Stoichiometric synthesis of fullerene compounds with lithium and sodium and analysis of their IR and EPR spectra

A modified method is proposed for preparing fullerene compounds with alkali metals in a solution. The compounds synthesized have the general formula Me _n C₆₀(THF)_x, where Me = Li or Na; n=1–4, 6, 8, or 12; and THF = tetrahydrofuran. The use of preliminarily synthesized additives MeC₁₀H₈ makes it possible to prepare fullerene compounds with an exact stoichiometric ratio between C ₆₀ ^n? and Me ⁺. The IR and EPR spectra of the compounds prepared are analyzed and compared with the spectra of their analogs available in the literature. The intramolecular modes T _u (1)-T _u (4) for the C ₆₀ ^n? anion are assigned. The splitting of the T _u (1) mode into a doublet at room temperature for Me _n C₆₀(THF)_x (n=1, 2, 4) compounds indicates that the fullerene anion has a distorted structure. An increase in the intensity of the T _u (2) mode, a noticeable shift of the T _u (4) mode toward the long-wavelength range, and an anomalous increase in the intensity of the latter mode for the Li₃C₆₀(THF)_x complex suggest that, in the fullerene anion, the coupling of vibrational modes occurs through the charge-phonon mechanism. The measured EPR spectra of lithium-and sodium-containing fullerene compounds are characteristic of C ₆₀ ^? anions. The g factors for these compounds are almost identical and do not depend on temperature. The g factor for the C ₆₀ ^n? anion depends on the nature of the metal and differs from the g factor for the C ₆₀ ^? anion.     

Stochastic dynamics and Parrondo’s paradox

The Spanish physicist Juan Parrondo has provided two stochastic losing games such that for certain stochastic combinations one may obtain a winning game. If a large number of players are involved and if they try to play such that their gain in the next round is maximized one arrives at the problem of investigating a random walk on a certain space of measures.The appropriate abstract setting is as follows. There is given a compact metric space (M,d), and M is written as the union of certain closed subsets A₁,…,A_r. For every ρ=1,…,r there is prescribed a strict contraction Γ_ρ:A_ρ→M. A random walk (X_m)_m∈N0 on M is then defined as follows. The starting position is X₀=x₀, where x₀∈M is fixed, and if the walk at the m’th step is at position X_m∈M, then one chooses a ρ among the ρ with X_m∈A_ρ (with equal probability, say) and defines X_m+1 as Γ_ρ(X_m). Associated with the walk is a gainφ(X_m) in every round, where φ:M→R is a continuous function.The aim of the present investigations is the study of the expectation G_m of φ(X_m) as a function of m. Our main result states that the sequence (G_m) is “eventually approximately periodic” provided that all A_ρ are not only closed but also open in M: for every ε there is an l₀∈N such that (G_m) is l₀-periodic up to an error of at most ε for sufficiently large m. In fact it turns out that the behaviour of our process can be described well with a finite Markov chain.In the general case, however, the process might behave rather chaotically. We give an example where M is the unit interval. M is written as the union of two closed subsets A₁,A₂, the contractions Γ₁,Γ₂ are rather simple, but the expectations of the gains are not even Cesáro convergent.     

Analyticity and renormalization group

We prove the inequalities ψ(y, α) ?α, |α_s(d/dα_s)(β(α_s)/α_s| ? 1 (for the Paterman-Stueckelberg-Gell-Mann-Low functions in QED and QCD) and γ₀(α_s ? 1 (for the anomalous dimension of the gauge-invariant operator O(x)). The consequences of the inequalities are discussed: for modern energies, comparison of theoretical and experimental moments of deep inelastic structure functions has a meaning only for N ? 7 (singlet case) and N ? 50 (non-singlet case); perturbation theory in QCD has a meaning only for α_rms ? 0.45.     

