Nonlinear desingularization in certain free-boundary problems

We consider a nonlinear, elliptic, free-boundary problem involving an initially unknown setA that represents, for example, the cross-section of a steady vortex ring or of a confined plasma in equilibrium. The solutions are characterized by a variational principle which allows us to describe their behaviour under a limiting process such that the diameter ofA tends to zero, while the solutions degenerate to the solution of a related linear problem. This limiting solution is the sum of the Green function of the linear operator and of a smooth function satisfying the boundary conditions. Mathematically speaking, this limiting process, that we call nonlinear desingularization, is a novel kind of bifurcation phenomenon since the nonlinear effect here involves smoothing the singularity of the associated linear problem.Research partially supported by A FOSR and NSF grants     

Co-ordination chemistry of amino pendant arm derivatives of 1,4,7-triazacyclononane

The binding properties of 1,4,7-triazacyclononane ([9]aneN3) to metal cations can be adapted through sequential functionalisation of the secondary amines with aminoethyl or aminopropyl pendant arms to generate ligands with increasing numbers of donor atoms. The new amino functionalised pendant arm derivative of 1,4,7-triazacyclononane ([9]aneN3), L1, has been synthesised and its salt [H2L1]Cl2 characterised by X-ray diffraction. The protonation constants of the ligands L1-L4 having one, two or three aminoethyl or three aminopropyl pendant arms, respectively, on the [9]aneN3 framework, and the thermodynamic stabilities of their mononuclear complexes with CuII and ZnII have been investigated by potentiometric measurements in aqueous solutions. In order to discern the protonation sites of ligands L1-L4, 1H NMR spectroscopic studies were performed in D2O as a function of pH. While the stability constants of the CuII complexes increase on going from L1 to L2 and then decrease on going from L2 to L3 and L4, those for ZnII complexes increase from L1 to L3 and then decrease for L4. The X-ray crystal structures of the complexes [Cu(L1)(Br)]Br, [Zn(L1)(NO3)]NO3, [Cu(L2)](ClO4)2, [Ni(L2)(MeCN)](BF4)2, [Zn(L4)](BF4)2.MeCN and [Mn(L4)](NO3)2.1/2H2O have been determined. In both [Cu(L1)(Br)]Br and [Zn(L1)(NO3)]NO3 the metal ion is five co-ordinate and bound by four N-donors of the macrocyclic ligand and by one of the two counter-anions. The crystal structures of [Cu(L2)](ClO4)2 and [Ni(L2)(MeCN)](BF4)2 show the metal centre in slightly distorted square-based pyramidal and octahedral geometry, respectively, with a MeCN molecule completing the co-ordination sphere around NiII in the latter. In both [Zn(L4)](BF4)2.MeCN and [Mn(L4)](NO3)2.1/2H2O the metal ion is bound by all six N-donors of the macrocyclic ligand in a distorted octahedral geometry. Interestingly, and in agreement with the solution studies and with the marked preference of CuII to assume a square-based pyramidal geometry with these types of ligands, the reaction of L4 with one equivalent of Cu(BF4)2.4H2O in MeOH at room temperature yields a square-based pyramidal five co-ordinate CuII complex [Cu(L6)](BF4)2 where one of the three propylamino pendant arms of the starting ligand has been cleaved to give L6.     

A high-frequency and high-field EPR study of new azide and fluoride mononuclear Mn(III) complexes

