A mechanism of energy transfer in binuclear fluoride lanthanide complexes in aqueous electrolyte solutions

The energy transfer between different pairs of lanthanide ions bonded by fluoride bridges into labile binuclear complexes is studied in aqueous solution at different ratios between the concentrations of lanthanide ions and fluoride anions ([Ln]: [F]). It is shown that, if the concentrations [Ln] and [F] are of the same order of magnitude, the energy transfer rate constant k _t does not depend on the choice of the pairs of interacting ions and is determined by the association rate constant of Ln(III) ions into binuclear complexes. If the concentration of the lanthanide ions is much greater than that of the fluoride ions, k _t varies proportionally to the monomolecular energy transfer rate constants in the binuclear complexes. It is assumed that, in the first case, Ln(III) ions are bonded through two fluoride anions, whereas, in the second case, they are bonded through one anion. The analysis of the variations in k _t in the latter systems shows that the exchange-resonance mechanism should be taken into account for the explanation of the experimental data. The effects that the introduction into the solution of different contents of salts of strong acids—AlCl₃, MgCl₂, Ca(NO₃)₂, CsCl, RbBr, and NaCl—have on k _t and on the regularities of the energy transfer between Ln(III) ions bonded into binuclear fluoride complexes are studied. The effects of these electrolytes on the luminescence intensity and spectrum of Eu(III) ions and on the values of k _t for the energy transfer between Ln(III) ions bonded into binuclear complexes are analyzed. It is shown that, at some concentration ratio [Ln]: [F], for all electrolytes studied except AlCl₃, the value of k _t increases despite the fact that the concentration of mononuclear complexes of Ln(III) ions with fluorine decreases in the presence of these electrolytes. It is ascertained that the anions of strong acids in the outer sphere of lanthanide ions increase the association constant of Ln(III) ions in binuclear fluoride complexes.     

Dependence of the mechanism and regularities of energy transfer in binuclear lanthanide complexes in solutions on the nature of the anion and solvent

The effect of anions contained in solutions on the energy transfer from Tb(III) and Dy(III) ions to different Ln(III) ions is investigated in aqueous and alcohol solutions. It is shown that the regularities revealed in the energy transfer are completely determined by the ratio between the dissociation rate of the binuclear complex and the rate of energy transfer in it. The rate constant k _t of energy transfer in solutions in which labile binuclear complexes of Ln(III) ions are linked through the strong acid anions Cl^?, NO ₃ ^? , and HSO ₄ ^? depends on the nature of ions in the pairs. It is demonstrated that the energy transfer in all the systems predominantly occurs through the induction-resonance mechanism. The rate constants k _t in aqueous solutions of weak (acetic, salicylic, and carbonic) acids also depend on the nature of ions interacting in pairs but do not correlate with the Förster overlap integral of the spectra. In labile binuclear complexes, the interaction between these ions proceeds by the exchange-resonance mechanism at a distance of ≈0.4 nm. It is established that the constants k _t in alcohol solutions of Ln(III) ions are virtually independent of the nature of the pairs of the ions interacting through the acetate bridge. A comparison of the dissociation rate constants for Ln-anion complexes in alcohol solutions and the expected intracomplex rates of energy transfer in the binuclear complexes offers a satisfactory explanation of the obtained results and makes it possible to determine the association constants for binuclear lanthanide complexes in these solutions.     

Energy transfer between lanthanide ions in nanostructures of their complexes. I

We study the regular features of the behavior of the intensity I _lum and the luminescence decay time τ _lum of complexes of Eu and Tb ions with several β-diketones and 1,10-phenanthroline in the case where these complexes from nanostructures with complexes of lanthanide ions that are electronic excitation acceptors of these Eu and Tb ions. The composition of mixed nanostructures formed in a solution is shown to depend on the method of their preparation, on the ability of complexes to form mixed rather than homogeneous nanostructures, and on the concentration of complexes in the solution. We reveal that complexes of Yb, Tm, and Dy ions simultaneously increase I _lum and τ _lum of Eu complexes due to energy transfer through ligands of complexes and decrease the value of these quantities for Eu complexes due to energy transfer from Eu(III) ions to ions of Yb, Tm, and Dy. For all interacting complexes, the changes in I _lum and τ _lum of complexes of Eu (Tb) in the presence of complexes, energy acceptors, are shown to be determined by competition between two processes: a decrease in these quantities due to energy transfer between ions and their increase caused by an increase in the probability of nonradiative transitions in Eu (Tb) ions due to an increase in the size of structures. We propose a method of separation of these two processes.     

