Dimensional confinement and superdiffusive rotational motion of uniaxial colloids in the presence of cylindrical obstacles

Abstract

In biological systems such as cells, the macromolecules, which are anisotropic particles, diffuse in a crowded medium. In the present work, we have studied the diffusion of spheroidal particles diffusing between cylindrical obstacles by varying the density of the obstacles as well as the spheroidal particles. Analytical calculation of the free energy showed that the orientational vector of a single oblate particle will be aligned perpendicular, and a prolate particle will be aligned parallel to the symmetry axis of the cylindrical obstacles in equilibrium. The nematic transition of the system with and without obstacles remained the same, but in the case of obstacles, the nematic vector of the spheroid system always remained parallel to the cylindrical axis. The component of the translational diffusion coefficient of the spheroidal particle perpendicular to the axis of the cylinder is calculated for the isotropic system, which agrees with analytical calculation. When the cylinders overlap such that the spheroidal particles can only diffuse along the direction parallel to the axis of the cylinder, we can observe dimensional confinement. This was observed by the discontinuous fall of the diffusion coefficient, when plotted against the chemical potential both for a single particle and for a finite volume fraction. The rotational diffusion coefficient quickly reached the bulk value as the distance between the obstacles increased in the isotropic phase. In the nematic phase, the rotational motion of the spheroid should be arrested. We observed that even though the entire system remained in the nematic phase, the oblate particle close to the cylinder underwent a flipping motion. The consequence is that when the rotational mean squared displacement was calculated, it showed a super-diffusive behavior even though the orientational self-correlation function never relaxed to zero, showing this to be a very local effect.