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

Abstract

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.

Controlling motile disclinations in a thick nematogenic material with an electric field

“…The slope changes from 0.8 to 1 as elastic anisotropy is increased. While the slope of unity is also obtained in experiments with 5 CB 7 , 29 , we re-establish our earlier claim 20 about the crucial contribution of the anisotropic elasticity of the medium. Intuitively, anisotropic elastic constant results into asymmetric diffusion constants in Cartesian directions and thus brings asymmetry in the speed of ±1/2 integer point defects 23 , 30 .…”

“…We qualitatively argue about the slowing down of disclination kinetics for a planar isolated disclination loop. An in-plane estimate is valid for 5 CB while twist constant is much smaller than splay or bend constants 20 . Also deep within the uniaxial phase where the director is aligned uniformly, Frank constant K can sufficiently define the medium elasticity 26 .…”

“…mentions, “molecular alignment in the inhomogeneous electric field has not yet been well studied as it is not easy to solve the Poisson equation with an inhomogeneous dielectric constant to calculate the local electric field”. Attributing to the scale invariant property of the Ginzburg-Landau-de Gennes (GLdG) field theory, relaxational kinetics of the orientation tensor has quantitatively reproduced experiments in silico from mesoscale 13 , 20 to nanoscale 21 . State of the art grand challenge is attributed to the nonavailability of a robust numerical scheme 22 which is, in descending order of complexity, (a) free from numerical artifacts of the traditional methods 23 , accounts for (b) local nonuniformity in electric field and (c) equilibrium thermal fluctuations by respecting physical laws, (d) guarantees zero-trace property of the orientation tensor and (e) incorporates anisotropic elasticity to probe beyond the single diffusion (one elastic constant) approximation 23 .…”

“…For MBBA , ( κ ,Θ) ≈ 1 while for 5 CB , κ ≈ 40,Θ ≈ 1 which designate nearly equal splay and bend constants for both materials (Θ ≠ 0) but the twist constant is an order smaller than splay or bend. This results into nucleation of integer topological charged nematic droplets in the metastable isotropic medium of 5CB, while topologically uncharged nematic droplets nucleate in the metastable medium of MBBA 20 , 50 .…”

“…State of the art grand challenge is attributed to the nonavailability of a robust numerical scheme 22 which is, in descending order of complexity, (a) free from numerical artifacts of the traditional methods 23 , accounts for (b) local nonuniformity in electric field and (c) equilibrium thermal fluctuations by respecting physical laws, (d) guarantees zero-trace property of the orientation tensor and (e) incorporates anisotropic elasticity to probe beyond the single diffusion (one elastic constant) approximation 23 . Recent advances in fluctuating hydrodynamics of isotropic suspensions 24 incorporating point (a) demand a natural, yet challenging, extension for anisotropic suspensions 25 while on the other hand, numerical achievement of points (c–e) is fairly recent 20 , 26 .…”