Separation feasibility for chiral particles with linear anisotropic susceptibility in rotating magnetic field: Theoretical study in low magnetic field

We theoretically discuss the separation of chiral particles having anisotropic magnetic susceptibility in a rotating magnetic field. Particles with anisotropic magnetic susceptibility can be aligned in either the parallel or perpendicular direction to the magnetic field, depending on their anisotropic properties. When a rotating magnetic field is applied, the particles undergo rotation. In our previous study, we theoretically demonstrated that chiral particles having a dipole moment in a rotating field can be separated from a racemic mixture; such chiral particles move along the axis of the rotating field in a direction that depends on their chirality. In this study, we show that the migration velocity of particles characterized by a susceptibility tensor can be estimated by the Brownian dynamics theory for arbitrary-shaped particles at a low Péclet number. The result indicates that the migration velocity is proportional to the fourth power of the magnetic field. The direction of the migration parallel to the rotation axis of the magnetic field depends on both the chirality of the particle and the frequency of the magnetic field. Propeller-like particles, which are composed of two thin disks and a thin rod, are used as illustrative examples. The migration direction is expressed as a function of the twist angle, which determines the degree of chirality of the propeller-like particle.