy current proportional to 1/N. On the theoretical level we employ the Peierls transport equation for phonons and note that beyond a mere exchange of labels it admits nondegenerate phonon collisions. These collisions are responsible for a finite heat conductivity. The predictions of kinetic theory are compared with molecular dynamics simulations. In the range of weak anharmonicity, respectively low temperatures, reasonable agreement is observed.     

Can Raman spectroscopy detect cumulenic structures of linear carbon chains?

The molecular and vibrational structures of cumulenic carbon chains are investigated by density functional theory calculations and compared with that of hydrogen‐capped polyynes. The small value of bond length alternation (BLA) along the CC bonds sequence obtained by geometry optimization of uncapped C_n chains and vinyl‐capped carbon chains confirms their cumulenic structure. It is demonstrated that for finite length chains the structural parameters are determined by end effects as far as the Peierls distortion, expected for very long molecules, does not occur. The Raman spectra of such molecules are calculated to verify the possibility of identifying markers of cumulenic chains by means of vibrational spectroscopy. As expected, the longitudinal mode consisting of the BLA oscillation, which is responsible for the strongest Raman transition of polyynes, becomes very weak for cumulenes; this behaviour is rationalized in terms of local polarizability derivatives. However, other longitudinal modes can be observed in the Raman spectra of C_n chains. The wavenumber behaviour and the optical activity of these modes are interpreted on the basis of the phonon dispersion branch of an ideally infinite cumulenic polymer. Raman intensities computed for chains of different lengths allow to conclude that cumulenic molecules could be detected and identified by means of Raman spectroscopy. Copyright © 2009 John Wiley & Sons, Ltd.     

First-order calculation of the phonon propagator of a quasi-one-dimensional electron-phonon system

Using Green function technics the phonon propagator is calculated consistently in the first order with respect to both the square of the electron-phonon interaction matrix element and the matrix element of the Coulomb interaction of the electronic subsystem. It is shown that the so-called self-energy and exchange contributions lead to an increase of the Peierls temperatureT _p in comparison with the result of the usual random-phase approximation (RPA), whereas the Umklapp processes tend to lowerT _p .     

Melting of the cooperative Jahn-Teller distortion in LaMnO 3 single crystal studied by Raman spectroscopy

We have studied the behavior of the Raman phonons of a stoichiometric LaMnO₃ single crystal as a function of temperature in the range between 77 K and 900 K. We focus on the three main phonon peaks of the Pbnm structure, related to the tilt, antisymmetric stretching (Jahn-Teller mode) and stretching modes of Mn-O octahedra. The phonon frequencies show a strong softening that can be fit taking into account their renormalization because of three phonon anharmonic effects in the pseudoharmonic approximation. Thermal expansion effects, in particular the variation of Mn-O bond lengths with temperature, are not relevant above 300 K. On the contrary, phonon width behavior deviates from the three phonon scattering processes well bellow T _c . The correlation between the magnitude of the cooperative Jahn-Teller distortion, that disappears at 800 K, and the amplitude of the Raman phonons in the orthorhombic phase is shown. Nevertheless, Pbnm phonons are still observable above this temperature. Phonon width and intensity behavior around T _c can be explained by local melting of the orbital order that begins quite below T _c and by fluctuations of the regular Mn-O octahedra that correspond to dynamic Jahn-Teller distortions. Received 25 January 2001 and Received in final form 14 March 2001     

Neural network learning dynamics in a path integral framework

Using the local-density approximation, calculating the Hellmann-Feynman forces and applying the direct method, the phonon dispersion relations for the rutile-like structure of crystalline SnO₂ have been derived for the first time. The phonon frequencies at the point agree very well with Raman and infrared data and other phenomenological model calculations. The LO/TO splitting is estimated by calculating phonons from an elongated supercell. The computations under pressure reveal a soft mode of B_1g symmetry which leads to a ferroelastic phase transition. The pressure-dependence of the lattice constants and the Grüneisen parameters of the modes are calculated. Received 18 July 1999     

Random-phase approximation for the grand-canonical potential of composite fermions in the half-filled lowest Landau level

We reconsider the theory of the half-filled lowest Landau level using the Chern-Simons formulation and study the grand-canonical potential in the random-phase approximation (RPA). Calculating the unperturbed response functions for current- and charge-density exactly, without any expansion with respect to frequency or wave vector, we find that the integral for the ground-state energy converges rapidly (algebraically) at large wave vectors k, but exhibits a logarithmic divergence at small k. This divergence originates in the k^-2 singularity of the Chern-Simons interaction and it is already present in lowest-order perturbation theory. A similar divergence appears in the chemical potential. Beyond the RPA, we identify diagrams for the grand-canonical potential (ladder-type, maximally crossed, or a combination of both) which diverge with powers of the logarithm. We expand our result for the RPA ground-state energy in the strength of the Coulomb interaction. The linear term is finite and its value compares well with numerical simulations of interacting electrons in the lowest Landau level. Received: 19 February 1998 / Revised: 25 March 1998 / Accepted: 17 April 1998     

On charged mesoscopic metallic bubbles

We investigate the existence of stable charged metallic bubbles using the shell correction method. We find that for a given mesoscopic system of n atoms of a given metal and (positive) elementary charges, a metallic bubble turns out to have a lower total energy than a compact spherical cluster, whenever the charge number q is larger than a critical charge number q_c. For a magic number (n-q) of free electrons, the spherical metallic bubble may become stable against fission. Received: 17 November 1997 / Revised: 28 May 1998 / Accepted: 20 July 1998     

Ab initio study of phonons and structural stabilities of the perovskite-type MgSi{O_3}

Using the local-density approximation, calculating the Hellmann-Feynman forces, applying the direct method and deriving the phonon dispersion relations, the stability of the perovskite-like structures of MgSiO₃ at T =0 have been studied. The cubic Pmm phase shows a dispersion-less soft phonon branch spreading from the R to M points of the cubic Brillouin zone. This soft branch persists up to high pressures of 150 GPa. The low-symmetry phases I4/mcm and Imma, P4/mbm can be considered as a result of the soft mode condensation at the M and R points, respectively. These phases prove to be unstable at T =0. The experimentally observed Pmnb phase is a consequence of the intersection of Imma and P4/mbm space groups. Thus, it can be regarded as a simultaneous condensation of two soft modes: one at the M and a second at the R high-symmetry points of the cubic Brillouin zone. The phonon dispersion relations of Pmnb show that this phase is stable and its optical phonons appear above 4.0 THz only. Received 15 October 1999 and Received in final form 14 January 2000     

Low temperature thermodynamics of inverse square spin models in one dimension

We present a field-theoretic renormalization group calculation in two loop order for classical O(N)-models with an inverse square interaction in the vicinity of their lower critical dimensionality one. The magnetic susceptibility at low temperatures is shown to diverge like with a=(N-2)/(N-1) and . From a comparison with the exactly solvable Haldane-Shastry model we find that the same temperature dependence applies also to ferromagnetic quantum spin chains. Received: 20 February 1998 / Revised: 27 April 1998 / Accepted: 30 April 1998