A Landau-de Gennes theory for hard colloidal rods: Defects and tactoids

Abstract

We construct a phenomenological Landau-de Gennes theory for hard colloidal rods by performing an order parameter expansion of the chemical-potential dependent grand potential. By fitting the coefficients to known results of Onsager theory, we are not only able to describe the isotropic-nematic phase transition as function of density, including the well-known density jump, but also the isotropic-nematic planar interface. The resulting theory is applied in calculations of the isotropic core size in a radial hedgehog defect, the density dependence of linear defects of hard rods in square confinement, and the formation of a nematic droplet in an isotropic background.

Electric-field-induced shape transition of nematic tactoids

“…These nematic droplets have characteristic shapes that have already been the subject of several theoretical studies [2][3][4][5][6][7][8] and experiments on systems such as vanadium pentoxide (V 2 O 5 ) [2,9], carbon nanotubes [10,11], rodlike viruses [12,13], F-actin in cells [14], chromonic liquid crystals [15], and cellulose nano-crystals [16][17][18]. These investigations showed that the typical tactoid shapes, for example the so-called spindle-like shape with a bipolar director field (see the right inset in Fig.…”

On the effect of capillarity and polarity in colloidal suspensions of nanoparticles

“…As shown in Ref. [80] and as we will review in Chapter 4, the expansion (1.11) can describe a first-order I-N transition at chemical potential µ IN . As shown in Fig.…”

“…As recently shown in Ref. [80], to deal with lyotropic systems it is convenient to set up a Landau expansion of the chemical-potential dependent grand potential Ω rather than of the temperature-dependent Helmholtz (or Gibbs) free energy F. By using Ω, the density dependence will naturally be encoded through the relation ∂(Ω/V )/∂µ| V,T = −ρ, with V the volume of the system and ρ the average density. In particular, in Ref.…”

“…In particular, in Ref. [80] it has been showed that by expanding Ω in powers of Q, a proper characterization of the I-N transition displayed by hard rods can be obtained. To show this we consider a system of hard rods of contour length L and diameter D, at chemical potential µ in a macroscopic volume V at a fixed temperature T. We write the LdG grand potential…”

“…In Chapter 4, we extend the Landau-de Gennes theory introduced in Ref. [80] and quickly reviewed in Section 1.3.2 of this Introduction, from the case of straight rods to that of curved rods. To this aim we exploit the bend flexoelectric effect as suggested in recent papers [53,54].…”