Page 77 - Introduction to Colloid and Surface Chemistry

Liquid-gas and liquid-liquid interfaces 67

phase by oil-oil dispersion forces and to the water phase by oil-water
42
dispersion forces. In a simple approach proposed by Fowkes the
oil-water dispersion interactions are considered to be the geometric
mean of the oil-oil and water-water dispersion interactions. Hence,
the interfacial tension is given by

d
Tow = 7& + ("Xw + Tw) - 2 x ( w x i&)* (4.3)
Substituting values from Table 4.1 for the n-hexane-water interface,

51.1 = 18.4 + 72.8 - 2 X (y w x 18.4)**

which gives

1
= 21.8 mNnr
y w
and

1
yw = 72.8 - 21.8 = 51.0 mNm"
Using surface and interfacial tension data for a range of alkanes,
1
Fowkes calculated that -y4 = 21.8 ± 0.7 mN m" .
Phenomena at curved interfaces - the Kelvin equation

As a consequence of surface tension, there is a balancing pressure
difference across any curved surface, the pressure being greater on
the concave side. For a curved surface with principal radii of
curvature r\ and r 2 this pressure difference is given by the Young-
Laplace equation, Ap = y(llri + l/r 2), which reduces to A/? = 2y/r
for a spherical surface.
The vapour pressure over a small droplet (where there is a high
surface/volume ratio) is higher than that over the corresponding flat
surface. The transfer of liquid from a plane surface to a droplet
requires the expenditure of energy, since the area and, hence, the
surface free energy of the droplet will increase.
If the radius of a droplet increases from r to r + dr, the surface area
2
2
will increase from 4-nr to 4tr(r + dr) (i.e. by 8irr dr) and the increase
in surface free energy will be Siryr dr. If this process involves the
transfer of dn moles of liquid from the plane surface with a vapour