INFLUENCE OF A LEVELNESS DEFECT IN A THRUST BEARING ON THE DYNAMIC BEHAVIOUR OF AN ELASTIC SHAFT

This paper examines the non-linear dynamic behaviour of a flexible shaft. The shaft is mounted on two journal bearings and the axial load is supported by a defective hydrodynamic thrust bearing at one end. The defect is a levelness defect of the rotor. The thrust bearing behaviour must be considered to be non-linear because of the effects of the defect. The shaft is modelled with typical beam finite elements including effects such as the gyroscopic effects. A modal technique is used to reduce the number of degrees of freedom. Results show that the thrust bearing defects introduce supplementary critical speeds. The linear approach is unable to show the supplementary critical speeds which are obtained only by using non-linear analysis.     

Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

 To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships. (Accepted May 1, 2002) Published online November 15, 2002 Communicated by S. S. ANTMAN     

Propagation of avalanches in Mn12-acetate: magnetic deflagration

Local time-resolved measurements of fast reversal of the magnetization of single crystals of Mn12-acetate indicate that the magnetization avalanche spreads as a narrow interface that propagates through the crystal at a constant velocity that is roughly 2 orders of magnitude smaller than the speed of sound. We argue that this phenomenon is closely analogous to the propagation of a flame front (deflagration) through a flammable chemical substance.     

Single-crystal 55Mn NMR spectra of two Mn12 single-molecule magnets

The initial application is reported of single-crystal 55Mn NMR spectroscopy, and associated orientation dependence studies, to single-molecule magnets (SMMs). The studies were performed on two members of the Mn12 family of SMMs, [Mn12O12(O2CMe)16(H2O)4].2MeCO2H.4H2O (Mn12-Ac) and [Mn12O12(O2CCH2Br)16(H2O)4].4CH)Cl) (Mn12-BrAc). Single-crystal spectra give a dramatic improvement in the spectral resolution over oriented powder spectra, allowing the clear observation of quadrupolar splittings, the determination of quadrupole coupling parameters (e2qQ), and an assessment of the symmetry-lowering perturbation of the core of Mn12-Ac by hydrogen-bonding interactions with lattice solvate molecules of crystallization. The results emphasize the utility of single-crystal NMR studies to probe the cores of these magnetic molecules.     

Technique for production of oil sorbents from renewable plant raw materials: Waste from cereal plants and sphagnum moss species

Technique for production of powder sorbents from renewable plant raw materials, wastes from cereal plants and sphagnum moss species, were considered. Their sorption properties with respect to dissolved and emulsified oil products were studied.     

New polynuclear manganese clusters from the use of the hydrophobic carboxylate ligand 2,2-dimethylbutyrate

