  Weakly attractive interactions between the tips of rod-like colloidal
particles affect their liquid-crystal phase behaviour due to a subtle interplay
between enthalpy and entropy. Here, we employ molecular dynamics simulations on
semi-flexible, repulsive bead-spring chains of which one of the two end beads
attract each other. We calculate the phase diagram as a function of both the
volume fraction of the chains and the strength of the attractive potential. We
identify a large number of phases that include isotropic, nematic, smectic A,
smectic B and crystalline states. For tip attraction energies lower than the
thermal energy, our results are qualitatively consistent with experimental
findings: we find that an increase of the attraction strength shifts the
nematic to smectic A phase transition to lower volume fractions, with only
minor effect on the stability of the other phases. For sufficiently strong tip
attraction, the nematic phase disappears completely, in addition leading to the
destabilisation of the isotropic phase. In order to better understand the
underlying physics of these phenomena, we also investigate the clustering of
the particles at their attractive tips and the effective molecular field
experienced by the particles in the smectic A phase. Based on these results, we
argue that the clustering of the tips only affects the phase stability if
lamellar structures (``micelles'') are formed. We find that an increase of the
attraction strength increases the degree of order in the layered
phases.Interestingly, we also find evidence for the existence of an
anti-ferroelectric smectic A phase transition induced by the interaction
between the tips. A simple Maier-Saupe-McMillan model confirms our findings.
