Surface Tension and Surface Energy of Curved Interfaces and Membranes

In this work we develop the basic idea that the mechanical properties of a curved Gibbsian dividing surface are characterized, not only by the surface tension, but also by surface moments. It is shown that an additional surface bending moment term is to be introduced in the interfacial balance of the force moments at a spherical dividing surface. The existence of surface bending moment leads to a difference between the dilational surface energy and the surface tension. These two quantities are expressed in terms of integrals over the components of the pressure tensor for an arbitrarily chosen spherical dividing surface (not necessarily the surface of tension). The relation between dilational surface energy and surface tension is generalized for interfaces with an arbitrary curvature. A similar relationship was derived for a surface shearing energy, which is important for interfaces exhibiting shearing elasticity, like biomembranes. The relation between the dilational surface energy and the interfacial density of the grand potential is discussed. The results can be useful for the analysis of data for microemulsions, interfacial waves, vesicles and biomembranes.