Solid Surfaces—Adsorption - Surface and Colloid Chemistry: Principles and Applications - page 107

which would then allow one to analyze the variation of γ with the change in the
other terms. The latter is important because complete wetting occurs when there is
no finite contact angle, and thus γ L <> γ S − γ LS . However, when γ L > γ S − γ LS , then
cos(θ) < 1, and a finite contact angle is present. The latter is the case when water, for
instance, is placed on a hydrophobic solid, such as Teflon, polyethylene, or paraffin.
The addition of surfactants to water, of course, reduces γ L , therefore, θ will decrease
on the introduction of such surface-active substances.
A complete discussion of wetting of solids is beyond the scope of this topic, and
the reader is therefore encouraged to look up other standard textbooks on surface
chemistry (Adamson and Gast, 1997; Chattoraj and Birdi, 1984; Birdi, 1997, 2002).
The state of a fluid drop under dynamic conditions, such as evaporation, becomes
more complicated (Birdi et al., 1988). However, in this text, we are interested in the
spreading behavior when a drop of one liquid is placed on the surface of another
liquid, especially when the two liquids are immiscible. Harkins (1952) analyzed the
spreading phenomena by introducing a quantity, spreading coefficient Sa/b , defined
as (Adamson and Gast, 1997; Birdi, 2002)

S a/b = γ a − (γ b + γ ab ) (5.5)

where S a/b is the spreading coefficient for liquid b on liquid a, γ a and γ b are the
respective surface tensions, and γ ab is the interfacial tension between the two liquids.
If the value of S b/a is positive, spreading will take place spontaneously, whereas, if it
is negative, liquid b will rest as a lens on liquid a .
However, the value of γ ab needs to be considered as the equilibrium value,
and therefore if one considers the system at nonequilibrium, then the spread-
ing coefficients would be different. For example, the instantaneous spreading of
benzene is observed to give a value of Sa/b as 8.9 dyn/cm, and therefore benzene
spreads on water. On the other hand, as the water becomes saturated with time,
the value of water decreases, and benzene drops tend to form lenses. The short-
chain hydrocarbons such as hexane and hexene also have positive initial spread-
ing coefficients, and spread to give thicker films. Longer-chain alkanes, on the
other hand, do not spread on water (e.g., the S a/b for C 16 (hexadecane)/water is −1.3
dyn/cm at 25°C.
It is also obvious that, since impurities can have very drastic effects on the inter-
facial tensions in Equation 2.24, the value of S a/b would be expected to vary accord-
ingly (see Table 5.1).
The spreading of a solid substance (e.g., cetyl alcohol [C 18 H 38 OH]), on the sur-
face of water has been investigated in some detail (Gaines, 1966; Adamson and
Gast, 1997; Birdi, 2002a). Generally, however, the detachment of molecules of the
amphiphile into the surface film occurs only at the periphery of the crystal in con-
tact with the air-water surface. In this system, the diffusion of amphiphile through
the bulk water phase is expected to be negligible because the energy barrier now
includes not only the formation of a hole in the solid but also the immersion of the
hydrocarbon chain in the water. It is also obvious that the diffusion through the bulk
liquid is a rather slow process. Furthermore, the value of Sa/b would be very sensi-
tive to such impurities as regard spreading of one liquid upon another.