Withdrawal of Electrodynamical Forbiddance and Peculiarities of the SERS Spectra in Fullerene C<Subscript>70</Subscript>

It is demonstrated that in fullerene C₇₀, which can be considered as a deformed fullerene C₆₀ in some mean sense there is a withdrawal of an Electrodynamical forbiddance of a strong quadrupole light-molecule interaction, which is realized in the fullerene C₆₀. This situation occurs because of the reduction of symmetry of C₆₀ from the icosahedral symmetry group Y_h to the group D_5h. The withdrawal results in appearance of the lines in the SERS spectra of C₆₀, which are forbidden in usual Raman scattering and are active in the infrared absorption spectra. The experimentally measured SERS spectra of C₇₀ demonstrates existence of such lines that strongly confirms our ideas about the dipole-quadrupole SERS mechanism.     

Hydrogen storage in Li-doped fullerene-intercalated hexagonal boron nitrogen layers

New materials for hydrogen storage of Li-doped fullerene (C₂₀, C₂₈, C₃₆, C₅₀, C₆₀, C₇₀)-intercalated hexagonal boron nitrogen (h-BN) frameworks were designed by using density functional theory (DFT) calculations. First-principles molecular dynamics (MD) simulations showed that the structures of the C _n -BN (n = 20, 28, 36, 50, 60, and 70) frameworks were stable at room temperature. The interlayer distance of the h-BN layers was expanded to 9.96–13.59 Å by the intercalated fullerenes. The hydrogen storage capacities of these three-dimensional (3D) frameworks were studied using grand canonical Monte Carlo (GCMC) simulations. The GCMC results revealed that at 77 K and 100 bar (10 MPa), the C₅₀-BN framework exhibited the highest gravimetric hydrogen uptake of 6.86 wt% and volumetric hydrogen uptake of 58.01 g/L. Thus, the hydrogen uptake of the Li-doped C _n -intercalated h-BN frameworks was nearly double that of the non-doped framework at room temperature. Furthermore, the isosteric heats of adsorption were in the range of 10–21 kJ/mol, values that are suitable for adsorbing/desorbing the hydrogen molecules at room temperature. At 193 K (–80 °C) and 100 bar for the Li-doped C₅₀-BN framework, the gravimetric and volumetric uptakes of H₂ reached 3.72 wt% and 30.08 g/L, respectively.     

Study of third-and fifth-order nonlinear optical processes in thin C<Subscript>60</Subscript> films

The nonlinear refraction in thin films of fullerene C₆₀ (100 nm) is studied by the Z-and RZ-scan methods using the second harmonic of a picosecond Nd:YAG laser (λ = 532 nm, τ = 55 ps). The combined effect of n₂ (self-focusing of laser radiation) and n₄ (self-defocusing) is analyzed. Mechanisms responsible for the nonlinear refraction in films are discussed.     

Influence of defects in the carbon network on the static polarizability of fullerenes

The static polarizability of the C₆₀, C₇₀, C₈₀, and C₁₈₆ fullerenes has been calculated within the semiempirical MNDO approximation implemented in the MOPAC quantum-chemical program package. It is demonstrated that the results obtained are comparable with experimental data and the results of the ab initio B3LYP method using the 6–31G(d, p) basis set. The influence of topological defects (five-, seven-, and eight-membered rings), vacancies produced by removing pentagons, and nitrogen and boron atoms on the geometric parameters and the polarizability of the C₆₀, C₂₄₀, and C₅₄₀ fullerenes has been investigated by the MNDO method. It is revealed that the polarizability of the fullerene with topological defects is higher than the polarizability of the perfect icosahedral fullerene. The formation of vacancies in the carbon cage leads to a linear decrease in the polarizability of the fullerene and an increase in the specific polarizability. The polarizability of the heterofullerene with nitrogen or boron atoms spaced apart in the carbon cage is higher than that of the fullerene with heteroatoms located adjacent to each other.     

The oxidation of fullerenes (C<Subscript>60</Subscript>, C<Subscript>70</Subscript>) with various oxidants under ultrasonication

The reaction of C₆₀, under ultrasonication, with various oxidants, such as 3-chloroperoxy benzoic acid (Fluka 99%), 4-methyl morpholine N-oxide (Aldrich 97%), chromium (VI) oxide (Aldrich 99.9%), and the oxone® monopersulfate compound, causes the oxidation of fullerenes at room temperature. The FAB-MS spectra and HPLC profile confirmed that the products of fullerene oxidation were [C₆₀(O)_n] (n=1～3 or n=1). C₇₀ also reacted, under ultrasonication, with various oxidants, but the reaction rate of C₇₀ was lower than that of C₆₀.     

