  Investigations of the phase diagram of biaxial liquid crystal systems through
analyses of general Hamiltonian models within the simplifications of mean-field
theory (MFT), as well as by computer simulations based on microscopic models,
are directed towards an appreciation of the role of the underlying
molecular-level interactions to facilitate its spontaneous condensation into a
nematic phase with biaxial symmetry. Continuing experimental challenges in
realising such a system unambiguously, despite encouraging predictions from MFT
for example, are requiring more versatile simulational methodologies capable of
providing insights into possible hindering barriers within the system,
typically gleaned through its free energy dependences on relevant observables
as the system is driven through the transitions. The recent brief report from
this group [B. Kamala Latha, et. al., Phys. Rev. E 89, 050501 (R), 2014]
summarizing the outcome of detailed Monte Carlo simulations carried out
employing entropic sampling technique, suggested a qualitative modification of
the MFT phase diagram as the Hamiltonian is asymptotically driven towards the
so-called partly-repulsive regions. It was argued that the degree of the
(cross) coupling between the uniaxial and biaxial tensor components of
neighbouring molecules plays a crucial role in facilitating, or otherwise, a
ready condensation of the biaxial phase, suggesting that this could be a
plausible f actor in explaining the experimental difficulties. In this paper,
we elaborate this point further, providing additional evidences from curious
variations of free-energy profiles with respect to the relevant orientational
order parameters, at different temperatures bracketing the phase transitions.
