The stress driven instability in elastic crystals: Mathematical models and physical manifestations

Summary Equilibrium equations and stability conditions for the simple deformable elastic body are derived by means of considering a minimum of the static energy principle. The energy is supposed to be sum of the volume (elastic) and the surface terms. The ability to change relative positions of different material particles is taken into account, and appropriate natural definitions of the first and second variations of the energy are introduced and calculated explicitly. Considering the case of negligible magnitude of the surface tension, we establish that an equilibrium state of a nonhydrostatically stressed simple elastic body (of any physically reasonable elastic energy potential and of any symmetry) possessing any small smooth part of free surface is always unstable with respect to relative transfer of the material particles along the surface. Surface tension suppresses the mentioned instability with respect to sufficiently short disturbances of the boundary surface and thus can probably provide local smoothness of the equilibrium shape of the crystal. We derive explicit formulas for critical wavelength for the simplest models of the internal and surface energies and for the simplest equilibrium configurations. We also formulate the simplest problem of mathematical physics, revealing peculiarities and difficulties of the problem of equilibrium shape of elastic crystals, and discuss possible manifestations of the above-mentioned instability in the problems of crystal growth, materials science, fracture, physical chemistry, and low-temperature physics.     

集化学家与化学教育家于一身的一代化学大师李比希--纪念李比希诞辰200周年

在德国著名化学家李比希诞辰200周年之际，对这位集化学家与化学教育家于一身的一代化学大师对科学和科学教育以及人类社会作出的贡献进行了评述。     

Determination of ethyl glucuronide in urine using reversed-phase HPLC and pulsed electrochemical detection (Part II)

A direct, versatile method for the determination of ethyl glucuronide (EtG), a biomarker of ethanol consumption, in urine has been developed using reversed-phase liquid chromatography with pulsed electrochemical detection (PED). EtG and methyl glucuronide (MetG), which serves as an internal standard, are readily separated using a mobile phase consisting of 1% acetic acid/acetonitrile (98/2, v/v). Post-column addition of NaOH allows for the detection of all glucuronides using PED at a gold working electrode. Upon optimization, EtG was found to have a limit of detection of 0.03 μg/mL (7 pmol; 50 μL injection volume) and repeatability at the limit of quantitation of 1.7%R.S.D. (relative standard deviation). Solid-phase extraction (SPE) using an aminopropyl phase was used to remove interferents in urine samples prior to their analysis. Compound recovery following SPE was approximately 50 ± 2%. The forensic utility of this method was further validated by the analysis of 29 post-mortem urine specimens, whose results agreed strongly with certified determinations.     

Indene and pseudoazulene discotic liquid crystals: a synthetic and structural study

Several new liquid-crystalline indene and pseudoazulene systems are reported. These molecules give rise to either columnar hexagonal mesophases and/or columnar plastic phases. The unique nature of these compounds stems from their non-classical discotic structure. Although the molecules have rigid aromatic cores, they lack terminal tails and instead the polarizable atoms (S, halogens) or polar groups (CN, CO) act as unusual soft parts. On the basis of many structurally related materials, we conclude that for this type of compound molecular stacking in the solid state is a prerequisite for the appearance of a columnar mesophase, although other intermolecular interactions within the layers are also important in establishing liquid-crystalline order. The behavior reported for these mesomorphic molecules opens up new possibilities in the search for related molecular interactions that might be useful for the construction of supramolecular architectures with particular properties.     

Synthesis and characterisation of bis(pentafluorophenyl)antimony(V) cations, [(C6F5)2SbL3]

Pentacoordinate complex cations of the general formula [(C₆F₅)₂SbL₃]³⁺ stabilized as solid salts in combination with tetraphenylborate (BPh₄), tetrafluorobroate (BF₄) anions, where L=DMSO, Ph₃AsO, PyO, DMF, α-, β- and γ-picoline have been isolated. The newly formed complexes were characterized by elemental analysis, molar conductance measurements, solid-state IR and and NMR. From these results, a five-fold coordination around antimony was required.     

New methods for data analysis of isothermal titration calorimetry

Heat divided by ligand concentration vs. heat, similar to the Scatchard plot, was introduced to obtain the equilibrium constant (K) and the enthalpy of binding (DH) using isothermal titration calorimetry data. Values of K and DH obtained by this linear pseudo-Scatchard plot for a system with a set of independent binding sites (such as binding fluoride ions on urease and monosaccharide methyl a-D-mannopyranoside on concavalin A) were remarkably like that obtained from a normal fitting Wiseman method and other our technical methods. On applying this graphical method to study the binding of copper ion on myelin basic protein (MBP), a concave downward curve obtained was consistent with the positive cooperativity in the binding. A graphical fitting by simple method for determination of thermodynamic parameters was also introduced. This method is general, without any assumption and restriction made in previous method. This general method was applied to the product inhibition study of adenosine deaminase. This revised version was published online in July 2006 with corrections to the Cover Date.     

Tetrakis(thiadiazolo)porphyrazines. 3. Acid-base Properties and Stability of Tetrakis-3,4-(1,2,5-thiadiazolo)porphyrazine in Sulfuric Acid Solutions

AM1 calculations gave the proton affinities of different types of donor sites in tetrakis-3,4-(1,2,5-thiadiazolo)porphyrazine, H₂{[SN₂)₄PA}, and protonation of the meso-nitrogen atoms was found to be favored. A spectrometric study showed that the basicity of the meso-nitrogen atoms of the porphyrazine macrocycle is strongly diminished and these atoms in CF₃CO₂H are involved in an incomplete acid-base interaction (ABI) to give acid solvates, while a complete ABI (protonation) is found only in the presence of sulfuric acid. The basicity constants of the meso-nitrogen atoms were determined spectrophotometrically in CF₃CO₂H-H₂SO₄. The kinetics of decomposition of the macrocyclic chromophore in concentrated sulfuric acid was studied and a possible mechanism for this process was proposed.__________Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 278–287, February, 2005.