Surfaces, Interfaces, and Changing Shapes in Multilayered Films

Extract

It is generally recognized that the capillary forces associated with internal and external interfaces affect both the shapes of liquid-vapor surfaces and wetting of a solid by a liquid. It is less commonly understood that the same phenomenology often applies equally well to solid-solid or solid-vapor interfaces.

The fundamental quantity governing capillary phenomena is the excess free energy associated with a unit area of interface. The microscopic origin of this excess free energy is often intuitively simple to understand: the atoms at a free surface have “missing bonds”; a grain boundary contains “holes” and hence does not have the optimal electronic density; an incoherent interface contains dislocations that cost strain energy; and the ordering of a liquid near a solid-liquid interface causes a lowering of the entropy and hence an increase in the free energy. In what follows we shall show how this fundamental quantity determines the shape of increasingly complex bodies: spheres, wires, thin films, and multilayers composed of liquids or solids. Crystal anisotropy is not considered here; all interfaces and surfaces are assumed isotropic.

Consideration of the equilibrium of a spherical drop of radius R with surface free energy γ shows that pressure inside the droplet is higher than outside. The difference is given by the well-known Laplace equation:

This result can be obtained by equating work done against internal and external pressure during an infinitesimal change of radius with the work of creating a new surface.