Unified Homogenization Theory for Magnetoinductive and Electromagnetic Waves in Split Ring Metamaterials

A unified homogenization procedure for split ring metamaterials taking into account time and spatial dispersion is introduced. The procedure is based on two coupled systems of equations. The first one comes from an approximation of the metamaterial as a cubic arrangement of coupled LC circuits, giving the relation between currents and local magnetic field. The second equation comes from macroscopic Maxwell equations, and gives the relation between the macroscopic magnetic field and the average magnetization of the metamaterial. It is shown that electromagnetic and magnetoinductive waves propagating in the metamaterial are obtained from this analysis. Therefore, the proposed time and spatially dispersive permeability accounts for the characterization of the complete spectrum of waves of the metamaterial. Finally, it is shown that the proposed theory is in good quantitative and qualitative agreement with full wave simulations.Comment: 4 pages, 3 figure

Salt Dependence of the Tribological Properties of a Surface-Grafted Weak Polycation in Aqueous Solution

The nanoscopic adhesive and frictional behaviour of end-grafted poly[2-(dimethyl amino)ethyl methacrylate] (PDMAEMA) films (brushes) in contact with gold- or PDMAEMA-coated atomic force microscope tips in potassium halide solutions with different concentrations up to 300 mM is a strong function of salt concentration. The conformation of the polymers in the brush layer is sensitive to salt concentration, which leads to large changes in adhesive forces and the contact mechanics at the tip–sample contact, with swollen brushes (which occur at low salt concentrations) yielding large areas of contact and friction–load plots that fit JKR behaviour, while collapsed brushes (which occur at high salt concentrations) yield sliding dominated by ploughing, with conformations in between fitting DMT mechanics. The relative effect of the different anions follows the Hofmeister series, with I − collapsing the brushes more than Br − and Cl − for the same salt concentration