Magnetic interaction in the metamaterial/magnet system

The stability of the magnetic dipole and the metamaterial with negative permeability are investigated. Analytical expressions of the interaction force and stiffness of the magnetic line and metamaterial with negative permeability are derived. The repulsive force between the magnetic line and the metamaterial exceeds the value of the maximum force in the magnet-superconductor system.     

Effects of Magnet Size and Geometry on Magnetic Levitation Force

We obtain analytical relations for the levitation force as a function of dimensions of the superconductor-magnet system. The force has been calculated on the basis of the dipole-dipole interaction model. The effect of thickness of the superconductor on the levitation force is investigated. The results show that the influence of geometry and thickness of the magnet becomes significantly large at small levitation distances. Furthermore, approximating the permanent magnet as a point dipole results in an inaccurate estimation of the levitation force.     

Association of Molybdenum Ionic Species with Alumina Surface

The adsorption isotherms at 25, 45, and 65 degrees C of molybdenum solutions of concentration ranges between 10(-3) and 3x10(-2) M(Mo) (pH 4-5) on different alumina samples are investigated. The analysis is conducted using a modified Frumkin isotherm which takes a more realistic account of the lateral interaction between adsorbed species and considers that the adsorption takes place on the most basic OH groups on the surface of alumina. The results are discussed in view of the difference in solutions speciation, and the changes in the pH of the remaining supernatant solutions. The solution temperature, PZC of the used aluminas, the configuration of the basic OH groups on their surface, and the pore structure have been shown to intervene effectively. Copyright 2000 Academic Press.     

The basis number of the Cartesian product of stars and wheels with different ladders

The basis number of a graph G is defined to be the least positive integer d such that G has a d-fold basis for the cycle space of G. We investigate the basis number of the cartesian product of stars and wheels with ladders, circular ladders and Möbius ladders.     

Levitation and lateral forces between a point magnetic dipole and a superconducting sphere

The dipole–dipole interaction model is employed to investigate the angular dependence of the levitation and lateral forces acting on a small magnet in an anti-symmetric magnet/superconducting sphere system. Breaking the symmetry of the system enables us to study the lateral force which is important in the stability of the magnet above a superconducting sphere in the Meissner state. Under the assumption that the lateral displacement of the magnet is small compared to the physical dimensions of our proposed system, analytical expressions are obtained for the levitation and lateral forces as a function of the geometrical parameters of the superconductor as well as the height, the lateral displacement, and the orientation of the magnetic moment of the magnet. The dependence of the levitation force on the height of the levitating magnet is similar to that in the symmetric magnet/superconducting sphere system within the range of proposed lateral displacements. It is found that the levitation force is linearly dependent on the lateral displacement whereas the lateral force is independent of this displacement. A sinusoidal variation of both forces as a function of the polar and azimuthal angles specifying the orientation of the magnetic moment is observed. The relationship between the stability and the orientation of the magnetic moment is discussed for different orientations.     

Hydrogen Cyanide Exchange on [Al(HCN)6]3+ – A DFT Study

The hydrogen cyanide exchange mechanism of [Al(HCN)₆]³⁺ has been investigated by DFT calculations (B3LYP/6‐311+G**). The calculations provide theoretical evidence that the hydrogen cyanide exchange proceeds via a limiting dissociative (D) mechanism involving a stable five‐coordinate intermediate [Al(HCN)₅ · (HCN)₂]³⁺. The activation energy for the D‐mechanism is 23.4 kcal · mol^–1, which is 2.8 kcal · mol^–1 lower than for the seven‐coordinate transition state [Al(HCN)₇]^3+? for the alternative associative (A) pathway. The difference in stability between the two intermediates [Al(HCN)₅ · (HCN)₂]³⁺ (12.1 kcal · mol^–1) and [Al(HCN)₇]³⁺ (25.7 kcal · mol^–1) in comparison to [Al(HCN)₆ · (HCN)]³⁺ is much more pronounced and further supports a limiting dissociative mechanism.     

Apparent or real water exchange reactions on [Zn(H2O)4(L)](2+)·2H2O (L = sp-nitrogen donor ligands)? A quantum chemical investigation

The exchange of a second coordination sphere water molecule in [Zn(H(2)O)(4)(L)](2+)·2H(2)O (L = HN(3), HCN, FCN, ClCN, BrCN, CH(3)CN, (C(4)H(3))CN, PhCN, (CH(3))(3)CCN, CF(3)CN, CCl(3)CN, CHCl(2)CN, and CH(2)ClCN) against a coordinated water molecule was studied by quantum chemical calculations (RB3LYP/6-311+G**). The complete reaction consists of an associative binding of one H(2)O from the second coordination sphere leading to a six-coordinate intermediate [Zn(H(2)O)(5)(L)](2+)·H(2)O, followed by the dissociation of a water molecule to reach the product state [Zn(H(2)O)(4)(L)](2+)·2H(2)O. For a real water exchange reaction to occur two different transition states have to be included, otherwise only an apparent water exchange reaction takes place. For the water exchange reaction in [Zn(H(2)O)(4)(L)](2+)·2H(2)O, nearly iso-energetic cis- and trans-orientated transition states are crossed. The gas-phase proton affinity of L shows instructive correlations with structural parameters and energy gaps for the investigated reactions.