macroscopic magnetic self assembly
Per Lothman as a joint degree PhD-Student in the research group Robotics and Mechatronics of the University of Twente. His supervisors are professor Leon Abelmann and professor Gijs Krijnen from the Faculty of Electrical Engineering, Mathematics and Computer Science. This doctoral degree program was undertaken jointly with the Saarland University (Germany).
Exploring the macroscopic scale's similarities to the microscale is part and parcel of this thesis as reflected in the research question: what can we learn about the microscopic scale by studying the macroscale? Investigations of the environment in which the self-assembly takes place, and the self-assembly itself helps to answer this question.
We mimicked the microscale and identified several analogue parameters. Instead of heat we use turbulence, instead of microscopic we use centimeter-sized particles. Gravity was counteracted by anupward directed water flow since its influence on macroscopic particles is considerable but has only a minor influence on microscopic particles. Likewise heat has a great influence on the microscopic scale but a minor influence on macroscopic particles. Turbulence proved to be an accurate representation for heat and was modelled as if on a microscopic scale, applying thermodynamical concepts such as Brownian motion, diffusion, kinetics and the Einstein relation. Those concepts proved suitable also on the macroscopic scale. Particle velocity is Maxwell-Boltzmann distributed and the average squared displacement is in agreement with a confined random walk. The diffusion coefficient and velocity is independent on particle size. This leads to the interpretation that the motion of a single centimeter-size sphere resembles the motion of a microscopic particle in that it conducts a random walk and Brownian motion.
To visualize micro- or nanoscopic particles electron- or light-microscopy is often used. Instead of microscopes we used video cameras to record the experiments with centimeter sized particles. A swimmingpool pump and asymmetric inflow is used to create upward flow and turbulence. The asymmetric inflow causes large macroscopic swirls representing the applied heat level at the microscale. In the microscopic case the Brownian motion of particles is result of propagating heat originating at its source whereas at the macroscopic scale the vortice propagation originating in the asymmetry of flow cause the Brownian motion of large particles. Despite of those analogies between heat and turbulence the values for the disturbing energy varies considerably depending on if they were determined via single sphere diffusion (Einstein relation) and velocity (kinetic energy) or via two sphere interactions over distance. The latter case is an order of magnitude lower, approximately 6.5mJ compared to 80mJ. This suggests that the heat or turbulence energy spectra may differ with respect to its action on the particle(s). There is a directional dependency of particle velocity, diffusion and disturbing energy. The horizontal dimensions are similar but the vertical component show a stronger dependency with respect to flow asymmetry and turbulence. The directional dependency can most likely be counteracted via future technical adjustments. It can also be interpreted as a temperature gradient.
Self-assembly was studied via structure formation of multiple magnetic spheres or twelve heptagonal magnetic platelets by systematic variation of turbulence and asymmetry. The multiple magnetic spheres form lines and rings and their occurance were in accordance with theory, however the absolute energies of the structures deviated from theory. For experiments with increasing number of spheres, four spheres represents a transition between lines and rings. The system proved to seak for the minimum energy structure which again makes the our macroscopic system behave similar to the microscale. Turbulence acted in a similar way as heat since almost only individual particles were observed at high turbulence whereas lines and rings formed as turbulence decreased which resembles a phase transition between a liquid and a solid or a gas and a liquid.
Self-assembly of twelve centimeter-sized pentagonal platelets showed the same energy minimum seaking behavior. A complete self-assembly of the dodecahedron was not achieved. Predominantley intermediate structures with maximum contacts to each particle formed (trimer and tetramer etc.) which is the minimum energy structure. Also in this more complex case the system prove to behave similar to the microscale.
The two examples of self-assembly represent on the one hand formation of simple structures (rings and lines) and on the other hand a more complex case of self-assembly (a hollow dodecahedron). The later example can be interpreted as self-assembly of geometrical construct or as a representation of self-assembly of a spherical virus. This underlines the potential of macroscopic self-assembly; it can be used in the investigation of general largely scale-independent problems or as an analogue representation in the investigations of natural occuring phenomena.