The syntheses, structures, and magnetic properties are reported of [Mn12O12(O2CPe(t))16(MeOH)4] (4), [Mn6O2(O2CH2)(O2CPe(t))11(HO2CPe(t))2(O2CMe)] (5), [Mn9O6(OH)(CO3)(O2CPe(t))12(H2O)2] (6), and [Mn4O2(O2CPe(t))6(bpy)2] (7, bpy = 2,2'-bipyridine), where Pe(t) = tert-pentyl (Pe(t)CO2H = 2,2-dimethylbutyric acid). These complexes were all prepared from reactions of [Mn12O12(O2CPe(t))16(H2O)4] (3) in CH2Cl2. Complex 4 x 2MeCN crystallizes in the triclinic space group P1 and contains a central [Mn(IV)4O4] cubane core that is surrounded by a nonplanar ring of eight alternating Mn(III) and eight mu3-O(2-) ions. This is only the third Mn12 complex in which the four bound water molecules have been replaced by other ligands, in this case MeOH. Complex 5 x (1/2)CH2Cl2 crystallizes in the monoclinic space group P2(1)/c and contains two [Mn3(mu3-O)]7+ units linked at two of their apexes by two Pe(t)CO2(-) ligands and one mu4-CH2O2(2-) bridge. The complex is a new structural type in Mn chemistry, and also contains only the third example of a gem-diolate unit bridging four metal ions. Complex 6 x H2O x Pe(t)CO2H crystallizes in the orthorhombic space group Cmc2(1) and possesses a [Mn(III)9(mu3-O)6(mu-OH)(mu3-CO3)]12+ core. The molecule contains a mu3-CO3(2-) ion, the first example in a discrete Mn complex. Complex 7 x 2H2O crystallizes in the monoclinic space group P2(1)/c and contains a known [Mn(III)2Mn(II)2(mu3-O)2]6+ core that can be considered as two edge-sharing, triangular [Mn3O] units. Additionally, the synthesis and magnetic properties of a new enneanuclear cluster of formula [Mn9O7(O2CCH2Bu(t))13(THF)2] (8, THF = tetrahydrofuran) are reported. The molecule was obtained by the reaction of [Mn12O12(O2CCH2Bu(t))16(H2O)4] (2) with THF. Complexes 2 and 4 display quasireversible redox couples when examined by cyclic voltammetry in CH2Cl2; oxidations are observed at -0.07 V (2) and -0.21 V (4) vs ferrocene. The magnetic properties of complexes 4-8 have been studied by direct current (DC) and alternating current (AC) magnetic susceptibility techniques. The ground-state spin of 4 was established by magnetization measurements in the 1.80-4.00 K and 0.5-7 T ranges. Fitting of the reduced magnetization data by full matrix diagonalization, incorporating a full powder average and including only axial anisotropy, gave S = 10, g = 2.0(1), and D = -0.39(10) cm(-1). The complex exhibits two frequency-dependent out-of-phase AC susceptibility signals (chi(M)') indicative of slow magnetization relaxation. An Arrhenius plot obtained from chi(M)' vs T data gave an effective energy barrier to relaxation (U(eff)) of 62 and 35 K for the slower and faster relaxing species, respectively. These studies suggest that complex 4 is a single-molecule magnet (SMM). DC susceptibility studies on complexes 5-8 display overall antiferromagnetic behavior and indicate ground-state spin values of S < or = 2. AC susceptibility studies at < 10 K confirm these small values and indicate the population of low-lying excited states even at these low temperatures. This supports the small ground-state spin values to be due to spin frustration effects.     

Single-molecule magnets: structural characterization, magnetic properties, and (19)F NMR spectroscopy of a Mn(12) family spanning three oxidation levels

