Nematic membranes: Shape instabilities of closed achiral vesicles

Abstract

We consider the coupling between the local curvature tensor of a membrane and the local two-dimensional nematic order parameter, deriving it from a quasi-microscopic argument. This coupling makes the nematic director aligned along the lowest curvature eigenvector in a local metric. Local bending of a membrane may then generate nematic ordering. Alternatively, emerging nematic order leads to shape instabilities of closed vesicles. The theory is applied to a spherical isotropic vesicle, which turns into a prolate shape with two +1 disclinations on its poles as the nematic order sets in the membrane, described within the Landau-de Gennes continuum model.

Structure and rheology of fiber-laden membranes via integration of nematodynamics and membranodynamics

“…The balance between these competing interactions is modified by the ambient curvature b, since the power dependence is linear for a 2 and quadratic for a 3 . The nature and meaning of the a 2 and a 3 terms has been previously discussed [4,38]. Fig.…”

“…A number of previous works have incorporated different nematic energies into the Helfrich membrane model; the reader is referred to [4,38] for comprehensive discussions of previous work. In this paper we neglect spatial gradients and focus and formulate a model with curvature-driven competing interactions.…”

Thermodynamic Model of Structure and Shape in Rigid Polymer‐Laden Membranes

“…[30] The interfacial torque vector G is given by surface stress asymmetry and by gradients of surface coupled stresses N:…”

A finite element scheme for the evolution of orientational order in fluid membranes

“…This elementary calculation does not show any preferred curvature direction, which seems to be consistent with interchanging the upper and the lower layer of the membrane. We point out that a model that is quadratic in the coupling expression D 2 u : Q was proposed in [8] and promotes the alignment of n with a zero curvature direction.…”