Dimensionality of a system of exchange-coupled grains and magnetic properties of nanocrystalline and amorphous ferromagnets

Characteristics of random magnetic anisotropy in ferromagnetic films of amorphous Co₉₀P₁₀ and nanocrystalline Ni₇₅C₂₅, Fe₈₀B₄C₁₆, and Co₈₀C²⁰ alloys and also in multilayer films [Co₉₃P₇(x)/Pd(14 Å)]₂₀ and [Co₉₀P₁₀(x)/Pd(14 Å)]₂₀ obtained by various technological procedures were studied experimentally. It was found that the spatial dimensionality (d) of the system of ferromagnetically coupled grains (2R _c ) in the materials under study determined the exponent in the power dependence of the approach of magnetization to saturation in the region of fields H<2A/MR _c ² . The dependence ΔM～H ^?1/2 was observed for nanocrystalline and amorphous films with a three-dimensional grain arrangement. The approach to saturation in multilayer films with a two-dimensional grain arrangement in an individual magnetic layer follows the law ΔM～H ^?1. The main micromagnetic characteristics of random anisotropy, such as the ferromagnetic correlation radius R _f and the average anisotropy 〈K〉 of a ferromagnetic domain with a size of 2R _f , were determined for multilayer Co/Pd films. Correlation was found between the coercive field and these characteristics of random anisotropy.     

Influence of surface roughness and contact load on friction coefficient and scratch behavior of thermoplastic olefins

To study the effects of surface roughness and contact load on the friction behavior and scratch resistance of polymers, a set of model thermoplastic olefins (TPO) systems with various surface roughness (R_a) levels were prepared and evaluated. It is found that a higher R_a corresponds to a lower surface friction coefficient (μ_s). At each level of R_a, μ_s gets larger as contact load increases, with a greater increase in μ_s as R_a level increases. It is also observed that with increasing contact load and increasing R_a, the μ_s tend to level off. In evaluating TPO scratch resistance, a lower μ_s would delay the onset of ductile drawing-induced fish-scale surface deformation feature, thereby raising the load required to cause scratch visibility. However, as the contact load is further increased, the μ_s evolves to become scratch coefficient of friction (SCOF) as significant sub-surface deformation and tip penetration occur and material displacement begins, i.e., ploughing. No dependence of R_a and μ_s on the critical load for the onset of ploughing is observed. In this work, the distinction between μ_s and SCOF will be illustrated. Approaches for improving scratch resistance of polymers via control of R_a are also discussed.     

Correlations and accuracy of estimation of spectroscopic constants and term values

A comparison and evaluation of the various methods for reducing spectroscopic data to spectroscopic constants or term values is made with the aid of an analysis of a number of “synthetic” Σ-Σ bands generated from fixed sets of constants with random noise superimposed on the line positions. It is shown that the strong correlations that exist between the upper-state constants B′, D′ and the lower-state constants B₀, D₀ can be effectively broken up by using the difference constants ΔB = B′ - B₀ and ΔD = D′ - D₀, along with ν₀, for representing the upper states. The lower state constants B₀ and D₀ and their standard errors calculated from the combination differences Δ₂F″(J) are shown to be as good as those obtained from direct polynomial fits. If data for a number of bands originating in the same lower state are available, a considerable increase in accuracy of estimating the lower-state constants can be attained by analyzing the bands simultaneously, e.g., using combination differences, provided the data are free from systematic errors. The dependence of the accuracy of determining the constants B₀, D₀, ν₀, ΔB, and ΔD on the extent of the band analyzed was investigated by varying the minimum and maximum J-values. The plots showing this dependence for both the actual errors and standard errors can be used e.g., to assess the band size necessary to attain a desired accuracy for a given constant.Åslund's term-value method is cast in a form which permits simple derivation of explicit formulas for the correlation coefficients connecting all the upper- and lower-state term values, and of explicit relations between the term values and the combination differences. Modifications of the term-value method suitable for the case where one or more transitions originate in an unperturbed state are explored. It is shown that the “difference term values” referred to the lower (unperturbed) state with the same value of J, T_i(J)-T₀(J), are essentially uncorrelated to the lower state constants B₀ and D₀. Since these quantities can be expressed directly as the eigenvalues of the energy matrix for a given J in the presence of perturbations, their use for representing the energies of perturbed rovibronic states is recommended.     

Mass relations and neutrino oscillations in an SO(10) model

We present in detail a grand unified model based on SO(10) which naturally reproduces known fermion mass relations and mixing angles. It predicts m_νe ? m_νμ, m_ντ, and predominant ν_μ-ν_τ oscillations. Several other features of the model are analyzed in detail: construction of the Higgs potential, predictions for τ_p and sin²θ_w in a temporarily free model and a relation between the mass of the t-quark and the lifetime of the B meson.     

