Mark J. Zakhary

Reconfigurable self-assembly through chiral control of interfacial tension

From determining the optical properties of simple molecular crystals to establishing the preferred handedness in highly complex vertebrates, molecular chirality profoundly influences the structural, mechanical and optical properties of both synthetic and biological matter on macroscopic length scales. In soft materials such as amphiphilic lipids and liquid crystals, the competition between local chiral interactions and global constraints imposed by the geometry of the self-assembled structures leads to frustration and the assembly of unique materials. An example of particular interest is smectic liquid crystals, where the two-dimensional layered geometry cannot support twist and chirality is consequently expelled to the edges in a manner analogous to the expulsion of a magnetic field from superconductors. Here we demonstrate a consequence of this geometric frustration that leads to a new design principle for the assembly of chiral molecules. Using a model system of colloidal membranes, we show that molecular chirality can control the interfacial tension, an important property of multi-component mixtures. This suggests an analogy between chiral twist, which is expelled to the edges of two-dimensional membranes, and amphiphilic surfactants, which are expelled to oil–water interfaces. As with surfactants, chiral control of interfacial tension drives the formation of many polymorphic assemblages such as twisted ribbons with linear and circular topologies, starfish membranes, and double and triple helices. Tuning molecular chirality in situ allows dynamical control of line tension, which powers polymorphic transitions between various chiral structures. These findings outline a general strategy for the assembly of reconfigurable chiral materials that can easily be moved, stretched, attached to one another and transformed between multiple conformational states, thus allowing precise assembly and nanosculpting of highly dynamical and designable materials with complex topologies.

Imprintable membranes from incomplete chiral coalescence

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-π-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.

Geometrical edgeactants control interfacial bending rigidity of colloidal membranes

A colloidal membrane is a one rod-length thick monolayer of aligned rods which spontaneously assembles in a mixture of rod-like viruses and non-adsorbing polymer. The complex structure of the monolayer edge modifies its fluctuations, effectively smoothing out the interface. We demonstrate that long filaments such as F-actin or flagella preferentially dissolve in the membranes edge and can be used to control its interfacial properties. This effect is not driven by energetic interactions, but is rather a direct consequence of the intrinsic geometry of the constituent particles; hence we call such filaments geometrical edgeactants. Using optical manipulation techniques we adsorb individual filaments onto the edge of the colloidal membrane and measure their influence on the edge fluctuations. Edgeactants stiffen the interface, increasing its bending rigidity by up to an order of magnitude. Furthermore, they also locally suppress a polymorphic transition into twisted ribbons inherent to colloidal membranes. These results demonstrate new ways to control soft materials in which the final structure is only determined by the geometry of the constituent objects.

Achiral symmetry breaking and positive Gaussian modulus lead to scalloped colloidal membranes

Significance A number of essential processes in biology and materials science, such as vesicle fusion and fission as well as pore formation, change the membrane topology and require formation of saddle surfaces. The energetic cost associated with such deformations is described by the Gaussian curvature modulus. We show that flat 2D colloidal membranes composed of achiral rods are unstable and spontaneously form scalloped edges. Quantitative analysis of such instability estimates the Gaussian curvature modulus of colloidal membranes. The measured sign and magnitude of the modulus can be explained by a simple excluded volume argument that was originally developed for polymeric surfactants. In the presence of a nonadsorbing polymer, monodisperse rod-like particles assemble into colloidal membranes, which are one-rod-length–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 cusp-shaped 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 long-ranged 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.