Enantiomeric Separation and the Hydrodynamic Properties of Chiral Molecules

We present a model to explain the mechanism behind enantiomeric separation under either shear flow or local rotational motion in a fluid. Local vorticity of the fluid imparts molecular rotation that couples to translational motion, sending enantiomers in opposite directions. Translation-rotation coupling of enantiomers is explored using the molecular hydrodynamic resistance tensor, and a molecular equivalent of the pitch of a screw is introduced to describe the degree of translation-rotation coupling. Molecular pitch is a structural feature of the molecules and can be easily computed, allowing rapid estimation of the pitch for arbitrary molecules. We have computed this pitch for 85 drug-like molecules, and a wide range of chiral molecules with high symmetry axes. A competition model and continuum drift diffusion equations are developed to predict separation of realistic racemic mixtures. We find that enantiomeric separation on a centimeter length scale can be achieved in hours, using experimentally achievable vorticities. Additionally, we find that certain achiral objects can also exhibit a non-zero molecular pitch. We also present a theory for pitch, a matrix property which is linked to the coupling of rotational and translational motion of rigid bodies. The pitch matrix is a geometric property of objects in contact with a surrounding fluid, and it can be decomposed into three principal axes of pitch and their associated moments of pitch. The moments of pitch predict the translational motion in a direction parallel to each pitch axis when the object is rotated around that axis, and can be used to explain translational drift, particularly for rotating helices. We also provide a symmetrized boundary element model for blocks of the resistance tensor, allowing calculation of the pitch matrix for arbitrary rigid bodies. We analyze a range of chiral objects, including chiral molecules, helices, and propellers. Chiral objects with a C_n symmetry axis with n > 2 show additional symmetries in their pitch matrices. We also show that some achiral objects have non-vanishing pitch matrices, and use this result to explain recent observations of achiral microswimmers. We also discuss the small, but non-zero pitch of Lord Kelvin's isotropic helicoid.