Hybrids of carbyne and fullerene

A new class of quasi-linear carbon molecules [C₆₀] _n [C _m ]_n?1 consisting of n fullerenes C₆₀ linked by n?1 carbyne-type C _m fragments with a system of conjugated bonds is described. The possible geometric configurations of such molecules and crystals on their base are discussed. The structure optimization by the empirical (MM+), semiempirical (PM3), and ab initio (HF/6-21) methods showed that these molecules are energetically stable.     

The effect of non-linear capacitances in the localization properties of aperiodic dual electric transmission lines

This study investigates the localization properties of dual electric transmission lines with non-linear capacitances. The V_C,n voltage across each capacitor is selected as a non-linear function of the electric charge q_n, i.e., V_C,n = q_n(1/C_n -ε_n|q_n|²)where C_n is the linear part of the capacitance and ε_n the amplitude of the non-linear term. We follow a binary distribution of values of ε_n, according to the Thue-Morse m-tupling sequence. The localization behavior of this non-linear case indicates that the case m = 2 does not belong to the m ≥ 3, family because when m changes from m = 2 to m = 3, the number of extended states diminishes dramatically. This proves the topological difference of the m = 2 and m = 3 families. However, by increasing m values, localization behavior of the m-tupling family resembles that of the m = 2, case because the system begins to regain its extended states. The exact same result was obtained recently in the study of linear direct transmission lines with m-tupling distribution of inductances. Consequently, we state that the localization behavior of the m-tupling family as a function of the m value is independent of both the linear and the non-linear system under study, but independent of the kind of transmission line (dual or direct). This is curious behavior of the m-tupling family and thus deserves more scholarly attention.     

Intensity of singlet-triplet transitions in C<Subscript>60</Subscript> fullerene calculated on the basis of the time-dependent density functional theory and taking into account the quadratic response

The singlet-singlet and triplet-triplet absorption spectra of C₆₀ fullerene are calculated using the density functional method and taking into account the theory of linear and quadratic responses. The B3LYP density functional and the 6–31G and 3–21G atomic basis sets are used. The calculations are performed using the D_2h and D_5d symmetry groups, although the real symmetry of the ground state is described by the I _h symmetry group. The matrix elements of the operator of the spin-orbit coupling are calculated and the probabilities of some singlet-triplet transitions are estimated. Taking into account the data in the literature on vibronic interactions of vibrations of the t_1u, t_2u, g _u , and h _u symmetry species, the radiative lifetime of the 1³T_2g → 1¹A _g phosphorescence was estimated to be 45 s. The fact that this time proved to be considerably greater than the experimentally observed total lifetime of the triplet testifies to a fast nonradiative deactivation of the lowest triplet state of C₆₀ fullerene and agrees with a low phosphorescence intensity. The zero-field splitting of some triplets and the intensities of magnetic dipole transitions are discussed.     

A strongly asymmetric single-electron transistor operating as a zero-biased electrometer

We have studied a strongly asymmetric Al single-electron transistor with R₁ ? R₂ and C₁ ? C₂, where R_{1, 2} and C_{1, 2} are the tunnel resistances and capacitances of the first and second junction respectively. Due to the asymmetry in its electric parameters leading to strong asymmetry of the nonlinear I–V curve at zero bias (V = 0), the transistor demonstrated a remarkable current response to an AC signal at the values of the gate charge Q₀ close to (n + 1/2)e, where n is integer. A rather delicate regime of the transistor operation (V ? e/C_Σ) being important for unperturbed measurements was examined. The measured curves are in good agreement with a model based on the orthodox theory of single electron tunneling. This specific zero bias regime of an asymmetric transistor opens new opportunities for a single-electron transistor as an ultrasensitive charge/field sensor.     

Morphological transformations of diblock copolymers in binary solvents: A simulation study

Morphological transformations of amphiphilic AB diblock copolymers in mixtures of a common solvent (S1) and a selective solvent (S2) for the B block are studied using the simulated annealing method. We focus on the morphological transformation depending on the fraction of the selective solvent C _S2, the concentration of the polymer C _p , and the polymer–solvent interactions ε _ij (i = A, B; j = S1, S2). Morphology diagrams are constructed as functions of C _p , C _S2, and/or ε _AS2. The copolymer morphological sequence from dissolved → sphere → rod → ring/cage → vesicle is obtained upon increasing C _S2 at a fixed C _p . This morphology sequence is consistent with previous experimental observations. It is found that the selectivity of the selective solvent affects the self-assembled microstructure significantly. In particular, when the interaction ε _BS2 is negative, aggregates of stacked lamellae dominate the diagram. The mechanisms of aggregate transformation and the formation of stacked lamellar aggregates are discussed by analyzing variations of the average contact numbers of the A or B monomers with monomers and with molecules of the two types of solvent, as well as the mean square end-to-end distances of chains. It is found that the basic morphological sequence of spheres to rods to vesicles and the stacked lamellar aggregates result from competition between the interfacial energy and the chain conformational entropy. Analysis of the vesicle structure reveals that the vesicle size increases with increasing C _p or with decreasing C _S2, but remains almost unchanged with variations in ε _AS2.     

