Stochastic kinetics reveal imperative role of anisotropic interfacial tension to determine morphology and evolution of nucleated droplets in nematogenic films (1603.05709v5)

Abstract: 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.

• The paper uses stochastic kinetics and simulations to reveal how anisotropic interfacial tension dictates the morphology and evolution of nucleated droplets in nematic films.
• The research reveals that anisotropic elastic energy dictates droplet shape and the presence of topological defects within nucleated droplets, aligning with experimental findings.
• The study reveals limitations of classical nucleation theories for anisotropic systems, suggesting the need for new theoretical models incorporating noise and anisotropy, with relevance for liquid crystal technology.

Anisotropic Interfacial Tension and Nucleation in Nematic Films

This paper investigates the complex dynamics of nucleation in monolayered nematogenic films, emphasizing the significance of anisotropic elastic energy in defining the morphology and evolution of droplets during phase transitions. The paper introduces a stochastic framework to better explain nucleation pathways compared to classical nucleation theory, particularly for materials where anisotropy plays a crucial role. Using numerical simulations, the research unveils how anisotropic interfacial tension dictates the formation of noncircular nematic droplets, which may encapsulate defects depending on the strength of anchoring.

Key Findings and Methodology

The paper explores the nucleation kinetics in two scenarios: the supercooled isotropic phase and the superheated nematic phase. For small anisotropic elastic energy (quantified by the parameter $\kappa$), noncircular nematic droplets with homogeneous director orientation form. As $\kappa$ becomes large, these droplets develop integer topological charge defects encapsulated within, aligning with experimental observations of 5CB microdroplets. The director anchoring at the interface is either planar or homeotropic, governed by the anisotropic elastic energy, validating and extending de Gennes's ansatz.

Numerical simulations were conducted using a stochastic extension of the Ginzburg-Landau-de Gennes (GLdG) free energy framework, which accommodates thermal fluctuations in the field evolution. This technique enables the identification of critical droplet characteristics and their growth kinetics in a two-dimensional monolayer, leading to insights into the overall system's nucleation behavior under varying degrees of anisotropic tension.

Implications and Future Directions

The findings highlight limitations of classical nucleation theories (CNTs) in describing anisotropic systems. The polynomial dependence of droplet growth in small-volume scenarios and a lack of correspondence to CNT predictions spotlight the unique challenges presented by anisotropic systems. The spatiotemporal correlation of nucleation events in a nematic phase, influenced by long-range elastic interactions, suggests new theoretical avenues to explore beyond CNT, particularly incorporating noise and anisotropy.

Practically, understanding nucleation in nematic films bears relevance for technologies such as liquid crystal displays, inkjet printing, and biological sensors, where control over droplet morphology and phase transitions is crucial. Future theoretical work could further refine nucleation models and explore coupling effects, such as flexoelectric or external fields, that impact orientation tensor dynamics, extending into three-dimensional systems.

In summary, the research offers valuable insights into how anisotropic interfacial energy and stochastic perturbations influence nucleation in nematic films, setting a foundation for advancing theoretical models that accommodate complex anisotropic interactions in thermotropic liquid crystals.