Columinescence of dye molecules in nanostructures of metal ion complexes

The mechanism of columinescence (fluorescence sensitization) of dyes incorporated in nanostructures of metal complexes is studied. It is shown for the first time that the columinescence of dyes is due to the transfer of excitation energy from ligands and metal ions of complexes that form nanostructures. It is proven that the dye columinescence of rhodamine 6G (R6G) molecules incorporated into nanostructures of Al(DBM)₃phen, Al(DBM) _n (OH)_{6 ? 2n} , and Eu(DBM)₃phen (DBM is dibenzoylmethane) nanostructures is completely determined by the singlet excitation energy migration from ligands to R6G molecules. It is shown that, at small concentrations of R6G, the R6G columinescence intensity is lower in nanostructures of metal complexes with a high probability of S-T conversion and that this difference disappears at large concentrations of R6G. In the case of Nile blue (whose S ₁ level lies below the ⁵ D ₀ level of Eu(III)) incorporated in nanostructures of Eu(DBM)₃phen complexes, as well as in nanostructures of Al(DBM)₃phen and Gd(DBM)₃phen complexes with admixture of Eu complexes, we observed the S-S energy transfer from DBM to NB in addition to the delayed sensitized fluorescence of NB previously observed in nanostructures of Eu complexes, which was caused by the energy transfer from the ⁵ D ₀ level of Eu(III) to NB. At dye concentrations below 100 nM, the efficiency of NB sensitization due to the migration of singlet excitation energy from DBM is lower than in the case of the energy transfer from Eu(III) ions, while, at large concentrations of the dye, the S-S energy transfer successfully competes with the sensitization of NB by Eu(III) ions. The use of dye columinescence makes it possible to easily determine dye concentrations of 2–100 nM in solutions with standard spectrofluorimeters.     

Energy transfer from Eu(III) and Tb(III) complexes to dyes in their mixed nanostructures. I

The formation of nanostructures that consist of complexes of β-diketones with 1,10-phenanthroline and involve dyes of the polymethine, triphenylmethane, oxazine, and xanthene series is observed in aqueous solutions. It is found that nanostructures of complexes of Ln(III) ions and dyes are reliably observed at concentrations of Ln complexes from 0.5 to 5 μM and at dye concentrations above 5 nM. Nanostructures of complexes Eu(MBTA)₃phen, Eu(NTA)₃phen, Eu(PTA)₃phen, Tb(PTA)₃phen, Gd(MBTA)₃phen, and Lu(MBTA)₃phen with dyes are studied, where MBTA is n-methoxybenzoyltrifluoroacetone, NTA is naphthoyltrifluoroacetone, PTA is pivaloyltrifluoroacetone, and phen is 1,10-phenanthroline. It is shown that nanostructures formed can contain dye molecules not only inside a nanostructure of Ln complexes but also on its outer shell. It is proved that, at a dye concentration in the solution of the order of nanomole or higher, the formation of mixed nanostructures of Eu complexes and dyes whose S ₁ level is below the ⁵ D ₀ level of Eu(III) leads to the quenching of the luminescence of Eu(III) and gives rise to the sensitized luminescence of dyes. The energy transfer efficiency from Eu(III) ions to dye molecules is determined by the ability of these molecules to incorporate into nanostructures of Eu complexes. The effect of the formation of nanostructures on the shape and position of the spectra of luminescence and absorption of dyes is studied. Comparison of the sensitized luminescence intensities of Nile blue in structures of Eu, Lu, and Gd complexes shows that the greater part of the excitation energy of Eu complexes is transferred directly from ions to dye molecules according to the inductive-resonance energy transfer mechanism rather than by means of energy migration over singlet levels of organic ligands in complexes of a nanostructure.     

