152 The solid-liquid interface
Figure 6,1When S is negative, the liquid remains as a drop having a definite
angle of contact, 0, with the solid surface. The equilibrium contact
angle is such that the total surface free energy of the system is a
minimum - i.e. ySG A$G + y$L ASL + yLG ALG is a minimum, where
A represents interfacial area. Consider a liquid making an equilibrium
contact angle, 0, to spread an infinitesimal amount further so as to
cover an extra area, dA, of the solid surface. The increase in liquid-
gas interfacial area is, therefore, dA cos 0 (see Figure 6.1) and the
increase in the free energy of the system is given by
+ yLGdA cos 0 -If the system is at equilibrium, dG = 0, andTSL + TLG cos 0 - ySG = 0 (6-2)In this expression (known as Young's equation), ySG is the surface
tension of the solid in equilibrium with the vapour of the wetting
liquid. If 7s is the surface tension of the solid against its own vapour,
then
7s ~~ Tso = ^SG
and
JSL- 7s + TLG cos 0 + TTSG = 0 * " '
where irso (the spreading pressure) is the reduction of the surface
tension of the solid due to vapour adsorption. In general, TTSG is small
for moderately large values of 0 (and equation (6.2) applies), but it
can become significant as 0 approaches zero^75.
If Fowkes' semiempirical interfacial tension theory (as described
on pages 65-67) is applied to the solid-liquid interface, then
TSL = 7s (^6 -^4 )