  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.
