Bond-orientational order and Frank’s constant in two-dimensional colloidal hard spheres

Recently, the full phase behaviour of two-dimensional colloidal hard spheres was experimentally established, and found to involve a first order liquid to hexatic transition and a continuous hexatic to crystal transition [A. L. Thorneywork et al., Phys. Rev. Lett. 118, 158001 (2017)]. Here, we expand upon this work by considering the behaviour of the bond-orientational correlation time and Frank’s constant in the region of these phase transitions. We also consider the excess entropy, as calculated from the radial distribution functions, for a wide range of area fractions covering the liquid, hexatic and crystal phases. In all cases, the behaviour of these quantities further corroborates the previously reported melting scenario of two-dimensional colloidal hard spheres