Abstract: The interplay between a magnetic field and the Coulomb potential from a charged vacancy on the electron states in graphene is investigated within the tight-binding model. The Coulomb potential removes locally Landau level degeneracy, while the vacancy introduces a satellite level next to the normal Landau level. These satellite levels are found throughout the positive-energy region, but in the negative-energy region, they turn into atomic collapse resonances. Crossings between Landau levels with different angular quantum number m are found. Unlike the point impurity system in which an anticrossing occurs between Landau levels of the same m, in this work anticrossing is found between the normal Landau level and the vacancy-induced level. The atomic collapse resonance hybridizes with the Landau levels. The charge at which the lowest Landau level m = -1, N = 1 crosses E = 0 increases with enhancing magnetic field. A Landau level scaling anomaly occurs when the charge is larger than the critical charge beta 0.6 and this critical charge is independent of the magnetic field.

Abstract: The plasma-based dry reforming in a dielectric barrier discharge (DBD) reactor is important to achieve sustainable goals, but many challenges remain. For example, the conversion and energy yield of DBD reactors are relatively low, and the catalysts or packing materials used in existing studies cannot improve them, possibly due to the unsuitable properties and structures of catalysts or packing materials for plasma processes. In order to study the effect of catalyst structure on plasma-based dry reforming, a controllable synthesis of the catalyst supports or templates was explored. In Chapter 2, an initially immiscible synthesis method was proposed to synthesize uniform silica spheres, which can replace the organic solvent-based Stöber method to successfully synthesize silica particles with the same size ranges as the original Stöber process without addition of organic solvents. Using the silica spheres as templates, 3D porous Cu and CuO catalysts with different pore sizes were synthesized in Chapter 3 to study the effect of catalyst pore size on the plasma-catalytic dry reforming. In most cases, the smaller the pore size, the higher the conversion of CH4 and CO2 due to the reaction of radicals and ions formed in the plasma. An exception are the samples synthesized from 1 μm silica, which show better performance due to the electric field enhancement for pore sizes close to the Debye length. Besides the pore size, the particle diameter of the catalyst or packing is also one of the important factors affecting the interaction between plasma and catalyst. In Chapter 4, SiO2 spheres (with or without supported metal) were used to study the effect of different support particle sizes on plasma-based dry reforming. We found that a uniform SiO2 packing improves the conversion of plasma-based dry reforming. The conversion of plasma-based dry reforming first increases and then decreases with increasing particle size, due to the balance between the promoting and hindering effect of the particle filling on the plasma discharge. Chapter 5 is to improve the design of the DBD reactor itself, in order to try to increase its low energy yield. Some stainless steel rings were put over the inner electrode rod of the DBD reactor. The presence of rings increases the local electric field, the displaced charges and the discharge fraction, and also makes the discharge more stable and with more uniform intensity. The placement of the rings improves the performance of the reactor at 30 W supplied power.