Curves and Tension Alter the Shapes of Crystals Growing in 2D Fluid Membranes*

It is understood that the growth of 2D crystals can be dramatically affected by template curvature. Contrasting crystal growth on a curved substrate, we employ a membrane that integrates the growing crystal to impose out of plane stresses that impart curvature. We show that besides the geometry of the interface, membrane tension, which is dictated by thermal contraction and water permeation, can together control the crystal morphology within the closed, flexible fluid membrane of lipid vesicles. Due to the area-to-volume ratio difference for different size vesicles, which affects the permeation process and thus, tension, crystal shapes show a size dependence: Small vesicles exhibit compact domains while larger vesicles produce floret shapes.  The observations run counter to the trends expected based on colloidal crystals on rigid spherical substrates. Theoretical models, accounting for elasticity and line energy, suggest solid domains with zero-Gaussian curvature form petals within the floret-shaped domains to help release elastic energy under high inflation. Experimental techniques like micropipette aspiration and phase contrast image tracking during controlled cooling can implicate the tension history of real samples. This shape dependence of crystals on vesicle size is ubiquitous among different choices of lipid composition, cooling rate, fluorescent tracer, or even a different system like lipid/copolymer hybrid membrane. The findings here could provide potential insight in industrial and pharmaceutical applications like nanoparticle coatings, drug delivery or even virus assembly.