Energy Variation of Soft Matter Interfaces

The variation of energies associated with soft matter interfaces where surface inhomogeneities are present. These energies include the total bending and splay energy, the variable surface tension energy, a coupling energy between the total curvature and an underlying surface concentration field, the energy due to an external field, and a phase segregation energy. When considering these energies the variation of material properties such a bending rigidity are taken into account, which results in more general variation expressions. These variations can be used to determine the equilibrium interface and concentration configuration or to determine the driving forces for non-equilibrium situations. While the focus of this work are energies associated with multicomponent vesicles, it can easily be extended to any soft matter interface.