Morphology of nematic and smectic vesicles

Abstract

Recent experiments on vesicles formed from block copolymers with liquid-crystalline side chains reveal a rich variety of vesicle morphologies. The additional internal order ("structure") developed by these self-assembled block copolymer vesicles can lead to significantly deformed vesicles as a result of the delicate interplay between two-dimensional ordering and vesicle shape. The inevitable topological defects in structured vesicles of spherical topology also play an essential role in controlling the final vesicle morphology. Here we develop a minimal theoretical model for the morphology of the membrane structure with internal nematic/ smectic order. Using both analytic and numerical approaches, we show that the possible low free energy morphologies include nano-size cylindrical micelles (nano-fibers), faceted tetrahedral vesicles, and ellipsoidal vesicles, as well as cylindrical vesicles. The tetrahedral vesicle is a particularly fascinating example of a faceted liquid-crystalline membrane. Faceted liquid vesicles may lead to the design of supramolecular structures with tetrahedral symmetry and new classes of nano-carriers.amphiphilic block copolymers | bending energy | Frank free energy | liquid crystalline polymers | self-assembled bilayer A mphiphilic block copolymers in water, like natural phospholipids, can self-assemble into various monolayer or bilayer structures, such as micelles and vesicles (1, 2). In particular, rodcoil block copolymers, with a flexible hydrophilic chain and one or more rod-like hydrophobic blocks, exhibit a rich morphology of structures, and therefore have significant potential to advance fundamental science and drive technological innovations (3-12). Among these rod-coil block copolymers, we are especially interested in liquid crystalline (LC) block copolymers in which the hydrophobic block is a nematic or smectic liquid crystal polymer (13)(14)(15)(16)(17)(18)(19)(20). The in-plane LC order that results from molecular pair interactions in these systems, and the associated defect structure, play very important roles in determining the preferred intermediate and final shapes of vesicles. The tailor-design of both material properties and vesicle morphology by controlling the molecular structures of the block polymers is state-of-the-art research in the fields of polymer science, materials science, and chemical engineering.Some of the structures formed by these LC side-chain block copolymers in aqueous solution are rather counterintuitive, such as faceted vesicles, nanotubes and compact vesicles with tiny inner space (15,20). In all these structures, the in-plane smectic order is clearly visible under Cryo-TEM. In this article we develop a theoretical explanation of the geometric structures of vesicles with in-plane nematic or smectic order. We present a simple model free energy as a functional of both the membrane geometry and the in-plane nematic order. Using both analytic and numerical methods, we then analyze the low free energy morphologies in various parameter regimes. Results ...

Topological Sound and Flocking on Curved Surfaces

“…The frustration associated with the interplay of curvature and order [30,68,69] has many consequences for crystals [70][71][72][73][74], tethered membranes [75,76], liquid crystalline membranes [77][78][79], and jammed and glassy systems [80,81]. The presence of activity adds an entirely new nonequilibrium dimension to the whole story, allowing for completely new physics arising from competing order, curvature, and the active drive.…”

Numerical insights into the phase diagram of p-atic membranes with spherical topology

“…The cooperative behaviour of such membrane systems and their interplay with the membrane shapes have been studied for a range of systems, e.g. chiral ribbons [3], membranes with gemini lipids [4] and liquid crystalline polymersomes [5]. The effects of such anisotropic membrane components have received renewed attention with the identification of whole families of membrane proteins with membrane shape remodelling capacity, e.g.…”

Elasticity of smectic liquid crystals with in-plane orientational order and dispiration asymmetry

“…Based partially upon the analysis of Refs. [9,10], and on the experimental demonstration of disclination induced buckling in nematic and smectic vesicles [12], we believe that our result on asymmetry in dispiration energies in SmC * is qualitatively robust, and would persist in a more detailed, fully covariant version of the elasticity theory of smectics with in-plane orientational order.…”

“…Positive and negative disclinations of equal strength prefer locally positive (sphere-like) and negative (saddle-like) Gaussian curvatures, respectively, leading to asymmetry in their energies [9][10][11]. Disclination induced buckling of nematic, and smectic vesicles has been observed experimentally [12].…”