Stochastic kinetics reveal imperative role of anisotropic interfacial tension to determine morphology and evolution of nucleated droplets in nematogenic films

For isotropic fluids, classical nucleation theory predicts the nucleation rate, barrier height and critical droplet size by ac- counting 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 par- ticular, we study the morphology and kinetic pathway in spontaneous formation and growth of droplets of the stable phase in the metastable background. The parameter κ 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 κ. For large κ, 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 κ 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 indi- cate the relevance of long-ranged elasticity-mediated interactions within the isotropic domains. Implications for a theoretical description of nucleation in anisotropic fluids are discussed.

In absence of thermal fluctuations (∂ ∂ ∂θ, ∂ ∂ ∂φ = 0) for a planar I-N interface along z-direction where the director is confined to a plain (φ = 0), the anisotropic elastic energy takes the form Thus, free energy is lowered for homeotropic anchoring (θ = 0) for κ < 0 and planar anchoring (θ = π/2) for κ > 0, in par with de Gennes argument [1]. However for a curved interface, which can be further reduced in a quasi two-dimensional geometry by taking ∂ z S, ∂ z T = 0. Depending on the sign of κ and according to the competing values of the gradients in S, T and φ, the film decides the favoured anchoring. Accounting to thermal fluctuations (∂ ∂ ∂θ, ∂ ∂ ∂φ = 0), director anchoring at the droplet surface interface is not intuitive.
Description: The animation sequentially portrays evolution of (a) S & n, (b) T & l and (c) Schlieren texture in one elastic approximation and for small values of elastic constant L 1 . Nucleation of circular nematic bubbles with uniform director field is observed, that amplify in size to coalesce with other droplets. Note that many droplets are formed as in shallow quench, and droplet coalescence resulted into defects of half integer charge due to lower surface energy. For higher surface energy (or larger L 1 ), only few droplets are nucleated whose coalescence does not generate defects (not shown). Almost no notable change in T and l fields is seen in the process. Finally, schlieren texture depicts the uniformity of director field within the droplets.
Animation S2 : Noncircular nematic droplets with encapsulated hyperbolic hendgehog defects for κ 0 and higher surface energy.
Description: The animation sequentially portrays evolution of (a) S & n, (b) T & l and (c) Schlieren texture in strong anchoring limit and for higher L 1 . Nucleation of noncircular nematic bubbles with encapsulated defect is observed, that amplify in size to coalesce with other droplets. The formation of biaxial ring at the droplet interface with hyperbolic hedgehog defect structure is also observed in T and l fields. Finally, schlieren texture depict the 4-brush geometry, that persist at very late stage of the kinetics.
Animation S3 : Double occurance of noncircular isotropic droplets for κ = 1 and lower surface energy.
Description: The animation sequentially portrays evolution of (a) S & n and (b) Schlieren texture in weak anchoring limit and for lower L 1 . Almost no notable change in T and l field is seen and thus omitted from the animation. Nucleation of noncircular isotropic bubbles without any defect in the bulk nematic film is observed. Note the double occurance of droplets, resulting to bimodality in the probability distribution of nucleation events. Nucleated droplets in later stage amplify in size to coalesce with other droplets and span the system size to form isotropic phase. Schlieren textures depict the nonuniformity of the director field more transparently.
Description: The animation sequentially portrays evolution of (a) S & n and (b) Schlieren texture in strong anchoring limit and for higher L 1 . Nucleation of noncircular isotropic bubbles is observed that amplify in size to coalesce with other droplets. Schlieren textures support the nonuniformity of director field within the droplets and absence of defects in the nematic environment, as well as in the squeezing nematic domains at the late stage of the kinetics.