Capillarity and Surface Forces (Liquids) - Surface and Colloid Chemistry: Principles and Applications - page 12

dG = − γ A S (2.3)

Thus, the tension per unit length in a single surface, or surface tension γ, is numeri-
cally equal to the surface energy per unit area. Then G s , the surface free energy per
unit area is

G s = γ = (d G/d A) (2.4)

Under reversible conditions, the heat ( q ) associated with it gives the surface
entropy S S :

d q = T dS S (2.5)

Combining these equations we find that

dγ/dT = −Ss (2.6)

Further, we find that

H S = G S + T S (2.7)

and we can also write for surface energy E S :

E S = G S + T S S (2.8)

These relations give

E S = γ − T (dγ/dT) (2.9)

The quantity E S has been found to provide more useful information on surface phe-
nomena than any of the other quantities.
Thus, S s is the surface entropy per square centimeter of surface. This shows that,
to change the surface area of a liquid (or solid, as described in later text), there exists
a surface energy (γ: surface tension ) that needs to be considered.
The quantity γ means that, to create 1 m 2 (= 10 20 Å 2 ) of new surface of water, one
will need to use 72 mJ energy. To transfer a molecule of water from the bulk phase
(where it is surrounded by about 10 near neighbors by about 7 k B T; k B T = 4.12
10 −21 J) to the surface, about half of these hydrogen bonds need to be broken (i.e., 7/2
k B T = 3.5 k B T). The free energy of transfer of one molecule of water (with area of
12 Å 2 ) will be thus about 10 −20 J (or about 3 k B T). This is a reasonable quantity under
these assumptions.
Further similar consideration is needed if one increases the surface area of a solid
(e.g., by crushing ). In the latter case, one needs to measure and analyze the surface
tension of the solid. It is found that energy needed to crush a solid is related to the
surface forces (i.e., solid surface tension). More examples as given later will provide