A comparison of correlation and Lyapunov dimensions

This paper investigates the relation between the correlation (D₂) and the Kaplan–Yorke dimension (D_KY) of three-dimensional chaotic flows. Besides the Kaplan–Yorke dimension, a new Lyapunov dimension (D_Σ), derived using a polynomial interpolation instead of a linear one, is compared with D_KY and D₂. Various systems from the literature are used in this analysis together with some special cases that span a range of dimension 2 < D_KY ≤ 3. A linear regression to the data produces a new fitted Lyapunov dimension of the form D_fit = α − βλ₁/λ₃, where λ₁ and λ₃ are the largest and smallest Lyapunov exponents, respectively. This form correlates better with the correlation dimension D₂ than do either D_KY or D_Σ. Additional forms of the fitted dimension are investigated to improve the fit to D₂, and the results are discussed and interpreted with respect to the Kaplan–Yorke conjecture.     

Investigations of UBe13 of other compounds of Be and U in normal and superconductive states

During the last few years superconductive systems of heavy fermions with highly large values ofm* and electronic heat capacityγT have been thoroughly investigated. The following compounds viz CeCu₂Si₂ (T _c=0.6 K;γ=1100*), UBe₁₃(T _c=0.95 K;γ=1000) and UPt₃ (T _c=0.5 K;γ=450)(I) may be referred to such systems as well as the U and Ce compounds: U₂Pt C₂ (T _c=1.47 K;γ=75), U₆Fe (T _c=3.86 K;γ=25), U₆Co (T _c=2.3 K;γ=21), URu₂Si₂ (T _c=0.68 K,γ=17.6), as well asα-U (T _c=2.1;γ=12), CeRu₃Si₂ (T _c=1 K;γ=39), CeOs₂ (T _c=1,1 K;γ=22), CeRu₂ (T _c=6 K;γ=23.3) and α-Ce (T _c?2K;γ=14) (Alekseevskii and Homskiy 1985). It should be noted that there exists a class of U and Ce compounds with a similar structure as those given above, which undergo transition to superconductive state, but are not characterized by abnormal values ofm* (Alekseevskii 1984). Many authors considered superconductivity of heavy fermion systems as unusually anisotropic where charge carrier coupling occurs in P-state (Stewart 1984). On the other hand such a view does not agree with many experimental results, e.g. lack of anisotropy Hc₂ for UBe₁₃ (Alekseevskiiet al 1985) as predicted by Gorkov (1984) and the results of investigation of the Josephson effect. The Hall-effect investigations for UBe₁₃ in a wide range of fields and temperatures (Alekseevskii 1984) make it possible to consider systems with two types of carriers—heavy and light. The unique properties of the above systems in a number of cases are possibly caused by these two types of carriers and the peculiarity of interaction between them.     

Ecological interaction and phylogeny, studying functionality on composed networks

We study a class of composed networks that are formed by two tree networks, T_P and T_A, whose end points touch each other through a bipartite network B_PA. We explore this network using a functional approach. We are interested in how much the topology, or the structure, of T_X (X=A or P) determines the links of B_PA. This composed structure is a useful model in evolutionary biology, where T_P and T_A are the phylogenetic trees of plants and animals that interact in an ecological community. We make use of ecological networks of dispersion of fruits, which are formed by frugivorous animals and plants with fruits; the animals, usually birds, eat fruits and disperse their seeds. We analyse how the phylogeny of T_X determines or is correlated with B_PA using a Monte Carlo approach. We use the phylogenetic distance among elements that interact with a given species to construct an index κ that quantifies the influence of T_X over B_PA. The algorithm is based on the assumption that interaction matrices that follows a phylogeny of T_X have a total phylogenetic distance smaller than the average distance of an ensemble of Monte Carlo realisations. We find that the effect of phylogeny of animal species is more pronounced in the ecological matrix than plant phylogeny.     

