Dynamics of paramagnetic permanent chains and self-assembled clusters under a rapidly rotating magnetic field.

We study experimentally and theoretically the dynamics of permanent paramagnetic chains and mixed clusters formed by permanent paramagnetic chains and paramagnetic particles under the influence of a time-varying magnetic field. First, we examine the dynamics of permanent chains at high frequencies (∼50 to 1000 Hz). These permanent chains exhibit continuous rotational motion with a frequency several orders of magnitude lower than that of the magnetic field. We develop a theoretical model that accurately describes the dependence of the rotational dynamics of chains on their length, as well as the amplitude and frequency of the external magnetic field in this high frequency regime. Next, we examine how cluster dynamics are affected by the presence of permanent chains. We show that the rotation of clusters composed of a high proportion of permanent chains is slowed down but remains qualitatively well described by the theoretical model we developed for homogeneous clusters of isotropic particles. We propose that the decrease in angular velocity for mixed clusters is due to the hardening of the cluster's 2D elastic modulus caused by the increase of the steric interaction parameter stemming from the presence of chemical links between particles in the chains.