Quark-antiquark composite systems: The Bethe-Salpeter equation in the spectral-integration technique

The Bethe-Salpeter equations for the quark-antiquark composite systems, q\(\bar q\), are written in terms of spectral integrals. For the q\(\bar q\) mesons characterized by the mass M, spin J, and radial quantum number n, the equations are presented for the following (n, M²) trajectories: π _J , η _J , a _J , f _J , ρ _J , ω _J , h _J , and b _J .     

Spin-Wave Resonance in Ge : Mn Thin Films with Percolation Magnetic Ordering

The mechanism of excitation and propagation of spin waves in Ge: Mn thin films with different nominal manganese concentrations (2, 4, and 8 at % Mn) with percolation magnetic ordering is explored. Concentration dependencies of Curie temperature T_C(n) and spin wave rigidity D(n) are determined, which enables to find the index of correlation distance. An exotic percolation magnetic state of samples of Ge: Mn thin films is confirmed by rectifying experimental dependences D(n) and D/T_C(n) in coordinates accepted in the percolation theory.     

Exchange and correlation in finite-temperature TDDFT

We discuss the finite-temperature generalization of time-dependent density functional theory (TDDFT). The theory is directly analogous to that at temperature T = 0. For example, the finite-T TDDFT exchange-correlation kernel f_xc(T, n) in the local density approximation can again be expressed as a density derivative of the exchange correlation potential f_xc(T, n) = [?v_xc(T, n)∕?n]δ(r ? r′), where n = N∕V is the electron number density. An approximation for the kernel f_xc(T, n) is obtained from the finite-T generalization of the retarded cumulant expansion applied to the homogeneous electron gas. Results for f_xc and the loss function are presented for a wide range of temperatures and densities including the warm dense matter regime, where T ≈ T_F, the electron degeneracy temperature. The theory also permits a physical interpretation of the exchange and correlation contributions to the theory.     

Effect of heating of the electronic subsystem on the thermal stability of the C<Subscript>60</Subscript> and C<Subscript>20</Subscript> fullerenes and (C<Subscript>20</Subscript>)<Subscript>2</Subscript> cluster molecule

The effect of heating of the electronic subsystem on the thermal stability of C₆₀ and C₂₀ fullerenes and a (C₂₀)₂ cluster molecule is investigated theoretically. It is demonstrated that the excitation of electrons to upper energy levels in accordance with the Fermi-Dirac distribution function does not lead to a substantial change in the activation energy E _a for decay of the C₂₀ fullerene. The stability of the C₆₀ fullerene and the (C₂₀)₂ cluster molecule likewise does not change radically. However, the inclusion of corrections associated with the finite sizes of the heat bath leads to the activation energy E _a which is in better agreement with the calculated height of the potential barrier preventing the cluster decay.     

Paramagnetische Resonanz von Zentren mit den Symmetrienn,\bar n undn/mundn/m

The consequences of applying the spin-Hamiltonians ofAbragam andPryce to paramagnetic centers with the low symmetriesn,\(\bar n\) andn/m(C _n ,C _nh ,S _n ) are examined. The asymmetry of theg- and the hfs-tensors, described in an earlier paper, is considered in this context. The point is that for the symmetries under consideration the coordinate systems are not determined by the symmetry elements. For this reason it is possible to introduce separate coordinate systems for the magnetic field, the electron spin and the spins of the nuclei and this allows the symmetrisation of the tensors under certain conditions. This procedure also leeds to an understanding of the independent parameters found in the Hamiltonians. Ambiguities between the spin-Hamiltonians and the esr-spectra indicate the limits of theAbragam andPryce formalism. The application of the theory to paramagnetic centers under the influence of external, electrical fields is discussed and reveals interesting aspects.     

