Lévy-statistics for partially equilibrated systems

We examine deviations from Boltzmann-Gibbs statistics for a certain class of partially equilibrated systems of finite size. We find that such systems are characterized by the Lévy distribution whose non-extensivity parameter is related to the number of internally equilibrated subsystems and to correlations among them. This concept is applicable to relativistic heavy ion collisions.     

Interaction between magnetic agglomerates and an extended free radicals network studied by magnetic resonance

Solids containing an extended network of free radicals have been prepared and studied by magnetic resonance techniques in the 4–290 K temperature range. One solid contained additionally a small amount of magnetic γ-Fe₂O₃ in the form of nanoparticle agglomerates. The solid without agglomerates displayed only a narrow, single resonance line centered at g _eff = 2.0043. The magnetic resonance measurements of the solid with γ-Fe₂O₃ agglomerates gave a spectrum composed of two lines attributed to two different magnetic centers: a narrow line due to free radicals and a broad line arising from magnetic iron oxide agglomerates. In the high temperature range the integrated intensities of both lines decreased with decreasing temperature. The resonance field of the broad line shifted to lower magnetic fields upon lowering the temperature with the gradient ΔH _r /ΔT = 2.3 G/K, while the narrow line shifted towards higher magnetic fields. The linewidth of the broader line increased with decreasing temperature while for the narrow lines in both samples this change was small. The magnetic iron oxide clusters produce a magnetic field which acts on the free radicals network and its strength depends essentially on the concentration of clusters. The reorientation process in the free radicals network is more intense in the sample without magnetic clusters.     

Interlayer Formation of Cyclobis(paraquat-o-phenylene) by the Reaction of Laponite-4,4'-bipyridinium Intercalates with α, α'-Dibromo-o-xylene: A One Electron Template Synthesis

Cyclobis(paraquat-o-phenylene) cyclophane can be synthesised in the form of a free radical within the gallery space of a synthetic aluminosilicate clay mineral. The interlayer formation of the cyclophane was revealed by XRD, IR and optical measurements. The mechanism of its formation is consistent with a one electron redox synthesis in which the electron donated by the clay mineral plays the role of the template towards the -electron deficient bipyridinium moieties.     

Extended free radical network from condensed cyanuric chloride with p-phenylenediamine: An EPR/FMR study

A covalent layered network was obtained by condensation of cyanuric chloride with bridging paraphenylenediamine. The local chemical environment of the layered solid can be changed by a redox reaction to obtain new reconstructed derivatives. A blue product was obtained by treating an alcoholic dispersion of the layered solid with ferric nitrate or potassium persulfate, indicating the possible formation of an extended free radical. When iron nitrate was used as oxidant, the temperature-dependent magnetic resonance spectra were measured in the 290–4 K region. The magnetic resonance measurements showed the coexistence at room temperature of two spectra arising from two different magnetic centers: a narrow line centered at g = 2.0038(1) with linewidth of ΔH = 7.42(2) G (free radical) and a broad line centered at g = 2.254(1) with linewidth of ΔH = 1300(5) G (magnetic iron-oxide cluster). A new sample was prepared so that the broader line was more intense. The temperature dependence of the magnetic resonance lines was subject to intense changes in both cases. The integrated intensities decreased with decreasing temperatures in both spectra in the high temperature region. This type of behavior is similar to that of magnetic nanoparticles in non-magnetic matrices. Upon reducing the temperature with the gradient of ΔH_r/ΔT = 1.5(1) G/K, the resonance field of the broad line was shifted towards lower magnetic fields, while the narrow line was shifted towards higher magnetic fields with ΔH_r/ΔT = 0.020(1) G/K. The linewidth of the broader line increased with decreasing temperature, while the narrow line remained almost constant. The magnetic iron-oxide clusters could produce an internal magnetic field acting on free radicals. This field could compel free radicals to form a magnetic ordered state at high temperatures.     

Study of hyperfine interactions by Mössbauer spectroscopy in mixed crystals

A mixed crystal technique, appropriate for the Mössbauer study of hyperfine interactions in molecules with D > 0, is described. It is based on the magnetic behavior of a |±$\text{1}\text{2}$〉 Kramers doublet. The method has been applied with success to the study of hyperfine structure of Fe(methdtc)₂Br.     

Structural Diversity in Thallium Chemistry. Part V

From thallium(III) bromide solution, the unsubstituted pyridinium cation yields a complex ( 1 ) with the [Tl₂Br₉]^3? anionic stoichiometry. The Raman spectrum and single‐crystal X‐ray crystallographic analysis showed that the salt contains independent [TlBr₄]^? and bromide anions. A variety of mono‐ and disubstituted pyridinium cations were also employed in similar syntheses. The 2‐bromopyridinium cation gave a salt 2 with [TlBr₅]^2? stoichiometry, but the crystal structure revealed very weakly interacting [TlBr₄]^? and bromide anions with a Tl ???Br^? distance of 4.1545(6) Å. The 2‐(ammoniomethyl)pyridinium and 2‐amino‐4‐methylpyridinium cations yielded complexes containing [TlBr₅]^2? ( 3 ) and [TlBr₄]^? ( 4 ) species, respectively, which were confirmed by Raman spectroscopy and X‐ray crystallographic analyses. For 3 , the [TlBr₅]^2? anion has a highly distorted trigonal bipyramidal conformation with one long axial Tl ???Br bond of 3.400(2) Å. Microanalytical results in conjunction with Raman spectra from a further five salts confirmed that they all contain the simple [TlBr₄]^? anion. N? H ???Br Hydrogen bonds clearly influence the nature of the anionic species obtained in these systems.     

New proofs of Plünnecke-type estimates for product sets in groups

We present a new method to bound the cardinality of product sets in groups and give three applications. A new and unexpectedly short proof of the Plünnecke-Ruzsa sumset inequalities for commutative groups. A new proof of a theorem of Tao on triple products, which generalises these inequalities when no assumption on commutativity is made. A further generalisation of the Plünnecke-Ruzsa inequalities in general groups.