Muonium Chemistry at Diiron Subsite Analogues of [FeFe]‐Hydrogenase

The chemistry of metal hydrides is implicated in a range of catalytic processes at metal centers. Gaining insight into the formation of such sites by protonation and/or electronation is therefore of significant value in fully exploiting the potential of such systems. Here, we show that the muonium radical (Mu^.), used as a low isotopic mass analogue of hydrogen, can be exploited to probe the early stages of hydride formation at metal centers. Mu^. undergoes the same chemical reactions as H^. and can be directly observed due to its short lifetime (in the microseconds) and unique breakdown signature. By implanting Mu^. into three models of the [FeFe]‐hydrogenase active site we have been able to detect key muoniated intermediates of direct relevance to the hydride chemistry of these systems.     

On the evolution of crystallographic dislocation density in non-homogeneously deforming crystals

A set of evolution equations for dislocation density is developed incorporating the combined evolution of statistically stored and geometrically necessary densities. The statistical density evolves through Burgers vector-conserving reactions based in dislocation mechanics. The geometric density evolves due to the divergence of dislocation fluxes associated with the inhomogeneous nature of plasticity in crystals. Integration of the density-based model requires additional dislocation density/density-flux boundary conditions to complement the standard traction/displacement boundary conditions. The dislocation density evolution equations and the coupling of the dislocation density flux to the slip deformation in a continuum crystal plasticity model are incorporated into a finite element model. Simulations of an idealized crystal with a simplified slip geometry are conducted to demonstrate the length scale-dependence of the mechanical behavior of the constitutive model. The model formulation and simulation results have direct implications on the ability to explicitly model the interaction of dislocation densities with grain boundaries and on the net effect of grain boundaries on the macroscopic mechanical response of polycrystals.     

Unveiling Talbot Effect under Fresnel Diffraction at a Fork-Shaped Grating

The near-field effect of diffraction image self-reproduction or self-imaging of a periodic grating illuminated by quasi-monochromatic wave is well-known as the Talbot effect. Introducing a dislocation to a periodic structure provides a fork-shaped modulation of the phase/amplitude, which produces discrete diffraction pattern in a far-field consisting of optical vortices. In this paper, Fresnel diffraction at amplitude fork-shaped grating is theoretically and experimentally studied. The coexistence of spatial ordering and local violation of translational symmetry of the structure manifests itself in a strict diffraction pattern consisting of optical vortices in the far-field, which is shown to be accompanied by formation of a spatially ordered intensity distribution in the near-field, reminiscent the Talbot carpets for periodic structures. These results demonstrate the first evidence of Talbot effect occurred under light diffraction at fork-shaped gratings, being promising for deep understanding of near-field singular optics phenomena.     

Kinetics of carbon dioxide sorption by the composite material K2CO3 in Al2O3

The kinetics of the CO₂ sorption by a composite sorbent K₂CO₃ in Al₂O₃ was studied in a gradientless adsorber at 295 K. The order of the sorption rate with respect to the CO₂ concentration was found to be n = 1.04 ± 0.07. The sorption rate constants were evaluated for sorbent grains of various sizes between 0.25 and 2.1 mm. It was shown that the rate constant is proportional to the grain reciprocal radius. The dynamic capacity was obtained as a function of the CO₂ concentration. The maximum sorption capacity was found to be 83 mg of CO₂ per 1 g of the sorbent. This revised version was published online in August 2006 with corrections to the Cover Date.     

Silver ion liquid-chromatographic mobility of plant diacylglycerols as a function of their composition and spatial arrangement

Coordination complexes of unsaturated rac-1,2-diacylglycerols (DAGs) with silver ions were separated by adsorption and reversed-phase TLC (silver ion TLC and silver ion RP-TLC, respectively). During silver ion TLC, silver ion complexes are formed by an indeterminate number of coordination centers of various nature and only at the adsorbent surface; separation of the complexes proceeds according to an adsorption mechanism, and there is an inverse exponential relationship between DAG unsaturation and their mobility. With silver ion RP-TLC, the complexes are formed only with double bonds, only in solution, and at a 1:1 ratio; the complexes are fractionated by lipophilic partitioning between two liquid phases, and the relationship between the unsaturation of DAGs and their mobility is a direct linear one. Nevertheless, in spite of all these differences, the use of both methods demonstrated that DAG species characterized by a coiled acyl configuration always greatly exceeded in polarity those with the same unsaturation, but with the configuration close to an extended one; in the former group, this excess amounted to two- to three-fold and 30-40% for silver ion TLC and silver ion RP-TLC, respectively. In addition, for both versions of silver ion LC, these two groups of species differ from each other quantitatively, but not qualitatively, in the pattern of the relationship between the unsaturation and mobility of DAG complexes. Thus, under all conditions of silver ion LC studied here, the polarity of DAG complexes and, therefore, their mobility are conditional not only on the number of double bonds, but also on their configuration.     