Investigation of the formation of nanostructures of Ln(III) salts with phosphate and carbonate anions using Eu(III) chelates as luminescent markers

The monitoring of variations in the luminescence intensity (I _lum) of nanostructures of Eu(MBTA)₃phen (MBTA is p-methoxybenzoyl trifluoroacetonate) complexes formed in aqueous solutions upon the introduction of anions is proposed as a method of analyzing the composition of Eu(III), Gd(III) and Lu(III) phosphate complexes in solutions with [PO ₄ ^3? ] < [Ln]. It is found that low-lability binuclear complexes, which rearrange within an hour or longer, are formed in these solutions. It is shown that the lability of Ln(III) carbonate complexes exceeds the lability of Ln(III) complexes with PO ₄ ^3? . An analysis of the dependence of I _lum of the solution on the concentration of Eu(III) ions and on the time from the instant of the solution preparation shows that, in aqueous solutions where the concentration of anions is higher than the concentration of Ln(III) ions, nanostructures of Eu(III) phosphate and carbonate salts are formed in the range of Ln(III) concentrations 0.5–5 μM at concentrations of anions on the order of 10 μM and at concentrations of exceeding 100 μM. The rearrangement of these nanostructures to nanostructures of Eu(MBTA)₃phen complexes is studied.     

1<Emphasis Type="Italic">∕</Emphasis><Emphasis Type="Italic">f</Emphasis><Superscript><Emphasis Type="Italic">β</Emphasis></Superscript> noise for scale-invariant processes: how long you wait matters

We study the power spectrum which is estimated from a nonstationary signal. In particular we examine the case when the signal is observed in a measurement time window [t _w , t _w + t _m ], namely the observation started after a waiting time t _w , and t _m is the measurement duration. We introduce a generalized aging Wiener–Khinchin theorem which relates between the spectrum and the time- and ensemble-averaged correlation functions for arbitrary t _m and t _w . Furthermore we provide a general relation between the non-analytical behavior of the scale-invariant correlation function and the aging 1∕f ^β noise. We illustrate our general results with two-state renewal models with sojourn times’ distributions having a broad tail.     

Ghost Dark Energy with Non-Linear Interaction Term

Here we investigate ghost dark energy (GDE) in the presence of a non-linear interaction term between dark matter and dark energy. To this end we take into account a general form for the interaction term. Then we discuss about different features of three choices of the non-linear interacting GDE. In all cases we obtain equation of state parameter, w _D = p/ρ, the deceleration parameter and evolution equation of the dark energy density parameter (Ω _D ). We find that in one case, w _D cross the phantom line (w _D < ?1). However in two other classes w _D can not cross the phantom divide. The coincidence problem can be solved in these models completely and there exist good agreement between the models and observational values of w _D , q. We study squared sound speed \({v_{s}^{2}}\), and find that for one case of non-linear interaction term \({v_{s}^{2}}\) can achieves positive values at late time of evolution.     

Equilibrium and stability of the charged particles’ fluxes drifting crosswise to the strong magnetic field at the expense of the Hall charge separation

The current equilibrium is investigated, where the generation of the Hall electric field on the magnetic Debye radius r _B = B ₀/(4πen _e) is considered by the drifting of the relativistic electrons crosswise to the strong magnetic field. In this case, the electron propagation is possible at the distance d that is essentially larger than the electron radius of the backward reflection in the magnetic field r ₀ ? m _e v _z c/(eB ₀). The instability of the joint drift motion of ions and electrons is investigated for the frequency oscillation w much higher than the ion cyclotron frequency w _Bi and by 4π n _i m _i c ² ? B ₀ ² and (k · B ₀) = 0. It is shown that the resonance effects by the ion beam’s plasma frequency w ? kv ₀ = w _pi leads to the generation of the nonpotential perturbations with the characteristic increment Imw ～ 10^?1 ÷ 10^{? 2} w _pi. Estimates show that the instability, associated with the propagation of the high-energy ion beam through the strong magnetic field, can essentially be like the edge-localized mode in tokamaks.     

