Distinct kinetic pathways for homogeneous nucleation in a time-dependent Ginzburg-Landau-de Gennes theory of nematic fluids

For isotropic fluids, classical nucleation theory predicts the nucleation rate, barrier height and critical droplet size by accounting for the competition between a bulk free energy and a surface interfacial tension. The situation for anisotropic fluids is less understood. Here, we numerically investigate nucleation phenomena in nematogenic fluids, using a mesoscopic framework based on a time-dependent Ginzburg-Landau-de Gennes description of isotropic and nematic phases. We compare the nucleation of uniaxial nematic droplets in isotropic background near and above the supercooling spinodal line with the nucleation of isotropic droplets in uniaxial nematic medium near and below the superheating spinodal line in a quasi two-dimensional geometry. The ratio between the anisotropic and isotropic elastic distortion $\kappa$ is found to play a key role in determining the geometric structure of the droplets. We find that nematic droplets have noncircular morphology with a homogeneous director orientation for $\kappa \lessgtr 0$, while the shapes of these droplets are circular for $\kappa=0$. However for $\kappa \gg 0$, a noncircular droplet with an integer topological charge accompanied by a biaxial ring at the outer core of the droplet is obtained. In contrast to the growth of the nematic, isotropic bubbles that grow and coalesce in a superheated nematic medium are seen at early stages. We obtain a growth law of the form $L\sim (at^2+bt+c)^{0.5}$ for both pathways, although the nucleation of isotropic droplets follows 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.