Peculiarities of magnetic field-induced ferromagnetic ordering in narrow-band manganites

The temperature dependences of the residual magnetization in narrow-band manganites (Pr_0.67Ca_0.33MnO₃, Sm_0.55Sr_0.45Mn¹⁸O₃, Sm_0.55Sr_0.45Mn¹⁶O₃, and (NdEu)_0.55Sr_0.45Mn¹⁸O₃) have been studied. All compounds studied are characterized by a fairly high residual magnetization M _R (about 0.5 μ_B/Mn) at 4.2 K, which vanishes upon sample heating to the temperature T _RE ≈ 30–35 K, which is much lower than the temperature T _C of the ferromagnetic transition. However, upon magnetization of the samples at T _RE < T < T _C , the residual magnetization (smaller in magnitude) remains up to T _C . For the composition (NdEu)_0.55Sr_0.45Mn¹⁸O₃, the residual magnetization remains at T < T _C , independent of the temperature of magnetization. The disappearance of the residual magnetization found at intermediate temperatures is apparently related to the destruction of the magnetic field-induced ferromagnetic ordering (which contains an additional contribution of the rare-earth sublattice).     

Intuitionistic Quantum Logic of an <Emphasis Type="Italic">n</Emphasis>-level System

A decade ago, Isham and Butterfield proposed a topos-theoretic approach to quantum mechanics, which meanwhile has been extended by Döring and Isham so as to provide a new mathematical foundation for all of physics. Last year, three of the present authors redeveloped and refined these ideas by combining the C*-algebraic approach to quantum theory with the so-called internal language of topos theory (Heunen et al. in arXiv:0709.4364). The goal of the present paper is to illustrate our abstract setup through the concrete example of the C*-algebra M _n (?) of complex n×n matrices. This leads to an explicit expression for the pointfree quantum phase space Σ _n and the associated logical structure and Gelfand transform of an n-level system. We also determine the pertinent non-probabilisitic state-proposition pairing (or valuation) and give a very natural topos-theoretic reformulation of the Kochen–Specker Theorem.In our approach, the nondistributive lattice ?(M _n (?)) of projections in M _n (?) (which forms the basis of the traditional quantum logic of Birkhoff and von Neumann) is replaced by a specific distributive lattice \(\mathcal{O}(\Sigma_{n})\) of functions from the poset \(\mathcal{C}(M_{n}(\mathbb{C}))\) of all unital commutative C*-subalgebras C of M _n (?) to ?(M _n (?)). The lattice \(\mathcal{O}(\Sigma_{n})\) is essentially the (pointfree) topology of the quantum phase space Σ _n , and as such defines a Heyting algebra. Each element of \(\mathcal{O}(\Sigma_{n})\) corresponds to a “Bohrified” proposition, in the sense that to each classical context \(C\in\mathcal{C}(M_{n}(\mathbb{C}))\) it associates a yes-no question (i.e. an element of the Boolean lattice ?(C) of projections in C), rather than being a single projection as in standard quantum logic. Distributivity is recovered at the expense of the law of the excluded middle (Tertium Non Datur), whose demise is in our opinion to be welcomed, not just in intuitionistic logic in the spirit of Brouwer, but also in quantum logic in the spirit of von Neumann.     

Observational Data Fitting to Constrain Variable Modified Chaplygin Gas in the Background of Horava-Lifshitz Gravity

FRW universe in Horava-Lifshitz (HL) gravity model filled with a combination of dark matter and dark energy in the form of variable modified Chaplygin gas (VMCG) is considered. The permitted values of the VMCG parameters are determined by the recent astrophysical and cosmological observational data. Here we present the Hubble parameter in terms of the observable parameters Ω _{d m0}, Ω _{v m c g0}, H ₀, redshift z and other parameters like α, A, γ and n. From Stern data set (12 points), we have obtained the bounds of the arbitrary parameters by minimizing the χ ² test. The best-fit values of the parameters are obtained by 66 %, 90 % and 99 % confidence levels. Next due to joint analysis with BAO and CMB observations, we have also obtained the bounds of the parameters (A, γ) by fixing some other parameters α and n. The best fit value of distance modulus μ(z) is obtained for the VMCG model in HL gravity, and it is concluded that our model is perfectly consistent with the union2 sample data.     

Rotation of the inner shell in a C<Subscript>20</Subscript>@C<Subscript>80</Subscript> nanoparticle

The stability of a C₂₀@C₈₀ nanoparticle and the rotation of its inner shell are studied theoretically within the tight-binding approximation. It is found that the C₂₀ skeleton in the free state is described by space group D_3d; in the case where C₂₀ is placed into the C₈₀(I _h ) fullerene field, the space group of C₂₀ is raised to I _h due to isomerization. The total energy surface of the C₂₀@C₈₀ compound is scanned over two rotation angles. Based on an analysis of the surface relief and energy isoline map, orientational melting of the nanoparticle is predicted. A nanoparticle gyroscope—C₂₀ rotating in the field of C₈₀ at a certain relative orientation and energy supply—is also predicted to exist.