Reactions of Sulfenamides with Compounds of Trivalent Phosphorus

Chloro-dimethylamino-phenyl-p-tolylthio-phosphonium chloride 2 , dimethylamino-diphenyl-p-tolylthio-phosphonium chloride 3 , bis(diethylamino)-dimethylamino-p-tolylthiophosphonium chloride 4 and tert-butyl-dimethylamino-phenyl-p-tolylthio-phosphonium chloride 5 were prepared by the reaction of N,N-dimethylamino-p-tolylsulfenamide 1 with PhPCl₂, Ph₂PCl, (Et₂N)₂PCl and ^tBu(Ph)PCl, respectively. The reaction of N,N′-dimethyl-N,N′-bis(trimethylsilyl)urea 9 and N-methyl-N′-phenyl-N,N′-bis(trimethylsilyl)urea 10 with phenylsulfenyl chloride 6 or p-nitrophenylsulfenyl chloride 8 furnished the N-arylthio-N,N′-diorgano-N′-(trimethylsilyl)-ureas 11 – 14 . The reaction of 11 – 14 and of the previously known compounds 15 and 16 with MePCl₂, ClCH₂PCl₂, ^tBuPCl₂ and PhPCl₂ resulted in the formation of the 2-arylthio-2-chloro-1,2,3-triorgano-1,3,2λ⁵-diazaphosphetidin-4-ones 17 – 26 . 1,3-Dimethyl-2-(1,1,1,3,3,3-hexafluoro-2-propoxy)-2-phenyl-2-phenylthio-1,3,2λ⁵-diazaphosphetidin-4-one 29 and the 2-arylthio-1,3-dimethyl-2-(p-nitrophenoxy)-2-organyl-1,3,2λ⁵-diazaphosphetidin-4-ones 30 – 32 were obtained in the reactions of compounds 17, 24 and 27 with 1,1,1,3,3,3-hexafluoro-2-propanol or p-nitrophenol in the presence of triethylamine. The reaction of compound 21 with thiophenol in the presence of triethylamine resulted in a mixture of products, from which 1,3,4,5,7-pentamethyl-1,3,5,7-tetraaza-4λ⁵-phosphaspiro[3.3]heptan-2,6-dione 33 was isolated. The identity and structure of all the new compounds were established by ¹H-, ¹³C- and ³¹P-NMR spectroscopy and by elemental analysis. A possible mechanism of reaction of sulfenamides with compounds of trivalent phosphorus is discussed. For the compounds 5a, 32 and 33 X-ray structure analyses were conducted. The cation of compound 5a involves four-coordinate phosphorus (essentially tetrahedral geometry) and is a rare example of a P–S single bond in such a system (P–S 207.37(9) pm). In 32 the geometry at phosphorus is distorted trigonal bipyramidal, with axial positions occupied by oxygen and nitrogen atoms. In the spirophosphorane 33 the geometry at phosphorus is intermediate between trigonal bipyramidal and square pyramidal, with essentially planar four-membered rings.     

On Bellman function for extremal problems in BMO

In this Note we describe our results on construction of the Bellman function solving an extremal problem for a large class of integral functionals on BMO.     

Fokker-Planck equation with fractional coordinate derivatives

Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations, with averaging with respect to a fast variable, is used. The main assumption is that the correlation function of probability densities of particles to make a step has a power-law dependence. As a result, we obtain a Fokker-Planck equation with fractional coordinate derivative of order 1<α<2.     

Stationary solutions of Liouville equations for non-Hamiltonian systems

We consider the class of non-Hamiltonian and dissipative statistical systems with distributions that are determined by the Hamiltonian. The distributions are derived analytically as stationary solutions of the Liouville equation for non-Hamiltonian systems. The class of non-Hamiltonian systems can be described by a non-holonomic (non-integrable) constraint: the velocity of the elementary phase volume change is directly proportional to the power of non-potential forces. The coefficient of this proportionality is determined by Hamiltonian. The constant temperature systems, canonical-dissipative systems, and Fermi-Bose classical systems are the special cases of this class of non-Hamiltonian systems.