Growing networks with preferential deletion and addition of edges

A preferential attachment model for a growing network incorporating the deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step t=1,2,…, with probability π₁>0 a new vertex with one edge attached to it is added to the network and the edge is connected to an existing vertex chosen proportionally to its degree, with probability π₂ a vertex is chosen proportionally to its degree and an edge is added between this vertex and a randomly chosen other vertex, and with probability π₃=1−π₁−π₂<1/2 a vertex is chosen proportionally to its degree and a random edge of this vertex is deleted. The model is intended to capture a situation where high-degree vertices are more dynamic than low-degree vertices in the sense that their connections tend to be changing. A recursion formula is derived for the expected asymptotic fraction p_k of vertices with degree k, and solving this recursion reveals that, for π₃<1/3, we have p_k∼k^{−(3−7π₃)/(1−3π₃)}, while, for π₃>1/3, the fraction p_k decays exponentially at rate (π₁+π₂)/2π₃. There is hence a non-trivial upper bound for how much deletion the network can incorporate without losing the power-law behavior of the degree distribution. The analytical results are supported by simulations.     

Studies on the Vibrational and Rovibrational Energies and Vibrational Force Constants of Diatomic Molecular States Using Algebraic and Variational Methods

Alternative expressions for vibrational and rotational spectrum constants and energies of diatomic molecular electronic states based on perturbation theory are suggested. An algebraic method (AM) is proposed to generate a converged full vibrational spectrum from limited energy data, and a potential variational method (PVM) is suggested to produce the vibrational force constants f_n and rotational spectrum constants using the perturbation formulae and the AM vibrational constants. The AM and PVM have been applied to study 10 diatomic electronic states: the X¹Σ_g⁺ and C¹Π_u⁻ states of H₂; the X¹Σ_g⁺, A³Σ_u⁺, B′³Σ_u⁻, and B³Π_g states of N₂; the X³Σ_g⁻, A³Σ_u⁺, and c¹Σ_u⁻ states of O₂; and the X¹Σ_g⁺ state of Br₂. Calculations show that (1) the AM E_υmax converges to the correct molecular dissociation energy; (2) the AM not only reproduce the input energies, but also generate the E_υ's of high vibrational excited states which may be difficult to obtain experimentally or theoretically; (3) the PVM vibrational force constants f_n may be used to measure the relative chemical bondstrengths of different diatomic electronic states for a molecule quantitatively.     

The relation between crystal structure and luminescence in β-alumina and magnetoplumbite phases

Crystallographic data of aluminate and gallate β-aluminas and magnetoplumbites are reviewed. For the XAl₁₁O₁₇ and XGa₁₁O₁₇ compounds c/a increases with increasing r_X+. The magnetoplumbites have c/a values ranging between 3.915 and 3.954 with the exception of BaAl₁₂O₁₉ and BaGa₁₂O₁₉. These compounds seem to have strongly distorted magnetoplumbite-derived structures. Upon activation of the MeAl₁₂O₁₉(Me = Ca, SrorBa) lattices with Eu²⁺ and Ce³⁺, the luminescence properties of Ba containing compounds deviate from the other compounds. This seems to be due to different co-ordinations of the activator ions. Substitution of Mg²⁺ for Al³⁺ in magnetoplumbite phases results in the case of SrAl₂O₁₉ in changes of the c/a ratio, of diffraction intensities and of the luminescence properties. The various data suggest a close similarity of this type of phases and BaAl₁₂O₁₉. In the MeGa₁₂O₁₉ series (Me = SrorBa), the quantum efficiency of BaGa₁₂O₁₉: Mn²⁺ was found to be anomalously low.     

Exact results of an alternating-bond mixed spin-1/2 and spin-1 Ising chain with both longitudinal and transverse single-ion anisotropies

The alternating-bond mixed spin-1/2 and spin-1 Ising chain with both longitudinal and transverse single-ion anisotropies are solved exactly by means of a mapping of the spin-1/2 transverse Ising chain and the Jordan-Wigner transformation. The ground state quantities are strongly dependent on the model Hamiltonian parameters J₁, J₂, D_x and D_z. We obtain the quasi-particles' spectra Λ_k, the dimerization gap Δ_d, the minimal energy Δ₀ for exciting a fermion quasi-particle, the minimal energy gap Δ_h for exciting a hole and the ground state energy E_g. The phase diagram of the ground state is also given. The results show that the alternating bond just quantitatively changes the ground state properties; no matter the nearest-neighbor exchange interactions J₁ and J₂ are equal or not, when D_z≥0 for any finite value of D_x, there is no quantum critical point and the ground state is always in a spin ordered phase.     

