Programming extrinsic geometry to control membrane self-assembly

Advancements in nanotechnology have furthered the ability for tailoring shape of building blocks for self-assembly. A current challenge is to develop theories of self-limiting assembly of distinct superstructures, e.g. to create ribbons with robustly self-regulating and finite dimensions that are much larger than the building block dimensions. Previous work successfully describes helical nanoribbon assembly and how molecular shape is related to the programmed intrinsic geometry of the assembly (i.e. the preferred Gaussian curvature), resulting in self-limitation via frustration-induced stresses.

In this talk, we show how an additional molecular shape parameter separately controls the extrinsic geometry (i.e. the directionality of curvature axis relative to inter-block packing directions), modulates the intrinsic frustration energetics and influences the size scale over which frustration stress accumulate in the assembly. We derive a continuum elastic description of intrinsic- and extrinsic-programmed membranes, relate it to a coarse-grained model that realizes these shape parameters and verify the role of extrinsic geometry with simulations.