F. Y. Alzoubi

pH effect on the aggregation of silver nanoparticles synthesized by chemical reduction

Silver colloidal nanoparticles were prepared according to the chemical reduction method in which the ascorbic acid was used as a reducing agent and sodium citrate as a stabilizing agent. The absorption spectra of all prepared samples obtained using the UV-Vis spectrophotometer showed a surface plasmon peak at a wavelength of about 420 nm. The size of the silver nanoparticles was controlled by changing the pH values of the reaction system. At high pH, smaller size silver nanoparticles were obtained compared to low pH values. This difference can be attributed to the difference in the reduction rate of the precursor. In addition to the inverse proportionality between the size and the pH value it is clear that increasing the pH value enables us to obtain spherical nanoparticles while at low pH, rods and triangular particle shapes were formed. Poor balance between nucleation and growth processes could be the cause of this result.

Angular dependence of the levitation force on a small magnet above a superconducting cylinder in the Meissner state

The dipole–dipole interaction model was used to calculate the levitation force on a small permanent magnet above a superconducting cylinder in the Meissner state lying on the cylinders axis. We obtained analytical expressions for the levitation force and energy in terms of the physical dimensions of the cylindrical superconductor as well as the height and the angle between the magnetic moment and the surface of the sample. Results show that the levitation force and energy are maxima when the magnetic moment is perpendicular to the surface and minima when it is parallel. Special cases of infinite radius and infinite thickness were discussed.

The Interaction Force Between a Permanent Magnet and a Superconducting Ring

The interaction force between a small magnet and a superconducting ring in assumptions of the Meissner state was analyzed using the dipole-dipole interaction model. Two configurations were evaluated: the vertical configuration when the magnetic moment lies parallel to the symmetry axis of the ring and the horizontal when it is perpendicular. The levitation force on the magnet increases by decreasing the distance from the center of the ring up to a maximum value and then decreases down to zero when the magnet is exactly at the center of the ring. The levitation force when the magnet is in the horizontal configuration is mostly higher than that when it is in the vertical configuration. Simulation results were compared with experimental results reported in literature.

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.

Levitation Force Between Monolayer of Magnetic Particles and Superconducting Plane in Meissner State

We have calculated the levitation force and the interaction energy between a thin monolayer of super-paramagnetic fine ferromagnetic particles system and a large flat superconductor in the Meissner state. Both energy and force depend on the temperature and the levitation height of the monolayer. Our results show that the interaction energy and the levitation force increases as the temperature of the momolayer increases. In the limit of zero Kelvin temperature, we found that our results for the levitation force goes over to the case where all the moments of the fine-particle system are parallel to the superconductor surface, which has the lowest interaction energy.

Synthesis and Characterization of Colloidal Gold Nanoparticles Controlled by the pH and Ionic Strength

Colloidal gold nanoparticles (GNPs) were prepared according to the Lee-Meisel method based on the chemical reduction of gold chloride trihydrate in aqueous solution. Different techniques were employed to characterize the gold nanoparticles, such as UV-Vis spectrometry, which was used to obtain absorption spectra of the colloidal samples. These spectra showed that the gold nanoparticles have an absorption peak at 520 nm, which corresponds to the surface plasmon resonance (SPR) of gold nanoparticles. Another technique is the use of a transmission electron microscope (TEM) to obtain images of the prepared GNPs to ensure their nano-size as well as their spherical shape. According to the obtained images, the inverse proportionality between the pH value of the solution and the size of the gold nanoparticles was clear. Moreover, for pH values less than 8.4 the particles were aggregated in the form of clusters, while above this value they were well dispersed in the solution. X-ray diffraction (XRD) analysis was performed to study the crystal structure of the GNPs. The aggregation of GNPs as a result of adding chemical compounds to the colloidal solution was investigated. As the concentration of the added compound is increased, a gradual decay of the surface plasmon resonance peak accompanied by the formation of a new peak in the long wavelength region was observed.

Angular Dependence of Lateral and Levitation Forces in Asymmetric Small Magnet/Superconducting Systems

The dipole–dipole interaction model is used to calculate the angular dependence of lateral and levitation forces on a small permanent magnet and a cylindrical superconductor in the Meissner state lying laterally off the symmetric axis of the cylinder. Under the assumption that the lateral displacement of the magnet is small compared with the physical dimensions of the system, we obtain analytical expressions for the lateral and levitation forces as functions of geometrical parameters of the superconductor as well as the height, the lateral displacement and the orientation of magnetic moment of the magnet. The effect of thickness and radius of the superconductor on the levitation force is similar to that for a symmetric magnet/superconducting cylinder system, but within the range of lateral displacement. The splitting in the levitation force increases with the increasing angle of orientation of the magnetic moment of the magnet. For a given lateral displacement of the magnet, the lateral force vanishes when the magnetic moment is perpendicular to the surface of the superconductor and has a maximum value when the moment is parallel to the surface. For a given orientation of the magnetic moment, the lateral force has a linear relationship with the lateral displacement. The stability of the magnet above the superconducting cylinder is discussed in detail.

LEVITATION FORCE BETWEEN A SHORT MAGNETIC BAR AND A SUPERCONDUCTING CYLINDER IN THE MEISSNER STATE

We have calculated the levitation force and interaction energy between a short magnetic bar and a superconducting cylinder in the Meissner state using the dipole–dipole interaction model. We derived analytical expression of the levitation force acting on the short magnet as a function of the orientation angle of magnetic dipole, and the physical dimensions of the magnet-superconductor system. The effects of the thickness of the superconductor and the length of the magnet on the levitation force were studied.

Vibrations in Magnet/Superconductor Levitation Systems

The problem of a small magnet levitating above a very thin superconducting disc in the Meissner state is analysed. The dipole–dipole interaction model is employed to derive analytical expressions for the interaction energy, levitation force, magnetic stiffness and frequency of small vibrations about the equilibrium position in two different configurations, i.e. with the magnetic moment parallel and perpendicular to the superconductor. The results show that the frequency of small vibrations decreases with the increasing levitation height for a particular radius of the superconducting disc, which is in good agreement with the experimental results. However, the frequency increases monotonically up to saturation by increasing the radius of the disc for a particular height of the magnet. In addition, the frequency of vibrations is higher when the system is in the vertical configuration than that when the system is in the horizontal configuration.

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.