# Surface energy

Surface energy, or interface energy, quantifies the disruption of intermolecular bonds that occur when a surface is created. In the physics of solids, surfaces must be intrinsically less energetically favorable than the bulk of a material (the molecules on the surface have more energy compared with the molecules in the bulk of the material), otherwise there would be a driving force for surfaces to be created, removing the bulk of the material (see sublimation). The surface energy may therefore be defined as the excess energy at the surface of a material compared to the bulk, or it is the work required to build an area of a particular surface. Another way to view the surface energy is to relate it to the work required to cut a bulk sample, creating two surfaces.

Cutting a solid body into pieces disrupts its bonds, and therefore consumes energy. If the cutting is done reversibly (see reversible), then conservation of energy means that the energy consumed by the cutting process will be equal to the energy inherent in the two new surfaces created. The unit surface energy of a material would therefore be half of its energy of cohesion, all other things being equal; in practice, this is true only for a surface freshly prepared in vacuum. Surfaces often change their form away from the simple "cleaved bond" model just implied above. They are found to be highly dynamic regions, which readily rearrange or react, so that energy is often reduced by such processes as passivation or adsorption.

Measuring the surface energy of a solid

The surface energy of a liquid may be measured by stretching a liquid membrane (which increases the surface area and hence the surface energy). In that case, in order to increase the surface area of a mass of liquid by an amount, δA, a quantity of work, γδA, is needed (where γ is the surface energy density of the liquid). However, such a method cannot be used to measure the surface energy of a solid because stretching of a solid membrane induces elastic energy in the bulk in addition to increasing the surface energy.

The surface energy of a solid is usually measured at high temperatures. At such temperatures the solid creeps and even though the surface area changes, the volume remains approximately constant. If γ is the surface energy density of a cylindrical rod of radius ${\displaystyle r}$ and length ${\displaystyle l}$ at high temperature and a constant uniaxial tension ${\displaystyle P}$, then at equilibrium, the variation of the total Helmholtz free energy vanishes and we have

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