Dynamic phenomena connected with magnetic and antiferroelectric interactions in trirutiles

Dynamic effects caused by the magnetoelectric and antiferroelectric interactions in tetragonal antiferromagnets are studied. The analysis is based on the example of trirutiles that are a series of antiferromagnets with different exchange structures and orientation states. We are mainly dealing with the excitation by an alternating electric field E(t) of spin waves typical of these magnets (antiferroelectric resonance) and the nuclear magnetoelectric resonance connected with these interactions. In the first case, special emphasis is placed on specific magnons (antimagnons), where only the antiferromagnetism vectors L take part in oscillations, whereas the total ferromagnetism vector M remains unchanged. The nuclear magnetoelectric resonance can be generated by oscillations of both L and M caused by field E(t). In this way, the field contributes to the hyperfine field, which acts on the nuclear spins. It is shown that the magnetic and antiferroelectric interactions in the dynamics can manifest themselves both at high (usually, exchange) frequencies ωw_E (antiferroelectric resonance) and at rather low nuclear frequencies of ω_n?ω_E. Particular cases of magnetic structures (phases) are considered where field E(t) can excite not only antimagnons, but also quasiantiferromagnons that have lower eigenfrequencies than those of quasimagnons (relativistic and semirelativistic).     

Doping induced spin state transition in Li<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>CoO<Subscript>2</Subscript> as studied by the GGA + DMFT calculations

The magnetic properties of Li _x CoO₂ for x = 0.94, 0.75, 0.66, and 0.51 are investigated within the method combining the generalized gradient approximation with dynamical mean field theory (GGA + DMFT). A delicate interplay between Hund’s exchange energy and t _2g ?e _g crystal field splitting is found to be responsible for the high-spin to low-spin state transition for Co⁴⁺ ions. The GGA + DMFT calculations show that the Co⁴⁺ ions at a small doping level adopt the high-spin state, while delithiation leads to an increase in the crystal field splitting and low-spin state becomes preferable. The Co³⁺ ions are found to stay in the low-spin configuration for any x values.     

Equilibrium magnetic and orbital states of the manganites with four manganese atoms in the unit cell

The carrier energy spectrum and the total energy of various magnetic and orbital crystal-structure configurations of the manganites R _1?x A _xMnO₃ (R=La, Pr, Nd, Sm, etc.; A=Ca, Sr, Ba) with four manganese atoms in the unit cell have been calculated for the electron doping region x>0.5. The equilibrium magnetic and orbital configurations of the model are determined by minimizing the total energy of the system with respect to the angles θ _i ^s , φ_i, and θ _i ^o , which define the directions of the local manganese magnetic moments and the type of orbital mixing of the e _g electrons in the manganites. Assuming the parameters of the Heisenberg exchange interaction to be 0.018t<J _AFM<0.022t, the Hund exchange interaction to be J _H=2.5t, and the Jahn-Teller splitting to be Δ=1.5ty, the model with four manganese atoms in the unit cell predicts the experimentally observed magnetic phase alternation sequence G-C-A with increasing doping level y=1?x. For the values J _AFM<0.018t and y<0.28, this model allows the existence of a collinear phase H not observed earlier.     

Consecutive Quasi-Phase-Matched Interactions of Light Waves in Periodically Poled Nonlinear Optical Crystals

A new type of quasi-phase-matched interactions of light waves is considered — consecutive interactions of waves with frequencies w, 2w, 3w and w, 2w, 4w. They are shown to be possible in a periodically poled LiNbO₃:Y:Mg crystal for both co- and counterpropagating waves. It is shown that under certain conditions the energy of a high-intensity pump wave in the consecutive three-frequency interactions under consideration can be completely converted to the energy of one of the other two waves.     

Cross sections of electron capture by Boron ions in gaseous media

We study the cross sections σ_{i, i?1}, σ_{i, i?2}, and σ _{i, i?3} of capture of one, two, and three electrons by boron ions with charges i=1?5 and velocities V=(1.83?5.50)V₀ in gaseous media with atomic numbers Z_t varying from 1 to 54. The oscillatory form of the Z_t dependence of electron capture cross section by boron ions, which has been established for lighter ions, is confirmed.     

