  The dynamics of a spherical chemically-powered synthetic colloidal motor that
operates by a self-diffusiophoretic mechanism and has a catalytic domain of
arbitrary shape is studied using both continuum theory and particle-based
simulations. The motor executes active rotational motion when self-generated
concentration gradients and interactions between the chemical species and
colloidal motor surface break spherical symmetry. Local variations of chemical
reaction rates on the motor catalytic surface with catalytic domain sizes and
shapes provide such broken symmetry conditions. A continuum theoretical
description of the active rotational motion is given, along with the results of
particle-based simulations of the active dynamics. From these results a
detailed description of the factors responsible for the active rotational
dynamics can be given. Since active rotational motion often plays a significant
part in the nature of the collective dynamics of many-motor systems and can be
used to control motor motion in targeted cargo transport, our results should
find applications beyond those considered here.
