  The anisotropic shape of calamitic LC particles results in distinct energy
values when nematogens are placed side-by-side or end-to-end. The energy
anisotropy governed by parameter K' has deep consequences on equilibrium &
non-equilibrium properties. Using GB model, which shows Nm & low temperature Sm
order, we undertake large-scale MC & MD simulations to probe effect of K' on
the equilibrium phase diagram & the non-equilibrium domain growth following a
quench in the temperature T (coarsening). There are 2 transitions in the model,
I->Nm at Tc1 & Nm->Sm at Tc2<Tc1. K' decreases Tc1 significantly, but has
relatively little effect on Tc2. Domain growth in Nm phase exhibits the
well-known LAC law, L(t)~t^0.5 & evolution is via annihilation of string
defects. The system exhibits dynamical scaling that is also robust with respect
to K'. We find that Sm phase at quench temperatures T (T>Tc1->T<Tc2) that we
consider has SmB order with a hexatic arrangement of the LC molecules in the
layers. Coarsening in this phase exhibits a striking two-time-scale scenario:
first the LC molecules align & develop orientational order, followed by
emergence of characteristic layering along with the hexatic
bond-orientational-order within layers. Consequently, the growth follows the
LAC law L(t)~t^0.5 at early times & then shows a sharp crossover to a slower
growth regime at later times. Our observations strongly suggest L(t)~t^0.25 in
this regime. Interestingly, the correlation function shows dynamical scaling in
both the regimes & the scaling function is universal. The dynamics is also
robust with respect to changes in K', but the smecticity is more pronounced at
larger values. Further, the early-time dynamics is governed by string defects,
while the late-time evolution is dictated by interfacial defects. We believe
this scenario is generic to Sm phase even with other kinds of local order
within Sm layers.
