A nematic liquid-crystal gel is a macroscopically homogeneous elastic medium with the rotational symmetry of a nematic liquid crystal. In this paper, we develop a general approach to the study of these gels that incorporates all underlying symmetries. After reviewing traditional elasticity and clarifying the role of broken rotational symmetries in both the reference space of points in the undistorted medium and the target space into which these points are mapped, we explore the unusual properties of nematic gels from a number of perspectives. We show how symmetries of nematic gels formed via spontaneous symmetry breaking from an isotropic gel enforce soft elastic response characterized by the vanishing of a shear modulus and the vanishing of stress up to a critical value of strain along certain directions. We also study the phase transition from isotropic to nematic gels. In addition to being fully consistent with approaches to nematic gels based on rubber elasticity, our description has the important advantages of being independent of a microscopic model, of emphasizing and clarifying the role of broken symmetries in determining elastic response, and of permitting easy incorporation of spatial variations, thermal fluctuations, and gel heterogeneity, thereby allowing a full statistical-mechanical treatment of these materials.

We study the organization of topological defects in a system of nematogens confined to the two-dimensional sphere (S2). We first perform Monte Carlo simulations of a fluid system of hard rods (spherocylinders) living in the tangent plane of S2. The sphere is adiabatically compressed until we reach a jammed nematic state with maximum packing density. The nematic state exhibits four +1/2 disclinations arrayed on a great circle. This arises from the high elastic anisotropy of the system in which splay (K1) is far softer than bending (K3). We also introduce and study a lattice nematic model on S2 with tunable elastic constants and map out the preferred defect locations as a function of elastic anisotropy. We find a one-parameter family of degenerate ground states in the extreme splay-dominated limit K_{3}/K_{1}-->infinity. Thus the global defect geometry is controllable by tuning the relative splay to bend modulus.

Graphical AbstractEllipsoidal smectic polymer vesicles were formed from amphiphilic block copolymers in which the hydrophobic block is a smectic liquid crystal polymer.2 SummaryPolymer vesicles are stable robust vesicles made from block copolymer amphiphiles. Recent progress in the chemical design of block copolymers opens up the exciting possibility of creating a wide variety of polymer vesicles with varying fine structure, functionality and geometry. Polymer vesicles not only constitute useful systems for drug delivery and micro/nano-reactors but also provide an invaluable arena for exploring the ordering of matter on curved surfaces embedded in three dimensions. By choosing suitable liquid-crystalline polymers for one of the copolymer components one can create vesicles with smectic stripes. Smectic order on shapes of spherical topology inevitably possesses topological defects (disclinations) that are themselves distinguished regions for potential chemical functionalization and nucleators of vesicle budding. Here we report on glassy striped polymer vesicles formed from amphiphilic block copolymers in which the hydrophobic block is a smectic liquid crystal polymer containing cholesteryl-based mesogens. The vesicles exhibit two-dimensional smectic order and are ellipsoidal in shape with defects, or possible additional budding into isotropic vesicles, at the poles.

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 ...

Dynamics of hydration water is essential for the function of biomacromolecules. Previous studies have demonstrated that water molecules exhibit subdiffusion on the surface of biomacromolecules; yet the microscopic mechanism remains vague. Here, by performing neutron scattering, molecular dynamics simulations, and analytic modeling on hydrated perdeuterated protein powders, we found water molecules jump randomly between trapping sites on protein surfaces, whose waiting times obey a broad distribution, resulting in subdiffusion. Moreover, the subdiffusive exponent gradually increases with observation time towards normal diffusion due to a many-body volume-exclusion effect.