Nematic disclinations as twisted ribbons

The disclination loops entangling colloidal structures in nematics are geometrically stabilized and restricted according to topological rules. We focus on colloidal dimers and show how the writhe and twist, which are constrained to sum to a constant value, are affected by changing the intercolloidal spacing, the twist angle of the cell, and the cholesteric pitch. We analyze the geometric properties of disclination loops using finite difference numerical simulations of colloidal dimers. The observed trends are explained and correlated to the symmetry properties and effects of liquid crystal elasticity.