Physical Chemistry , 1st ed.

surface energies at several interfaces: the liquid-solid interface, the liquid-

vapor interface, and the vapor-solid interface. At each interface, a different sur-

face tension can be defined. Figure 22.7 shows an idealized drop on a surface

and three different interfaces with three surface tensions. They are labeled s,

v, and svfor the liquid-solid, liquid-vapor, and solid-vapor interfaces, re-

spectively. Note that although the liquid and vapor are the same chemical

species, the solid may be a different chemical species.

Surface tension is a planar effect. It acts at a surface, which at any infinites-

imal point can be marked with a tangent line. For flat liquid-solid and vapor-

solid interfaces, these tangents are coplanar with the interface: the flat surface

is where surface tension exists. For the liquid-vapor interface, because this sur-

face is curved, the surface tension acts colinearly to a tangent to the curve. The

tangent at the edge of the liquid-solid interface (that is, at the edge of the

droplet) is drawn as a solid line in Figure 22.7, and the angle that this tangent

makes with the solid surface is defined as . This angle is called the contact

angle.

Why have we defined parameters this way? Consider what Figure 22.7 would

look like if, for example, the surface tension of the liquid-vapor interface was

very, very high compared to the other surface energies. The droplet would take

on an almost spherical shape, as shown in Figure 22.8a. In this case, the con-

tact angle is almost 180°. On the other hand, what if the surface tension of the

liquid-vapor interface was comparable to the other surface energies? The

droplet would then spread out substantially, as shown in Figure 22.8b. In this

extreme,would be almost 0°. In this second instance, we say that the liquid

is wettingthe solid.

The point here is that the behavior of the liquid on the solid will be depen-

dent on the relative magnitudes of the three interfacial surface tensions. In

1805 Thomas Young deduced an expression, later derived by A. Dupré in 1869,

that relates the three surface tensions and the contact angle:

svsvcos  (22.16)

This equation is called the Young-Dupré equation.It can actually be considered

as a balance of three vectors: the solid-liquid interfacial tension pulling in one

direction, and the liquid-solid and liquid-vapor tensions pulling in the other

direction. But in the case of the liquid-vapor surface tension, only its compo-

nent along the liquid-solid interface contributes to the balance of forces. The

term cos accounts for that component.

The Young-Dupré equation is useful in predicting what is necessary to

wet or to not wet a surface with a liquid. In terms of cos , equation 22.16 is

rewritten as

cos 

sv





v

s

 (22.17)

If you want a liquid to wet a surface (that is,0, therefore cos 1), a bal-

ance is required between the numerator and denominator of equation 22.17;

that is,svsshould be approximately equal to v. For example, solders

are alloys whose liquids wet other metals because surface tensions have the ap-

propriate values. By the same token, detergents and soaps help water wet solids

(like synthetic fabrics) because they reduce the surface tension of water to the

appropriate point.

Surface tension effects also show themselves in systems where a cylindrical

solid surface is present. A very narrow cylindrical surface is called a capillary.

What happens if a capillary is immersed into a liquid? The surface tension that

22.3 Interface Effects 775

Liquid

Solid

lv sv

ls



Figure 22.7 A liquid on a solid surface has a
behavior dictated by three interfaces: the one be-
tween liquid and solid, the one between liquid
and vapor, and the one between vapor and solid.
The tangential angle that the liquid’s edge makes
with the surface is defined as the contact angle .

Figure 22.8 (a) If a liquid does not wet a solid
surface at all, the liquid would (ideally, in the ab-
sence of gravity and other effects) be a small
sphere on the solid surface. In this case, the
contact angle approaches 180°. (b) If a liquid
wets a solid surface very well, it would spread out
over the solid and have a contact angle ap-
proaching 0°.

Liquid

Vapor

Solid

(b) lv very low

Vapor

Solid

(a) lv very high

Liquid