K. H. Michel

Nanotube field of C60 molecules in carbon nanotubes: atomistic versus continuous tube approach

We calculate the van der Waals energy of a

Induced polarization and electronic properties of carbon-doped boron nitride nanoribbons

{\mathrm{C}}_{60}

Crystal field, orientational order, and lattice contraction in solid C60

molecule when it is encapsulated in a single-walled carbon nanotube with discrete atomistic structure. Orientational degrees of freedom and longitudinal displacements of the molecule are taken into account, and several achiral and chiral carbon nanotubes are considered. A comparison with earlier work where the tube was approximated by a continuous cylindrical distribution of carbon atoms is made. We find that such an approximation is valid for high and intermediate tube radii; for low tube radii, minor chirality effects come into play. Three molecular orientational regimes are found when varying the nanotube radius.

Unified rotational dynamics of molecular crystals with orientational phase transition

The electronic properties of boron-nitride nanoribbons (BNNRs) doped with a line of carbon atoms are investigated by using density functional calculations. Three different configurations are possible: the carbon atoms may replace a line of boron or nitrogen atoms or a line of alternating B and N atoms which results in very different electronic properties. We found that: i) the NCB arrangement is strongly polarized with a large dipole moment having an unexpected direction, ii) the BCB and NCN arrangement are non-polar with zero dipole moment, iii) the doping by a carbon line reduces the band gap independent of the local arrangement of boron and nitrogen around the carbon line, iv) an electric field parallel to the carbon line polarizes the BN sheet and is found to be sensitive to the presence of carbon dopants, and v) the energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital decreases linearly with increasing applied electric field directed parallel to the carbon line. We show that the polarization and energy gap of carbon doped BNNRs can be tuned by an electric field applied parallel along the carbon line.

Superposition of quantum and classical rotational motions in Sc2C2@C84 fullerite

A model of the intermolecular potential in solid C60, which is based on Born–Mayer repulsions, van der Waals attractions, and electrostatic multipoles, is presented. The potential is expanded in terms of multipolar rotator functions. The orientation–orientation interaction and the crystal field are calculated. The orientational phase transition to the Pa3 phase is studied with the methods of statistical mechanics. The discontinuity of the order parameter at the transition and the temperature evolution of the order parameter are calculated. The lattice contraction at the phase transition is evaluated. The influence of the lattice contraction on the crystal field and on the orientational order is studied.

Crystal structures of polymerized fullerides AC60, A=K, Rb, Cs, and alkali-mediated interactions

A unified theory for the rotational dynamics of molecular crystals with orientational phase transitions is given. As basic secular variables one takes symmetry adapted functions, which describe the molecular orientations, and the angular momenta of the molecules. Using Mori’s projection operator technique, one obtains a coupled set of two dynamic matrix equations for the corresponding relaxation functions. The coupling is proportional to the order parameter and accounts for the reactive coefficients. The corresponding collective excitations are librons. The damping of librons is described by two transport coefficients that account for orientational relaxation and angular momentum relaxation, respectively. By approaching the phase transition, both matrix equations decouple, the orientational relaxation describes the critical dynamics. In the disordered phase, this equation describes collective hindered rotations. In the same framework one describes phases of partial order as CD4 II. Comparison is made with...

The C60 molecules in (C60)N@SWCNT peapods: crystal field, intermolecular interactions and dynamics

The superposition of the quantum rotational motion (tunneling) of the encapsulated Sc(2)C(2) complex with the classical rotational motion of the surrounding C(84) molecule in a powder crystal of Sc(2)C(2)@C(84) fullerite is investigated by theory. Since the quantum rotor is dragged along by the C(84) molecule, any detection method which couples to the quantum rotor (in casu the C(2) bond of the Sc(2)C(2) complex) also probes the thermally excited classical motion (uniaxial rotational diffusion and stochastic meroaxial jumps) of the surrounding fullerene. The dynamic rotation-rotation response functions in frequency space are obtained as convolutions of quantum and classical dynamic correlation functions. The corresponding Raman scattering laws are derived, and the overall shape of the spectra and the width of the resonance lines are studied as functions of temperature. The results of the theory are confronted with experimental low-frequency Raman spectra on powder crystals of Sc(2)C(2)@C(84) [M. Krause et al., Phys. Rev. Lett. 93, 137403 (2004)]. The agreement of theory with experiment is very satisfactory in a broad temperature range.

Charge Transfer and Polymer Phases in AC60 (A = K, Rb, Cs) fullerides

Starting from a model of rigid interacting C60 polymer chains on an orthorhombic lattice, we study the mutual orientation of the chains and the stability of the crystalline structures Pmnn and I2/m. We take into account (i) van der Waals interactions and electric quadrupole interactions between C60 monomers on different chains as well as (ii) interactions of the monomers with the surrounding alkali atoms. The direct interactions (i) always lead to an antiferrorotational structure Pmnn with alternate orientation of the C60 chains in planes (001). The interactions (ii) with the alkalis consist of two parts: translation-rotation (TR) coupling where the orientations of the chains interact with displacements of the alkalis, and quadrupolar electronic polarizability (ep) coupling, where the electric quadrupoles on the C60 monomers interact with induced quadrupoles due to excited electronic d-states of the alkalis. Both interactions (ii) lead to an effective orientation-orientation interaction between the C60 ch...

Mode–mode coupling theory of translations and rotations in orientationally disordered crystals

Abstract We calculate the crystal field experienced by a single C60 molecule encapsulated in a single‐walled carbon nanotube. We take the icosahedral symmetry of the C60 molecule fully into account by treating it as a cluster of interaction centers. Although we do not distinguish between armchair, zig‐zag and chiral nanotubes since we consider a nanotube as a uniform cylindrical surface density, we can vary the tube radius R T. We observe a flip of the lowest‐energy C60 molecular orientation when increasing the radius: below R T≈6.5 Å, the lowest energy occurs when two pentagons are perpendicular to the nanotubes long axis, while for higher values, an orientation with hexagons perpendicular to the tubes long axis is energetically more favorable. Then, we consider a linear chain of C60 molecules inside a carbon nanotube, all experiencing the crystal field as a confinement potential. We find tube radius‐dependent effects: distinct equilibrium lattice spacings and lattice contractions. We calculate the structure factor and demonstrate the presence of pseudo‐Bragg peaks. Finally, we briefly comment on the calculation of infrared and Raman absorption spectra within the presented framework.

Librational excitations in ordered and in partially ordered molecular crystals

Starting from a microscopic model of interactions in A+C60− crystals, where A+ is an alkali metal ion and C60− the molecular ion, we present a theory of the phase transitions from the orientationally disordered Fm3m structure to polymer and dimer phases. The electronic charge transfer is accounted for by the t1u molecular orbitals of C60−. The resulting Coulomb interactions between neighboring C60− and between C60− and the sublattice of alkali metal ions lead to new orientation dependent potentials which have to be added to the intermolecular pair potential and to the crystal field. By studying the orientation dependence of the crystal field and the molecular field, we find that, in comparison with the phase transition Fm3m→Pa3 known from C60-fullerite, additional channels to a Pmnn structure with subsequent polymerization and dimerization are opened. We study the symmetry of the low temperature phases and compare with experimental results. The present work comprises an extension of the formalism of ro...