Magnetooptical,optical, and magnetotransport properties of Co/Cu superlattices with ultrathin cobalt layers

We investigated the field dependences of the magnetization and magnetoresistance of superlattices [Co(t _x, Å)/Cu(9.6 Å)]30 prepared by magnetron sputtering, differing in the thickness of cobalt layers (0.3 Å ≤ t _Co ≤ 15 Å). The optical and magnetooptical properties of these objects were studied by ellipsometry in the spectral region of hω= 0.09–6.2 eV and with the help of the transverse Kerr effect (hω= 0.5–6.2 eV). In the curves of an off-diagonal component of the tensor of the optical conductivity of superlattices with t _Co = 3–15 Å, a structure of oscillatory type (“loop”) was detected in the ultraviolet region, resulting from the exchange splitting of the 3d band in the energy spectrum of the face-centered cubic structure of cobalt (fcc Co). Based on magnetic experiments and measurements of the transverse Kerr effect, we found the presence of a superparamagnetic phase in Co/Cu superlattices with a thickness of the cobalt layers of 3 and 2 Å. The transition from superlattices with solid ferromagnetic layers to superparamagnetic cluster-layered nanostructures and further to the structures based on Co and Cu (t _Co = 0.3–1 Å) with a Kondo-like characteristics of the electrical resistivity at low temperatures is analyzed.     

Bound states of three and four resonantly interacting particles

We present an exact diagrammatic approach for the problem of dimer-dimer scattering in 3D for dimers being a resonance bound state of two fermions in a spin-singlet state, with corresponding scattering length a _F . Applying this approach to the calculation of the dimmer-dimer scattering length a _B , we recover exactly the already known result a _B = 0.6 a _F . We use the developed approach to obtain new results in 2D for fermions and bosons. Namely, we calculate bound state energies for three bbb and four bbbb resonantly interacting bosons in 2D. For the case of resonance interaction between fermions and bosons, we exactly calculate bound state energies of the following complexes: two bosons plus one fermion bbf, two bosons plus two fermions bf↑bf↓, and three bosons plus one fermion bbbf.     

Energy transfer from Eu(III) complexes to dyes in their mixed nanostructures. II

The effects of the concentration of a number of dyes in an aqueous solution and of the method of formation of mixed nanostructures of dyes and Eu(MBTA)₃phen (MBTA is p-methoxybenzoyltrifluoroacetone; phen is 1,10-phenanthroline) complexes that form these structures on the luminescence decay kinetics of Eu(III) ions are studied. It is shown that, in the concentration range 5–50 nM of Nile blue, the concentration dependences of the luminescence decay and of the decrease in τ _lum of Eu(III) nearly coincide and are nearly linear. The dependence of the ratio of I _lum of Eu(III) to the intensity of the sensitized delayed fluorescence of Nile blue on the delay time of the probe pulse is analyzed; it is found that the majority of dye molecules incorporated in nanostructures of Eu(MBTA)₃phen complexes emit sensitized delayed fluorescence with times 1–50 μs. Analysis of the effect of the structure of nanostructures on the quenching of I _lum of Eu(III) by the dye at different concentrations of Eu(III) shows that nanostructures of Eu(MBTA)₃phen and Eu(NTA)₃phen (NTA is 2-naphthoyltrifluoroacetone) complexes appear in the aqueous solution at a concentration of Eu(III) of 0.1 μM (the MBTA or NTA concentration is 50 μM, and the concentration of phen is 17 μM) and exist in the solution at the Eu(III) concentrations up to ～5 μM. This confirms the conclusion on the occurrence range of nanostructures of Ln complexes previously made based on the analysis of columinescence in these structures.     

Asymptotic Behavior of a Network of Oscillators Coupled to Thermostats of Finite Energy

We study the asymptotic behavior of a finite network of oscillators (harmonic or anharmonic) coupled to a number of deterministic Lagrangian thermostats of finite energy. In particular, we consider a chain of oscillators interacting with two thermostats situated at the boundary of the chain. Under appropriate assumptions, we prove that the vector (p, q) of moments and coordinates of the oscillators in the network satisfies (p, q)(t) → (0, q _c ) as t → ∞, where q _c is a critical point of some effective potential, so that the oscillators just stop. Moreover, we argue that the energy transport in the system stops as well without reaching thermal equilibrium. This result is in contrast to the situation when the energies of the thermostats are infinite, studied for a similar system in [14] and subsequent works, where the convergence to a nontrivial limiting regime was established.The proof is based on a method developed in [22], where it was observed that the thermostats produce some effective dissipation despite the Lagrangian nature of the system.