  A Landau-de Gennes model that integrates the nematic quadrupolar tensor order
parameter and complex smectic-A order parameters is used to simulate the
two-dimensional growth of an initially homogeneous smectic-A spherulite in an
isotropic matrix. These simulations are performed in the shape-dynamic
(nano-scale) regime of growth under two material conditions: isotropic nematic
elasticity and equal splay-bend nematic elasticity. A comparison of the growth
kinetics, spherulite morphology, interfacial/bulk energy landscapes between
both cases is made showing that equal nematic splay-bend elasticity is required
to reproduce past experimental and theoretical observations. Additionally, a
previously unknown undulation instability during spherulite growth is found
which, in conjunction with preferred planar anchoring and defect shedding
mechanisms at micron length scales, could explain the formation mechanism of
focal conic curvature defects and ultimately smectic-A "batonnet" structures
observed experimentally.
