  For isotropic fluids, classical nucleation theory predicts the nucleation
rate, barrier height and critical droplet size by accounting for the
competition between bulk energy and interfacial tension. The nucleation process
in liquid crystals is less understood. We numerically investigate nucleation in
monolayered nematogenic films using a mesoscopic framework, in particular, we
study the mor- phology and kinetic pathway in spontaneous formation and growth
of droplets of the stable phase in the metastable background. The parameter
$\kappa$ that quantifies the anisotropic elastic energy plays a central role in
determining the geometric structure of the droplets. Noncircular nematic
droplets with homogeneous director orientation are nucleated in a background of
supercooled isotropic phase for small $\kappa$. For large $\kappa$, noncircular
droplets with integer topological charge, accompanied by a biaxial ring at the
outer surface, are nucleated. The isotropic droplet shape in a superheated
nematic background is found to depend on $\kappa$ in a similar way. Identical
growth laws are found in the two cases, although an unusual two-stage mechanism
is observed in the nucleation of isotropic droplets. Temporal distributions of
successive events indicate the relevance of long-ranged elasticity-mediated
interactions within the isotropic domains. Implications for a theoretical
description of nucleation in anisotropic fluids are discussed.
