Abstract
Colloidal particles trapped at an interface effectively constitute a two-dimensional nanoscale system embedded in three-dimensional space. The packing of particles at the interface is disrupted if the interface is curved, thereby affecting structure, thermodynamics, and dynamics. In this chapter, we explore the effects of curvature on two-dimensional colloidal clusters. Starting with uniform curvature, we show how classical nucleation theory can be modified to account for the shape and finite area available to colloids on a spherical surface. Moving to a torus as an example of a surface with nonuniform curvature, we demonstrate that the phase of matter and location on the surface can become coupled, leading to wholesale migration of clusters at phase transitions. Finally, we illustrate the sensitivity of packing defects to the apex angle on conical surfaces.
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