  We have recently investigated the phase behaviour of model colloidal
dumbbells constituted by two identical tangent hard spheres, with the first one
being surrounded by an attractive square-well interaction (Janus dumbbells,
Muna\`o G et al 2014 Soft Matter 10 5269). Here we extend our previous analysis
by introducing in the model the size asymmetry of the hard-core diameters, and
study the enriched phase scenario thereby obtained. By employing standard Monte
Carlo simulations we show that in such "heteronuclear Janus dumbbells" a larger
hard-sphere site promotes the formation of clusters, whereas in the opposite
condition a gas-liquid phase separation takes place, with a narrow interval of
intermediate asymmetries wherein the two phase behaviours may compete. In
addition, some peculiar geometrical arrangements, such as lamellae, are
observed only around the perfectly symmetric case. A qualitative agreement is
found with recent experimental results, where it is shown that the roughness of
molecular surfaces in heterogeneous dimers leads to the formation of colloidal
micelles.
