Density dependence of orientational order in one-patch particles

Closely packed spherical patchy particles exhibit a range of orientationally ordered equilibrium structures depending on patch size and particle arrangement due to the existence of a sticky inter-patch interaction and rotational degrees of freedom. We experimentally study the packing density dependence of such ordering in particles with a thin deposited patch which imparts a shape anisotropy of a few percent in aspect ratio. These are confined between flat substrates with a chamber thickness of up to two particle layers. When the particles are tightly packed and almost in contact with each other, the anisotropic hard-body interaction dictates the orientational order. Thus, the order depends little on patch size, with rotational motion almost frozen. A small decrease in the density allows free rotational motion while translation is restricted to vibrational motion. This drastically changes the ordering mechanism, giving rise to a patch-size dependent equilibrium orientational order. Furthermore, within this density regime, we find yet another density-dependent transition within the tetragonal bilayer. This transition is reproduced by numerical simulation assuming no shape anisotropy, indicating that shape anisotropy is unnecessary for the transition and translational entropy significantly affects the equilibrium orientational order even in such a closely packed structure. Our study demonstrates the sensitivity of the ordering mechanism and the resulting order to the packing density, where the effect of such a tiny shape anisotropy is clearly observable owing to the patch opacity. The dependence of cluster structure in particle dispersions on patch size, confinement thickness and packing density is also reported.