The syntheses, crystal structures, and magnetic properties of [Mn(12)O(12)(O(2)CC(6)F(5))(16)(H(2)O)(4)] (2), (NMe(4))[Mn(12)O(12)(O(2)CC(6)F(5))(16)(H(2)O)(4)] (3), and (NMe(4))(2)[Mn(12)O(12)(O(2)CC(6)F(5))(16)(H(2)O)(4)] (4) are reported. Complex 2 displays quasi-reversible redox couples when examined by cyclic voltammetry in CH(2)Cl(2): one-electron reductions are observed at 0.64 and 0.30 V vs ferrocene. The reaction of complex 2 with 1 and 2 equiv of NMe(4)I yields the one- and two-electron reduced analogues, 3 and 4, respectively. Complexes 2.3CH(2)Cl(2), 3.4.5CH(2)Cl(2).(1)/(2)H(2)O, and 4.6C(7)H(8) crystallize in the triclinic P, monoclinic P2/c, and monoclinic C2/c space groups, respectively. The molecular structures are all very similar, consisting of a central [Mn(IV)O(4)] cubane surrounded by a nonplanar alternating ring of eight Mn and eight mu(3)-O(2)(-) ions. Peripheral ligation is provided by 16 bridging C(6)F(5)CO(2)(-) and 4 H(2)O ligands. Bond valence sum calculations establish that the added electrons in 3 and 4 are localized on former Mn(III) ions giving trapped-valence Mn(IV)(4)Mn(III)(7)Mn(II) and Mn(IV)(4)Mn(III)(6)Mn(II)(2) anions, respectively. (19)F NMR spectroscopy in CD(2)Cl(2) shows retention of the solid-state structure upon dissolution and detrapping of the added electrons in 3 and 4 among the outer ring of Mn ions on the (19)F NMR time scale. DC studies on dried microcrystalline samples of 2, 3, and 4.2.5C(7)H(8) restrained in eicosane in the 1.80-10.0 K and 1-70 kG ranges were fit to give S = 10, D = -0.40 cm(-)(1), g = 1.87, D/g = 0.21 cm(-)(1) for 2, S = 19/2, D = -0.34 cm(-)(1), g = 2.04, D/g = 0.17 cm(-)(1) for 3, and S = 10, D = -0.29 cm(-)(1), g = 2.05, D/g = 0.14 cm(-)(1) for 4, where D is the axial zero-field splitting parameter. The clusters exhibit out-of-phase AC susceptibility signals (chi(M)' ') indicative of slow magnetization relaxation in the 6-8 K range for 2, 4-6 K range for 3, and 2-4 K range for 4; the shift to lower temperatures reflects the decreasing magnetic anisotropy upon successive reduction and, hence, the decreasing energy barrier to magnetization relaxation. Relaxation rate vs T data obtained from chi(M)' ' vs AC oscillation frequency studies down to 1.8 K were combined with rate vs T data from DC magnetization decay vs time measurements at lower temperatures to generate an Arrhenius plot from which the effective barrier (U(eff)) to magnetization reversal was obtained; the U(eff) values are 59 K for 2, 49 and 21 K for the slower- and faster-relaxing species of 3, respectively, and 25 K for 4. Hysteresis loops obtained from single-crystal magnetization vs DC field scans are typical of single-molecule magnets with the coercivities increasing with decreasing T and increasing field sweep rate and containing steps caused by the quantum tunneling of magnetization (QTM). The step separations gave D/g values of 0.22 cm(-)(1) for 2, 0.15 and 0.042 cm(-)(1) for the slower- and faster-relaxing species of 3, and 0.15 cm(-)(1) for 4.     

The properties of the [Mn12O12(O2CR)16(H2O)4] single-molecule magnets in truly axial symmetry: [Mn12O12(O2CCH2Br)16(H2O)4].4CH2Cl2

Detailed studies are reported of a Mn(12) single-molecule magnet (SMM) in truly axial (tetragonal) symmetry. The complex is [Mn(12)O(12)(O(2)CCH(2)Br)(16)(H(2)O)(4)].4CH(2)Cl(2) (2.4CH(2)Cl(2) or Mn(12)-BrAc), obtained by the standard carboxylate substitution method. The complex has an S = 10 ground state, typical of the Mn(12) family, and displays frequency-dependent out-of-phase AC susceptibility signals and hysteresis in single-crystal magnetization vs applied DC field sweeps. Single-crystal high-frequency EPR spectra in frequencies up to 360 GHz exhibit narrow signals that are not overlapping multiplets, in contrast to [Mn(12)O(12)(O(2)CMe)(16)(H(2)O)(4)].2MeCO(2)H.4H(2)O (1 or Mn(12)-Ac), which also crystallizes in an axial (tetragonal) space group but which now is recognized to consist of a mixture of six hydrogen-bonded isomers in the crystal and thus gives multiple, inhomogeneously broadened EPR signals. Similarly, single-crystal (55)Mn NMR spectra on Mn(12)-BrAc display much sharper signals than a single crystal of Mn(12)-Ac, and this allows one Mn(III) signal to show an almost baseline-resolved quintet from quadrupolar splitting ((55)Mn, I = 5/2, 100%), allowing quadrupole coupling parameters (e(2)qQ) to be determined. In addition, it was found that crushing crystals of Mn(12)-BrAc into a microcrystalline powder causes severe broadening and shifts of the NMR resonances, emphasizing the superiority of single-crystal studies. The combined results establish that Mn(12)-BrAc is far superior to Mn(12)-Ac for the study of the intrinsic properties of the Mn(12) family of SMMs in axial symmetry, and for the search for new phenomena such as quantum interference effects caused by higher-order (>2nd-order) transverse terms in the spin Hamiltonian.