Renormalization group and dynamical symmetry breakdown in abelian gauge theories

Generalized renormalization group equations are used to analyze the dynamical mechanism of particle mass generation in terms of the Cornwall-Norton model both with and without cut-off. We look for solutions which contain non-zero physical masses of the two fermions (m₁, m₂) and of one of the vector bosons (μ) when the bare masses m_1Λ, m_2Λ, μ_Λ approach zero. For a theory without cut-off we obtain results which are similar to those of Cornwall. For a theory with cut-off the mass generation mechanism may only occur when a bare coupling constant α_Λ of the A_μ vector boson, which remains massless, exceeds some critical value α_c. In this case the fermion masses turn out to be of the superconductivity type.The model's “memory” of the nature of spontaneous symmetry breaking lim_{m1Λ, m2Λ → 0}m_1Λ/m_2Λ ≠ 1 is an indispensible factor for the vector boson to acquire a mass.     

Transverse water relaxation in whole blood and erythrocytes at 3T, 7T, 9.4T, 11.7T and 16.4T; determination of intracellular hemoglobin and extracellular albumin relaxivities

Blood is a physiological substance with multiple water compartments, which contain water-binding proteins such as hemoglobin in erythrocytes and albumin in plasma. Knowing the water transverse (R₂) relaxation rates from these different blood compartments is a prerequisite for quantifying the blood oxygenation level-dependent (BOLD) effect. Here, we report the Carr-Purcell-Meiboom-Gill (CPMG) based transverse (R_2CPMG) relaxation rates of water in bovine blood samples circulated in a perfusion system at physiological temperature in order to mimic blood perfusion in humans. R_2CPMG values of blood plasma, lysed packed erythrocytes, lysed plasma/erythrocyte mixtures, and whole blood at 3 T, 7 T, 9.4 T, 11.7 T and 16.4 T were measured as a function of hematocrit or hemoglobin concentration, oxygenation, and CPMG inter-echo spacing (τ_cp). R_2CPMG in lysed cells showed a small τ_cp dependence, attributed to the water exchange rate between free and hemoglobin-bound water to be much faster than τ_cp. This was contrary to the tangential dependence in whole blood, where a much slower exchange between cells and blood plasma applies. Whole blood data were fitted as a function of τ_cp using a general tangential correlation time model applicable for exchange as well as diffusion contributions to R_2CPMG, and the intercept R_20blood at infinitely short τ_cp was determined. The R_20blood values at different hematocrit and the R_2CPMG values of lysed erythrocyte/plasma mixtures at different hemoglobin concentration were used to determine the relaxivity of hemoglobin inside the erythrocyte (r_2Hb) and albumin (r_2Alb) in plasma. The r_2Hb values obtained from lysed erythrocytes and whole blood were comparable at full oxygenation. However, while r_2Hb determined from lysed cells showed a linear dependence on oxygenation, this dependence became quadratic in whole blood. This possibly suggests an additional relaxation effect inside intact cells, perhaps due to hemoglobin proximity to the erythrocyte membrane. However, we cannot exclude that this is a consequence of the simple tangential model used to remove relaxation contributions from exchange and diffusion. The extensive data set presented should be useful for future theory development for the transverse relaxation of blood.     

Angular dependence of coercivity and remanence of Ni nanowire arrays and its relevance to magnetoviscosity

Ni nanowire arrays with varying wire dimensions (diameter d, length l) and center-to-center distances d_CC were synthesized by pulsed electrodeposition of Ni in porous Al templates. The magnetization-reversal behavior of the arrays was investigated by means of magnetometry for different angles θ between the wire axes and the applied magnetic field. The functional dependences of the characteristic parameters coercivity H_C(θ) and reduced remanence m_R/m_S(θ) exhibit a strong dependence on the wire dimensions and the center-to-center distance. For instance, for nanowire arrays with d=40 nm, d_CC=100 nm, and for θ=0°, the coercivity takes on a rather large value of μ₀H_C=85 mT and m_R/m_S≅94%; reducing d_CC to 30 nm and d to 17 nm results in μ₀H_C=49 mT and m_R/m_S≅57%, an observation which suggests an increasing magnetostatic interwire interaction at increased (d/d_CC)-ratio. The potential application of nanowires as the constituents of ferrofluids is discussed.     

