Mechanical resolution of chiral objects in achiral media: where is the size limit?

Macroscopic chiral objects (boats and planes with turned rudders, shoes, etc.) get separated from their mirror-image counterparts by motion in achiral media. However, chiral molecules are not enantio-differentiated without the presence of a chiral environment, which may be due to other chiral molecules in the medium. This article explores the reasons of this micro/macro difference as well as the size borderline between the two regimes. There are two major demarcation lines, both related to the object's chaotic thermal motion. The first one is due to destruction of the necessary spatial orientation by the fast rotational diffusion. Only particles larger than 1 μm can maintain their original orientation for 1 sec or longer. For smaller particles, an additional external orienting factor, e.g., a strong electric field has to be applied. The second limitation is defined by the ratio of the hydrodynamic separation of the enantiomers (which is directly proportional to time) to their displacement due to the translational Brownian motion (which is proportional to square root of time). On the laboratory time scales (up to a year), the chiral objects have to be larger than 0.25 μm to be resolved. On evolutionary time scales, much smaller object could be resolved. For enantiomers approaching the molecular size, periods comparable to the age of the universe would be required.