The spectrum of 2D electrons subjected to a weak 2D potential and a perpendicular magnetic field is composed of Landau bands with a fractal internal pattern of subbands and minigaps referred to as Hofstadter's butterfly. The Hall conductance may serve as a spectroscopic tool as each filled subband contributes a specific quantized value. Advances in sample fabrication now finally offer access to the regime away from the limiting case of a very weak potential. Complex behavior of the Hall conductance is observed and assigned to Landau band-coupling-induced rearrangements within the butterfly.

Recently developed chain walking (CW) catalysis is an elegant approach to produce materials with controllable structure and properties. However, there is still a lack in understanding of how the reaction mechanism influences the macromolecular structures. In this study, a series of dendritic polyethylenes (PE) synthesized by Pd-α-diimine-complex through CW catalysis (CWPE) is investigated by means of theory and experiment. Thereby, the exceptional ability of in situ tailoring polymer structure by varying synthesis parameters was exploited to tune the branching architecture, which allowed us to establish a precise relationship between synthesis, structure, and solution properties. The systematically produced polymers were characterized by state-of-the-art multidetector separation and neutron scattering experiments as well as atomic force microscopy to access molecular properties of CWPE. On a global scale, the CWPE appear in a worm-like conformation independently on the synthesis conditions. However, severe differences in their contraction factors suggested that CWPE differ substantially in topology. These observations were verified by NMR studies that showed that CWPE possess a constant total number of branches but varying branching distribution. Small angle neutron scattering experiments gave access to structural characteristics from global to segmental scale and revealed the unique heterogeneity of CWPE, which is predominantly based on differences in their dendritic side chains. The experimental data were compared to theoretical CW structures modeled with different reaction-to-walking probabilities. Simple theoretical arguments predict a crossover from dendritic to linear topologies yielding a structural range from purely linear to dendritic chain growth. Yet, comparison of theoretical and empirical scattering curves gave the first evidence that a transition state to worm-like topologies is actually experimentally accessible. This crossover regime is characterized by linear global features and dendritic local substructures contrary to randomly hyperbranched systems. Instead, the obtained CWPE systems have characteristics of disordered dendritic bottle brushes and can be adjusted by the walking rate/reaction probability of the catalyst.

Thermal field-flow fractionation (ThFFF) was designed to investigate the retention behavior of a series of dendritic polyethylenes synthesized using a chain walking catalyst (cwPE) with variations in the branching architecture. The retention behavior of these macromolecules correlates with their branching. Based on differences in the Soret coefficient, a new model has been developed for the application of ThFFF as an alternative to the branching calculation approach based on light scattering or viscosity for the branching analysis of novel short-chain branched PEs.