For experiments on chiral self-assembly, we used a two-component mixture consisting of 880 nm long rod-like fd viruses and the non-adsorbing polymer Dextran. In aqueous suspension, fd viruses alone exhibit purely repulsive interactions 13. Adding non-adsorbing polymer to a dilute isotropic suspension of fd rods induces attractive interactions via the depletion mechanism and leads to their condensation into colloidal membranes, equilibrium structures consisting of one-rod-length thick liquid-like monolayers of aligned rods (Fig. 1a) 11. Despite having different structures on molecular lengthscales, the longwavelength coarse-grained properties of colloidal membranes are identical to those of conventional lipid bilayers. However, unlike their amphiphilic counterparts, colloidal membranes do not form vesicles and are instead observed as freely suspended disks with exposed edges. Here, we investigate the behavior of these exposed edges in a manner analogous to previously studied liquid-liquid domains embedded in lipid bilayers [14][15][16] . For our experiments, it is essential that fd viruses are chiral, i.e. a pair of aligned viruses minimizes their interaction energy when they are slightly twisted in a preferred direction with respect to each other. The strength of chiral interactions can be continuously tuned to zero through either genetic or physical methods ( Supplementary Fig. 1) 13,17 .Before investigating chiral membranes, we determined the structure of a membrane's edge composed of simpler achiral rods using three complimentary imaging techniques, namely 2D and 3D polarization microscopy and electron microscopy. The local tilting of the rods within a membrane was determined using 2D LC-PolScope, which produces images in which the intensity of each pixel represents the local retardance of the membrane (Fig. 1d) 18. Such images can be quantitatively related to the tilting of the rods away from the layer normal, the z-axis 19. Rods in the bulk of a membrane are aligned along the zaxis, so that 2D LC-PolScope images appear black in that region (Fig. 1e). In contrast, the bright birefringent ring along the membrane's periphery reveals local tilting of the rods (Fig. 1e, Supplementary Fig. 2). For achiral rods, this indicates that a membrane has a hemi-toroidal curved edge (Fig. 1b, c). In comparison to an untilted edge, a curved edge structure lowers the area of the rod/polymer interface, thus reducing interfacial tension, at the cost of increasing the elastic energy due to twist distortion. This hypothesis is confirmed by visualizing the 3D membrane structure using electron tomography, whichshows that the viruses' long axis transitions from being parallel to the z-axis in the membrane bulk to perpendicular to the z-axis and tangent to the edge along the membrane periphery ( When viewed with optical microscopy, a membrane's edge exhibits significant thermal fluctuations, the analysis of which yields the line tension γ eff , the energetic cost required to move rods from the membrane interior to the periphe...
Establishing precise control over the shape and the interactions of the microscopic building blocks is essential for design of macroscopic soft materials with novel structural, optical and mechanical properties. Here, we demonstrate robust assembly of DNA origami filaments into cholesteric liquid crystals, one-dimensional supramolecular twisted ribbons and two-dimensional colloidal membranes. The exquisite control afforded by the DNA origami technology establishes a quantitative relationship between the microscopic filament structure and the macroscopic cholesteric pitch. Furthermore, it also enables robust assembly of one-dimensional twisted ribbons, which behave as effective supramolecular polymers whose structure and elastic properties can be precisely tuned by controlling the geometry of the elemental building blocks. Our results demonstrate the potential synergy between DNA origami technology and colloidal science, in which the former allows for rapid and robust synthesis of complex particles, and the latter can be used to assemble such particles into bulk materials.
In the presence of a nonadsorbing polymer, monodisperse rod-like particles assemble into colloidal membranes, which are one-rodlength-thick liquid-like monolayers of aligned rods. Unlike 3D edgeless bilayer vesicles, colloidal monolayer membranes form open structures with an exposed edge, thus presenting an opportunity to study elasticity of fluid sheets. Membranes assembled from single-component chiral rods form flat disks with uniform edge twist. In comparison, membranes composed of a mixture of rods with opposite chiralities can have the edge twist of either handedness. In this limit, disk-shaped membranes become unstable, instead forming structures with scalloped edges, where two adjacent lobes with opposite handedness are separated by a cuspshaped point defect. Such membranes adopt a 3D configuration, with cusp defects alternatively located above and below the membrane plane. In the achiral regime, the cusp defects have repulsive interactions, but away from this limit we measure effective longranged attractive binding. A phenomenological model shows that the increase in the edge energy of scalloped membranes is compensated by concomitant decrease in the deformation energy due to Gaussian curvature associated with scalloped edges, demonstrating that colloidal membranes have positive Gaussian modulus. A simple excluded volume argument predicts the sign and magnitude of the Gaussian curvature modulus that is in agreement with experimental measurements. Our results provide insight into how the interplay between membrane elasticity, geometrical frustration, and achiral symmetry breaking can be used to fold colloidal membranes into 3D shapes.self-assembly | membranes | liquid crystals | Gaussian curvature | chirality T he possible configurations and shapes of 2D fluid membranes can be described by a continuum energy expression that accounts for the membrane's out-of-plane deformations as well as the line tension associated with the membrane's exposed edge (1, 2). Because an arbitrary deformation of a thin layer can have either mean and/or Gaussian curvature, the full theoretical description of membranes, in principle, requires two parameters, the bending and Gaussian curvature moduli. However, lipid bilayers almost always appear as edgeless 3D vesicles, which further simplify theoretical modeling. In particular, integrating Gaussian curvature over any simply closed surface yields a constant (3). Thus, the shape fluctuations of a closed vesicle only depend on the membrane-bending modulus. Consequently, experiments that interrogated mechanics or shape fluctuations of vesicles provided extensive information about the membrane curvature modulus and how it depends on the structure of the constituent particles (4-6). In comparison, significantly less is known about the Gaussian modulus, despite the significant role it plays in fundamental biological and technological processes such as pore formation as well as vesicle fusion and fission (7)(8)(9)(10)(11).Recent experiments have demonstrated that, in the presence of a d...
Coalescence is an essential phenomenon that governs the equilibrium behaviour in a variety of systems from intercellular transport to planetary formation. In this report, we study coalescence pathways of circularly shaped two-dimensional colloidal membranes, which are one rod-length-thick liquid-like monolayers of aligned rods. The chirality of the constituent rods leads to three atypical coalescence pathways that are not found in other simple or complex fluids. In particular, we characterize two pathways that do not proceed to completion but instead produce partially joined membranes connected by line defects-p-wall defects or alternating arrays of twisted bridges and pores. We elucidate the structure and energetics of these defects and ascribe their stability to a geometrical frustration inherently present in chiral colloidal membranes. Furthermore, we induce the coalescence process with optical forces, leading to a robust on-demand method for imprinting networks of channels and pores into colloidal membranes.
We study edge fluctuations of a flat colloidal membrane comprised of a monolayer of aligned filamentous viruses. Experiments reveal that a peak in the spectrum of the in-plane edge fluctuations arises for sufficiently strong virus chirality. Accounting for internal liquid crystalline degrees of freedom by the length, curvature, and geodesic torsion of the edge, we calculate the spectrum of the edge fluctuations. The theory quantitatively describes the experimental data, demonstrating that chirality couples in-plane and out-of-plane edge fluctuations to produce the peak.
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