Curvature control of valence on nematic shells

Within a two-dimensional Landau–de Gennes tensorial formalism we study the equilibrium
configurations of nematic shells, thin films of nematic liquid crystal deposited on the boundary of
colloidal particles of arbitrary shape enforcing a degenerate tangential anchoring on the nematic
molecules. In this formalism, defects appear wherever a scalar order parameter vanishes. Their total
number is the colloidal valence, as this is the number of molecular bridges that can bind every colloid to
its peers. We show how the defect organization on a colloidal particle is affected by the Gaussian
curvature of the colloidal boundary, to the point of changing its valence.