  Disklike molecules with aromatic cores spontaneously stack up in linear
columns with high, one-dimensional charge carrier mobilities along the columnar
axes making them prominent model systems for functional, self-organized matter.
We show by high-resolution optical birefringence and synchrotron-based X-ray
diffraction that confining a thermotropic discotic liquid crystal in
cylindrical nanopores induces a quantized formation of annular layers
consisting of concentric circular bent columns, unknown in the bulk state.
Starting from the walls this ring self-assembly propagates layer by layer
towards the pore center in the supercooled domain of the bulk
isotropic-columnar transition and thus allows one to switch on and off
reversibly single, nanosized rings through small temperature variations. By
establishing a Gibbs free energy phase diagram we trace the phase transition
quantization to the discreteness of the layers' excess bend deformation
energies in comparison to the thermal energy, even for this near
room-temperature system. Monte Carlo simulations yielding spatially resolved
nematic order parameters, density maps and bond-forientational order parameters
corroborate the universality and robustness of the confinement-induced columnar
ring formation as well as its quantized nature.