The isolation, structural characterization and electronic properties of three new six-coordinated Mn(III) complexes, [Mn(bpea)(F)(3)] (1), [Mn(bpea)(N(3))(3)] (2), and [Mn(terpy)(F)(3)] (3) are reported (bpea = N,N-bis(2-pyridylmethyl)-ethylamine; terpy = 2,2':6',2' '-terpyridine). As for [Mn(terpy)(N(3))(3)] (4) (previously described by Limburg J.; Vrettos J. S.; Crabtree R. H.; Brudvig G. W.; de Paula J. C.; Hassan A.; Barra A-L.; Duboc-Toia C.; Collomb M-N. Inorg. Chem. 2001, 40, 1698), all these complexes exhibit a Jahn-Teller distortion of the octahedron characteristic of high-spin Mn(III) (S = 2). The analysis of the crystallographic data shows an elongation along the tetragonal axis of the octahedron for complexes 1 and 3, while complex 2 presents an unexpected compression. The electronic properties were investigated using a high-field and high-frequency EPR study performed between 5 and 15 K (190-575 GHz). The spin Hamiltonian parameters determined in solid state are in agreement with the geometry of the complexes observed in the crystal structures. A negative D value found for 1 and 3 is related to the elongated tetragonal distortion, whereas the positive D value determined for 2 is in accordance with a compressed octahedron. The high E/D values, in the range of 0.103 to 0.230 for all complexes, are correlated with the highly distorted geometry present around the Mn(III) ion. HF-EPR experiments were also performed on complex 1 in solution and show that the D value is the only spin Hamiltonian parameter which is slightly modified compared to the solid state (D = -3.67 cm(-1) in solid state; D = -3.95 cm(-1) in solution).     

A new pyridine-based 12-membered macrocycle functionalised with different fluorescent subunits; coordination chemistry towards Cu(II), Zn(II), Cd(II), Hg(II), and Pb(II)

The coordination chemistry of the new pyridine-based, N2S2-donating 12-membered macrocycle 2,8-dithia-5-aza-2,6-pyridinophane (L1) towards Cu(II), Zn(II), Cd(II), Hg(II), and Pb(II) has been investigated both in aqueous solution and in the solid state. The protonation constants for L1 and stability constants with the aforementioned metal ions have been determined potentiometrically and compared with those of ligand L2, which contains a N-aminopropyl side arm. The measured values show that Hg(II) in water has the highest affinity for both ligands followed by Cu(II), Cd(II), Pb(II), and Zn(II). For each metal ion considered, 1:1 complexes with L1 have also been isolated in the solid state, those of Cu(II) and Zn(II) having also been characterised by X-ray crystallography. In both complexes L1 adopts a folded conformation and the coordination environments around the two metal centres are very similar: four positions of a distorted octahedral coordination sphere are occupied by the donor atoms of the macrocyclic ligand, and the two mutually cis-positions unoccupied by L1 accommodate monodentate NO3- ligands. The macrocycle L1 has then been functionalised with different fluorogenic subunits. In particular, the N-dansylamidopropyl (L3), N-(9-anthracenyl)methyl (L4), and N-(8-hydroxy-2-quinolinyl)methyl (L5) pendant arm derivatives of L1 have been synthesised and their optical response to the above mentioned metal ions investigated in MeCN/H2O (4:1 v/v) solutions.     

Heterogeneous kinetics of the dissolution of an inorganic salt, potassium carbonate, in an organic solvent, dimethylformamide

Understanding the mechanisms of solid-liquid systems is fundamental to the development and operation of processes for the production of agrochemicals and pharmaceuticals. The use of a strong inorganic base in an organic solvent, typically, potassium carbonate in dimethylformamide, is often used to facilitate the formation of a required anionic organic nucleophile. In this paper, the dissolution kinetics of potassium carbonate in dimethylformamide at elevated temperatures is studied in the presence of ultrasound, as revealed via monitoring of the deprotonation of 2-cyanophenol by dissolved K2CO3. Two independent experimental methods were employed; the loss of 2-cyanophenol was detected electrochemically at a platinum microdisk working electrode, and the formation of the 2-cyanophenolate anion was monitored via UV/visible spectroscopic analysis. The results were modeled by fitting the experimental data to a theoretical model for the surface-controlled dissolution of solid particles. The dissolution rate constant, k, for the dissolution of K2CO3 in DMF was found to have a value of (1.3 +/- 0.2) x 10(-7) mol cm(-2) s(-1) at 100 degrees C, and the activation energy for the dissolution was 44.2 +/- 0.4 kJ mol(-1) over the temperature range of 70-100 degrees C studied.     

