Flowering of Developable 2D Crystal Shapes in Closed, Fluid Membranes

TL;DR

This paper explores how 2D crystal shapes within fluid membranes depend on size, mechanics, and thermal effects, revealing size-dependent shape formation and potential for scalable production of complex molecular crystals.

Contribution

It uncovers the size-dependent morphologies of 2D crystals in fluid membranes and explains how mechanics and thermal effects influence shape development.

Findings

Large vesicles form complex flower-like shapes during crystal growth.

Small vesicles tend to produce compact, planar crystals.

Shape formation is governed by size-dependent mechanical and thermal factors.

Abstract

The morphologies of two-dimensional (2D) crystals, nucleated, grown, and integrated within 2D elastic fluids, for instance in giant vesicle membranes, are dictated by an interplay of mechanics, permeability, and thermal contraction. Mitigation of solid strain drives formation of crystals with developable shapes (e.g. planar or cylindrical) that expel Gaussian curvature into the 2D fluid. However, upon cooling to grow the crystals, large vesicles sustain greater inflation and tension because their small area to volume ratio slows water permeation. As a result, more elaborate shapes, for instance flowers with bendable but inextensible petals form on large vesicles despite their more gradual curvature, while small vesicles harbor compact planar crystals. This size dependence runs counter to the known cumulative growth of strain energy of 2D colloidal crystals on rigid spherical templates. This interplay of intra-membrane mechanics and processing points to the scalable production of flexible molecular crystals of controllable complex shape.