Origin of the ESR spectrum in the Prussian Blue analogue RbMn[Fe(CN)6]*H2O

We present an ESR study at excitation frequencies of 9.4 GHz and 222.4 GHz of powders and single crystals of a Prussian Blue analogue (PBA), RbMn[Fe(CN)6]*H2O in which Fe and Mn undergoes a charge transfer transition between 175 and 300 K. The ESR of PBA powders, also reported by Pregelj et al. (JMMM, 316, E680 (2007)) is assigned to cubic magnetic clusters of Mn2+ ions surrounding Fe(CN)6 vacancies. The clusters are well isolated from the bulk and are superparamagnetic below 50 K. In single crystals various defects with lower symmetry are also observed. Spin-lattice relaxation broadens the bulk ESR beyond observability. This strong spin relaxation is unexpected above the charge transfer transition and is attributed to a mixing of the Mn3+ - Fe2+ state into the prevalent Mn2+ - Fe3+ state.

The chemistry of British bituminous coals : an assessment of phase transfer catalysed reactions in the determination of coal structure

Three British bituminous coals, (Gedling, Cresswell, and Cortonwood Silkstone) were selected for study. Procedures were developed, using phase transfer catalysts (PTC's), to degrade the solvent insoluble fractions of the coals. PTC's are of interest because they have the potential to bring about selective high conversion reactions, under mild conditions, (often in the past, severe reaction conditions have had to be used to degrade the coals, this in turn resulted in the loss of much of the structural information). We have applied a variety of physical and chemical techniques to maximise the amount of structural information, these include, elemental analysis, 1H-NMR, 13C-CPMAS-NMR, GPC, GC-MS, FTIR spectroscopy, DRIFT spectroscopy, and gas adsorption measurements. The main conclusions from the work are listed below:- ( 1 ) PTC O-methylation; This reaction removes hydrogen bonds within the coal matrix by 'capping' the phenolic groups. It was found that the polymer-like matrix could be made more flexible, but not significantly more soluble, by O-methylation. I.E. the trapped or 'mobile' phase of the coals could be removed at a faster rate after this reaction had been carried out. ( 2 ) PTC Reductive and Acidic Ether Cleavage; The three coals were found to contain insignificant amounts of dialkyl and alkyl aryl ethers. The number of diaryl ethers could not be estimated, by reductive ether cleavage, (even though a high proportion of all three coals was solublised). The majority of the ethers present in the coals were inert to both cleavage methods, and are therefore assumed to be heterocyclic ethers. ( 3 ) Trif!uoroperacetic Acid Oxidation; This oxidant was used to study the aliphatic portions of the polymer-like macromolecular matrix of the coals. Normally this reagent will only solublise low rank coals, we however have developed a method whereby trifluoroperacetic acid can be used to degrade high rank bituminous coals. ( 4 ) PTC/Permanganate Oxidation; This reagent has been found to be much more selective than the traditional alkaline permanganate oxidation, with a lot more structural information being retained within the various fractions. This degradative method therefore has the potential of yielding new information about the molecular structure of coals.

On an indirect integral equation approach for stationary heat transfer in semi-infinite layered domains in R3 with cavities

Regions containing internal boundaries such as composite materials arise in many applications.We consider a situation of a layered domain in IR3 containing a nite number of bounded cavities. The model is stationary heat transfer given by the Laplace equation with piecewise constant conductivity. The heat ux (a Neumann condition) is imposed on the bottom of the layered region and various boundary conditions are imposed on the cavities. The usual transmission (interface) conditions are satised at the interface layer, that is continuity of the solution and its normal derivative. To eciently calculate the stationary temperature eld in the semi-innite region, we employ a Green's matrix technique and reduce the problem to boundary integral equations (weakly singular) over the bounded surfaces of the cavities. For the numerical solution of these integral equations, we use Wienert's approach [20]. Assuming that each cavity is homeomorphic with the unit sphere, a fully discrete projection method with super-algebraic convergence order is proposed. A proof of an error estimate for the approximation is given as well. Numerical examples are presented that further highlights the eciency and accuracy of the proposed method.

Interaction of Kelvin waves and nonlocality of energy transfer in superfluids

We argue that the physics of interacting Kelvin Waves (KWs) is highly nontrivial and cannot be understood on the basis of pure dimensional reasoning. A consistent theory of KW turbulence in superfluids should be based upon explicit knowledge of their interactions. To achieve this, we present a detailed calculation and comprehensive analysis of the interaction coefficients for KW turbuelence, thereby, resolving previous mistakes stemming from unaccounted contributions. As a first application of this analysis, we derive a local nonlinear (partial differential) equation. This equation is much simpler for analysis and numerical simulations of KWs than the Biot-Savart equation, and in contrast to the completely integrable local induction approximation (in which the energy exchange between KWs is absent), describes the nonlinear dynamics of KWs. Second, we show that the previously suggested Kozik-Svistunov energy spectrum for KWs, which has often been used in the analysis of experimental and numerical data in superfluid turbulence, is irrelevant, because it is based upon an erroneous assumption of the locality of the energy transfer through scales. Moreover, we demonstrate the weak nonlocality of the inverse cascade spectrum with a constant particle-number flux and find resulting logarithmic corrections to this spectrum.