# surface energy

The surface energy of a solid or liquid is the amount of energy needed to create 1 square meter of new surface.
The process can be pictured as follows. Imagine a column of solid or liquid
of 1 square meter cross-section to be broken apart by some means. Energy
must be used in order to overcome the interactions between molecules on either side of the break. We can easily calculate this energy. Let there
be *N* molecules per square meter of cross-section; if the diameter
of one molecules is *a*_{0}, then *N* is something
like 1/*a*_{0}^{2} /m^{2}.

After the break, each molecule in the surface is no longer surrounded by
the full number *n* of nearest neighbors. Instead it has, on average,
only ½*n* neighbors, in the one hemisphere; therefore ½*nN* nearest neighbor interactions must be broken. This requires an amount of
energy ½*nNε*, whereas ε is the binding energy
between two molecules; but it produces 2 square metersof new surface, 1
square meter each for the top and bottom halves of the columns. The surface
energy is therefore ¼*nNε* J/m^{2}.