Distinct nucleation kinetic pathways in a stochastic time-dependent Ginzburg-Landau-de Gennes theory of nematic films

For isotropic fluids, classical nucleation theory predicts the nucleation rate, barrier height and critical droplet size by accounting for the competition between bulk free energy and surface interfacial tension. The situation for anisotropic fluids is less understood. Here, we numerically investigate nucleation phenomena in nematogenic fluids in quasi two-dimensional geometry, using a mesoscopic framework of anisotropic phases. We compare the nucleation of nematic droplets in metastable isotropic medium with the nucleation of isotropic droplets in metastable nematic medium. Ratio between the anisotropic and isotropic elastic distortion $\kappa$ is found to play a central role in determining the geometric structure of the droplets. We show how {\it de Gennes ansatz} do not hold for curved interfaces. Noncircular nematic droplets with homogeneous director orientation are nucleated for small $\kappa$, while droplet shape remain circular in absence of $\kappa$. However for large $\kappa$, noncircular droplets are nucleated with integer topological charge accompanied by a biaxial ring at the outer surface. Furthermore, shape change from circular to noncircular geometry of isotropic droplets in nematic background for $\kappa\neq0$ are also obtained. The growth law is found to be $L\sim(at^2+bt+c)^{0.5}$ for both pathways, although the droplets follow an unusual two-stage nucleation and growth mechanism. The temporal distribution of successive nucleation events signals the relevance of long ranged elasticity mediated interactions in the nematic. We critically discuss the consequences of our results for classical nucleation theory extended to anisotropic situations.