Kinetically blocked self-assembly of colloidal strings with tunable interactions in magnetic fields

Tunable self-assembly driven by external electric or magnetic fields is of significant interest in modern soft matter physics. While extensively studied in two-dimensional systems, it remains insufficiently explored in three-dimensional systems. In this study, we investigated the formation of vertical strings from an initial monolayer system of particles deposited on a horizontal substrate under the influence of an external magnetic field using experiments, computer simulations, and theoretical frameworks. We demonstrated that the main mechanism of string self-assembly is merging, driven by the interplay between gravity and induced tunable interparticle interactions. During this process, the system has to overcome a saddle point on the energy landscape, whose height increases with the string height. At a certain point, further self-assembly becomes kinetically blocked in a metastable state, far from equilibrium. This contrasts sharply with the typical scenario for tunable self-assembly in two dimensions, where the resulting structures usually correspond to the equilibrium state. Therefore, this finding opens up opportunities for more detailed control of three-dimensional tunable self-assembly by designing and tuning various potential barriers along the kinetic pathways.