Continuous director-field transformation of nematic tactoids

Abstract

We theoretically investigate the director field inside spindle-shaped nematic droplets, known as tactoids. Tactoids typically form in dispersions of rod-like colloidal particles. By optimising the bulk elastic and surface energies, we find that the director field crosses over smoothly from a homogeneous to a bipolar configuration with increasing droplet size, in a process that we postulate to involve two virtual point defects that move in from infinity towards the poles on the surface of the droplet. Our calculations show that these hypothesised virtual defects become true surface point defects or boojums only in the limit of infinite droplet volume, and that the more elongated the droplets are, the larger their volume has to be before a uniform director field distorts so as to become discernibly bipolar. The theory agrees well with available experimental data on the size dependence of the aspect ratio of tactoids.

Experimental realization of crossover in shape and director field of nematic tactoids

“…Our largest tactoids are comparable in size to the thickness of the capillary (200 μm) and hence we do not expect to see spherical tactoids in our system. The equilibrium shape (described by the unit surface normal q) and director-field configuration (described by the unit vector n) minimize the sum of elastic and surface free energies [1]:…”

“…The equilibrium shape of a tactoid can be computed by minimizing the free energy F at a fixed value of the volume V . Rather than doing an unconstrained minimization, we follow Prinsen and van der Schoot [1] and assume a bispherical director field and axial symmetry that capture the shape of our tactoids. The optimization is then with respect to the aspect ratio and bipolarness of the director field.…”

“…The optimization is then with respect to the aspect ratio and bipolarness of the director field. It is convenient to group free-energy parameters into λ ≡ (k 11 − k 24 )/τ ω, ω ≡ W/τ , and γ 33 ≡ k 33 /(k 11 − k 24 )-for a symmetric tactoid k 24 merely rescales k 11 [1]. A scaling analysis of Eq.…”

“…A scaling analysis of Eq. (1) shows that λ is the extrapolation length that controls the crossover from elasticity-dominated alignment (homogeneous) to anchoring-dominated alignment (bipolar) [1]. The magnitude of ω determines the aspect ratio of the tactoids in the limit of small size corresponding to a homogenous director field configuration [17].…”

“…In complex fluids such as liquid crystals, interfacial shape is controlled by the competition of interfacial tension and bulk elasticity, which in turn depend on the molecular orientation and alignment. A good example of this competition is the spindle shape of nematic droplets (tactoids) coexisting with the isotropic phase in liquid crystals [1,2] [ Fig. 1(a)].…”