Organometallic complex compounds,part 6(1). Property-specific ligand control of stability and reactivity of (1,3-dimethyl-η3-allyl)methylnickel-ligand complexes. Separation of electronic and steric effects

Summary The property-specific ligand control of 28 ligands on the decomposition temperatures in solution, measured by d.t.a. of a four-coordinate nickel(II)-complex is reported. A quantitative separation of electronic and steric effects by a multilinear regression analysis (75% electronic and 25% steric influence for the chosen ligands) is presented. The controlling effect of the selectivity on the decomposition (fraction of the C-C-linked product) (25 P-ligands) leads to an electronic: steric ratio of the property-specific ligand control of 5545 for the chosen ligands. An increase in the relative acceptor character of the P-ligands relatively destabilizes the complexes and thereby favours formation of a C-C-bond. An increase in steric hindrance also favours C-C-bond formation. A method for revising the steric parameter of P-ligands is presented and is used to correct the -value of (PhCH₂)₃P is corrected to 135°. SCCC-MO-calculations for testing the chemical reasoning of the separated electronic and steric ligand property control are shown.     

Multilayer adsorption with variable thickness at solid-liquid interfaces

 The multilayer adsorption on the solid/liquid interface in binary mixtures was studied by adsorption space filling with constant and variable layer thickness. Adsorption from benzene/n-heptane mixtures was examined on hydrophilic and hydro-phobic surfaces. The free enthalpy of adsorption, Δ₂₁ G=f (x ₁), was calculated from the adsorption excess isotherm by integration of the Gibbs equation. Supposing that the free enthalpy is mainly due to adsorption in the first layer, the composition of this layer can be calculated from the Δ₂₁ G=f (x ₁) function. It was established that the adsorption layer thickness in benzene/heptane mixtures increases significantly with increasing benzene content. This statement was supported by X-ray diffraction on hydrophobic clay minerals. Received: 2 April 1997 Accepted: 10 June 1997     

Characterization of structural transitions in the SLS/decanol/water system

The ternary system sodium-dodecylsulphate (SLS)/decanol/water has been investigated at three different water contents and varying ratios of cosurfactant to surfactant by means of polarized optical microscopy,²H-NMR quadrupole splittings and small angle x-ray scattering. Upon addition of decanol a hexagonal phase transforms into a lamellar phase. For the highest water content of 0.65 no intermediate two-phase regions are detected but nematic phases are formed between. The lamellar phase at low cosurfactant content is very sensitive to changes of temperature and seems to be a so-called defective one with curved interfaces. From the scaling behavior it is concluded that the building units seem to be ribbons of increasing width on addition of cosurfactant or amphiphilic substance. By reaching a decanol mole fraction of 0.4 a classical lamellar phase with well-known behavior is formed. During these transformations the position of the first diffraction maximum changes gradually irrespective of phase transitions. The maximum mole fraction of cosurfactant the lamellar phase of our system can incorporate is 0.77.     

FOURIER TRANSFORM INFRARED SPECTROELECTROCHEMISTRY OF THE BACTERIOCHLOROPHYLL a ANION RADICAL

Abstract— Fourier transform infrared (FTIR) difference spectroscopy of the electrochemically generated anion radical of bacteriochlorophyll a was used to follow the molecular changes upon one-electron reduction. An IR spectroelectrochemical cell was constructed, allowing in situ electrolysis in connection with spectroscopic investigations from 200 to 10 000 nm. FTIR difference spectra of the BChl a anion formation in THF d₈ at U =+0.9 V (as determined by ferrocene calibration) were obtained. After complete formation of the radical, the reverse process was followed. Comparison of visible and IR spectra of the reduction and re-oxidation processes indicates that more than 90% of the BChl a anion could be formed with 90% of it being reversible. The main IR absorbance changes are observed for the conjugated and even for the non-conjugated C=O groups of BChl a . These results demonstrate the use of the combination of FTIR spectroscopy and electrochemistry for the characterization of radicals of the isolated pigments and of their in vivo bonding to the protein environment.     

Effect of mobile phase density gradients on efficiency in packed column supercritical fluid chromatography

Summary The efficiency of packed columns was measured as a function of flow rate, temperature, outlet density, and the density differential across the column, unsing pure carbon dioxide as the mobile phase. Although density differentials are often blamed for a serious loss in efficiency in packed column supercritical fluid chromatography, the results show that efficiency was not a function of the density differential. Peak shapes suggest that apparent loss in efficiency is actually due to inadequate solubility of the solute in carbon dioxide.