An YBCO film as a Josephson medium near T c : Frequency and field dependences and scaling relationships

The diamagnetic response of a laser-deposited YBCO film was studied in weak exciting magnetic fields H _ac =H ₀sinωt (H ₀=2–500 mOe, ω/2π=1–30 kHz). An analysis of the experimentally measured diamagnetic response showed evidence of a ring character of the electric field flowing in the sample at small H ₀ values. The plots of T _m (the temperature of maximum dissipative losses χ″₁) versus H ₀ measured at various frequencies showed the existence of a certain critical field strength H*(ω) at which the (1?T _m /T _c ) versus H ₀ ^2/3 plots exhibit a break. A logarithmic dependence of T _m on the frequency ω of the exciting field H _ac is reliably valid only in the region of (ω/2π)>5 kHz. Verification of the scaling relationship showed that this relationship is valid (to within the experimental accuracy) for the frequencies ω above 5 kHz and the field amplitudes H ₀>H*(ω). However, the exponent n in the scaling relationship under consideration is not correlated with the exponent n in the power relationship describing the current-voltage characteristic.     

Electronic spectroscopy of N- and C-substituted chlorocarbazoles in homogeneous media and in solid matrix

Electronic spectra (absorption, fluorescence and phosphorescence emission spectra) of chlorocarbazoles 1a-e, 2a-b, 3a, 4a-b, 5a, 6a, 7a, 8a-c, 9a and 9b in acetonitrile and in solid matrix have been recorded at 298 and 77 K. The dynamic properties of the lowest excited singlet and triplet states in term of fluorescence and phosphorescence lifetime, τ_f and τ_p, fluorescence and phosphorescence quantum yield, φ_f and φ_p have been measured in the same experimental conditions and from these data the radiative and the radiationless rate constants (k_f⁰, k_isc, k_f⁰(77), k_isc(77), k_p⁰ and k_nr⁰) and the intersystem crossing quantum yield, φ_isc, were derived.The intramolecular heavy atom effect (HAE) on the spectroscopic data and photophysical rate constant was analyzed and the incorporation of chlorine atoms to the carbazole moiety proved their ability to quench the fluorescence emission by spin-orbital coupling.The values of the HOMO and LUMO energy, the oscillator strength (f) and the λ_max(abs) associated to the electronic transitions, the heat of formation of the chlorocarbazoles and the corresponding radical cation (ΔH_f and ΔH_f(RC)) and the adiabatic ionization potential (I_a) were also calculated by using the semiempirical PM3 method after HF/3-21G geometrical optimization, and were compared with the spectroscopic and photophysical data as well as with the one electron oxidation potential data (E_p/2).     

A simple Fourier photopolarimeter with rotating polarizer and analyzer for measuring Jones and Mueller matrices

The classic and simplest polarimetric scheme of examining a “sample” by placing it between a pair of linear polarizers and observing the intensity of the transmitted light can be transformed into a powerful photopolarimeter if the two polarizers are synchronously rotated at different speeds and the transmitted flux is linearly detected and its periodic waveform Fourier analyzed. In particular, if the angular speed of rotation of one polarizer is ω and that of the other is 3ω, the detected signal has the waveform, i=a₀ + Σ⁴_n=1a_n cos nω_ft + b_n sin nω_ft, where ω_f=2ω is the fundamental frequency. The nine Fourier amplitudes a₀ and (a_n, b_n), n=1,2,3,4, to be derived by performing a discrete Fourier transform (DFT) of the signal i, determine all nine elements of the 3×3 submatrix M_3×3 obtained by deleting the fourth row and fourth column of the Mueller matrix M. If the sample is nondepolarizing, the absolute values of all the four elements of the equivalent Jones matrix $\text{J}\text{=(J}{}_{\mathrm{ij}}\text{)}$, i,j=1,2 and their angle differences θ_ij?θ₂₂ (where θ_ij=argJ_ij) can be determined.