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

• Main Authors: Gibaud, Thomas, Kaplan, C. Nadir, Sharma, Prerna, Ward, Andrew, Zakhary, Mark J, Oldenbourg, Rudolf, Meyer, Robert B, Kamien, Randall D, Powers, Thomas R, Dogic, Zvonimir
• Format: Journal Article
• Language: English
• Published: 07-11-2016
• Subjects: Physics - Soft Condensed Matter
• DOI: 10.48550/arxiv.1610.06653

In the presence of a non-adsorbing 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 physics of thin elastic sheets. Membranes assembled
from single-component chiral rods form flat disks with uniform edge twist. In
comparison, membranes comprised of 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.