Simultaneous polydirectional transport of colloidal bipeds

Abstract

Detailed control over the motion of colloidal particles is relevant in many applications in colloidal science such as lab-on-a-chip devices. Here, we use an external magnetic field to assemble paramagnetic colloidal spheres into colloidal rods of several lengths. The rods reside above a square magnetic pattern and are transported via modulation of the direction of the external magnetic field. The rods behave like bipeds walking above the pattern. Depending on their length, the bipeds perform topologically distinct classes of protected walks. We design parallel polydirectional modulation loops of the external field that command up to six classes of bipeds to walk on distinct predesigned paths. Using such loops, we induce the collision of reactant bipeds, their polymerization addition reaction to larger bipeds, the separation of product bipeds from the educts, the sorting of different product bipeds, and also the parallel writing of a word consisting of several letters. Our ideas and methodology might be transferred to other systems for which topological protection is at work.

Enhanced colloidal transport in twisted magnetic patterns

“…Using single patterns it is possible to transport the particles via modulation loops of the orientation of the external field 21,22 . The loops are closed such that the orientation returns to its initial value after one loop.…”

“…The patterns can be experimentally realized using e.g., exchangebias thin magnetic films irradiated through a lithographic mask 26,27 as well as garnet films 28,29 . Using micrometer-sized colloidal particles at a distance comparable to the length of a lattice vector above these patterns 21,22 results in magnetic potential energies significantly larger than the thermal energy (at room temperature). Hence, the use of similar setups 21,22 would result in experiments on twisted patterns that are effectively close to the zero-temperature limit.…”

“…Using micrometer-sized colloidal particles at a distance comparable to the length of a lattice vector above these patterns 21,22 results in magnetic potential energies significantly larger than the thermal energy (at room temperature). Hence, the use of similar setups 21,22 would result in experiments on twisted patterns that are effectively close to the zero-temperature limit. The observation of the finite temperature effects discussed here should be possible by either decreasing the magnetic forces (e.g., weaker patterns and larger colloid-pattern distance) or increasing the Brownian force (using e.g., magnetic nanocolloids).…”

Phase separation of active Brownian particles in two dimensions: Anything for a quiet life

“…Given the experimental control of colloidal particles that e.g. nudging with light [92][93][94][95][96] and topological transport by magnetic fields [97,98] allows, thinking into such directions seems both reasonable and exciting.…”

The geometric phase and the dry friction of sleeping tops on inclined planes

“…The geometric phase also named Berry-phase in quantum sytems and Hannay-angle in classical systems is invariant under rescaling of the time schedule with which one passes the path in parameter space. It also carries along a gauge freedom of choice of reference points and the concept has been used in high energy particle physics [4], in solid state physics of topological materials [5][6][7], in the explanation of the rotation of the Foucaultpendulum [8], in the explanation of the propulsion of active swimmers in low Reynolds number fluids [9,10], the propulsion of light in twisted fibers [11,12], the propulsion of acoustic [13] or stochastic [14] waves, the motion of edge waves in coupled gyroscope lattices [15], the rolling of nucleons [16] and in the control of the transport of macroscopic [17] and colloidal [18][19][20][21] particles above magnetic lattices. The independence of the geometric phase of the speed, makes the Foucault pendulum rotation independent of the length of the pendulum as well as independent of the value of the gravitational acceleration, similarly the propulsion of an active shape changing swimmer is independent of the viscosity of the embedding fluid.…”